Remedial Maths Series: Number by Teacher Superstore

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Ages 10+ r o e t s Bo r e p ok u S

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Number

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Remedial Maths Series:

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For students requiring assistance with number concepts.

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Written by Jane Bourke. Illustrated by Rod Jefferson. © Ready-Ed Publications - 2001 Published by Ready-Ed Publications, P.O. Box 276, Greenwood ,WA, 6024 Email: info@readyed.com.au Website: www.readyed.com.au COPYRIGHT NOTICE Permission is granted for the purchaser to photocopy sufficient copies for non-commercial educational purposes. However this permission is not transferable and applies only to the purchasing individual or institution.

ISBN 1 86397 176 9

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Contents

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4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52

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Teacher’s Notes Mental Maths Place Value 1 Place Value 2 Addition Revision Addition: Place Value 1 Subtraction with Regrouping Decimals: Place Value 1 Decimals: Place Value 2 Decimals: Place Value 3 Word problems Money Adding and Subtracting Money: Rounding Whole Numbers 1 Rounding Whole Numbers 2 Rounding Decimals 1 Rounding Decimals 2 Adding and Subtracting Decimals 1 Adding and Subtracting Decimals 2 Adding and Subtracting Decimals 3 Subtracting Decimals Basic Facts 1 Basic Facts 2 Basic Facts - Multiplication Mixed Basic Facts Multiplying Whole Numbers 1 Multiplying Whole Numbers 2 Mental Multiplication 1 Multiplying Whole Numbers 3 Multiplying Whole Numbers 4 Multiplying Decimals 1 Multiplying Decimals 2 Multiplication Grids Mental Multiplication 2 Multiplying Fractions and Whole Numbers 1 Multiplying Fractions and Whole Numbers 2 Division - Revision Division - Basic Facts Division of Whole Numbers 1 Mixed Division Problems Expressing Remainders 1 Expressing Remainders 2 Division of Decimals Division - Recurring Decimals Expressing Fractions as Decimals Percentages 1 Percentages 2 Mixed Word Problems Answers

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Teacher’s Notes Mathematics education encompasses a wide range of topics and concepts, many of which are only briefly dealt with in the classroom due to time constraints. It is important that these fundamental concepts are understood before students move onto the next mastery level. Students often fail to grasp all concepts and are unable to catch up to the level at which the rest of the class are working. It is here that the real difficulty for these students begins as they will sometimes withdraw from activities and miss further valuable concepts, simply because they had not mastered the prerequisite skills.

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Remediation for many students is frequently associated with a reduced self esteem as students are aware that they are working behind the rest of the class, especially when text books and worksheets for lower grades are used to help them to catch up.

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This remediation series is designed to provide upper primary students with the necessary skills and knowledge of mathematical concepts required for their year level and can be used both in the classroom and as a “take-home” package for extra consolidation of concepts. The reading and style is appropriate to the age of the student, even though many of the remedial activities are focused on previous stages of the maths syllabus. It is hoped that this series will boost the students’ self esteem as they realise that they are able to successfully complete the maths activities in the book. In addition, students will not feel as if they are doing “baby” work as is the case when maths sheets for 8 year olds are given to 12 year old students. For best results the series should be used to complement a remedial maths programme for a small group or for individual students who need to catch up. Many of the worksheets explain the mathematical concepts and provide examples, however, it is assumed that this is not the student’s first experience with the concept. Each book in the series follows the same format and is directed at upper primary groups, yet is appropriate for the secondary school if required.

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The Challenge questions and word problems at the bottom of some pages test the child’s knowledge of the mathematical concept for that particular page. The challenge is usually presented as a word problem in a real world context so as to highlight the need for the skill. This book explains the basic concepts of number, exploring in detail the processes of addition, subtraction, multiplication and division. Decimals are explored in detail as well as the relationship between decimals and percentages. The activities are sequenced in line with the standard syllabus structure, covering a number of stages as opposed to activities restricted to one year level. The activities are basically designed to provide students with the opportunity to catch up on much needed mathematical skills.

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Mental Maths 42 + 8 = ............ 23 + 4 = ..............

337 + 9 = ........... 743 + 2 = ........... 954 + 3 = ..........

442 + 8 = .......... 623 + 4 = ............

Set 2. 58 + 7 = ............. 43 + 2 =............. 66 + 3 = ............

56 + 9 = ............ 33 + 8 = ..............

897 + 9 = ........... 475 + 8= ............ 754 + 3 = ..........

342 + 6 = .......... 976 + 4 = ............

Set 3. 57 + 6 = ............. 43 + 0 =............. 45 + 7 = ............

92 + 8 = ............ 68 + 7 = ..............

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ADDITION Set 1. 37 + 9 = ............. 43 + 2 =............. 54 + 3 = ............

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682 + 2 = .......... 396 + 6 = ............

Set 4. 43 + 5 = ............. 24 + 9=.............. 58 + 5 = ............

49 + 4 = ............ 47 + 4 = ..............

137 + 9 = ........... 867 + 2 = ........... 245 + 2 = ..........

977+ 8 = ........... 625 + 5 = ............

SUBTRACTION Set 1. 43 - 2 = .............. 54 - 3 = ............. 42 - 8 = .............

57 - 6 = ............. 43 - 0 = ...............

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336 + 2 = ........... 756 + 8 = ........... 227 + 6 = ..........

© ReadyEdPub l i cat i ons 742 - 8 = ........... 923 - 4 = ............. Set 2. •f orr evi ew pur posesonl y• 42 - 5 = .............. 43 - 2 = ............. 54 - 9 = ............. 58 - 7 = ............. 43 - 9 = ............... 545 - 7 = ............ 692 - 8 = ........... 568 - 7 = ...........

Set 3. 82 - 2 = .............. 96 - 6 = ............. 97 - 9 = .............

75 - 8= .............. 64 - 3 = ...............

142 - 6 = ............ 576 - 4 = ........... 337 - 9 = ...........

223 - 4 = ........... 536 - 2 = .............

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256 - 8 = ........... 127 - 6 = .............

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866 - 3 = ............ 556 - 9 = ........... 323 - 8 = ...........

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Set 4. 43 - 5 = .............. 24 - 9= .............. 58 - 5 = .............

49 - 4 = ............. 47 - 4 = ...............

336 - 9 = ............ 687 - 2 = ........... 846 - 2 = ...........

696- 8 = ............ 529 - 5 = .............

MULTIPLICATION

3 x 6 = ............ 4 x 6 = .......... 2 x 8 =........... 8 x 5 = .......... 6 x 9 = .......... 9 x 5 = ........... 7 x 5 = ............ 2 x 4 = .......... 3 x 9 =........... 4 x 9 = .......... 3 x 7 = .......... 4 x 5 = ........... DIVISION 7 ) 21

3 ) 27

6 ) 18

4 ) 36

5 ) 35

9 ) 54

2 ) 12

1 ) 10

8 ) 64

5 ) 20

3 ) 15

7 ) 42

Mental problems using the four operations.

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Place V alue 1 Value Our counting system is based on groups of ten and is known as a decimal system. In this system ten ones make ten; ten tens make one hundred; ten hundreds make one thousand. In the table we can see how the same digit can represent a different amount. Where there is no number zeros are used to hold the place.

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Hundreds 0 9

Tens 0 0 9

Ones 0 0 0 9

shows nine thousands shows nine hundreds shows nine tens shows nine ones

= 9000 = 900 = 90 =9

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Thousands 9

1. What is the place value of the underlined digits in each number below. e.g. 2764 = thousands ................. 3678 =

............. 7645 = ............... 9078 = ................ 5766 =

2. What is the face value of the underlined digits below? e.g. 2873 = 800

2983 = ................ 8765 = .............

5788 =............... 4565 = ................

3. Write these numbers in expanded form. The first one has been done for you. a.

c. 3876 = ..................................................... d. 7764 = .......................................................

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4. Write these numbers in digit form.

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Five thousand, three hundred and seventy-six = .................................................................... Seven thousand, eight hundred and thirty-nine = ...................................................................

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Eight thousand and sixty-four = ............................................................................................. Nine thousand, two hundred and six = ................................................................................... Three thousand and seventeen = .......................................................................................... 5. Circle the number representing the tens in each amount below. $529.00

65 m

72 min

145 km

2535 mm

$34.00

6. Circle the number representing the hundreds in each amount below. $200.00

163 m

180 min

735 km

9465 mm

625 mL

7. What is the value of 8 in each number below? e.g. 82 - 80

18 ....................... 835 ................... 28 ..................... 8652 ...................

Exploring the relation of digit placement to value in the base ten system for whole numbers up to 1000.

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Place V alue 2 Value The table below shows the place value of numbers beyond the thousands. Write this number in the spaces below so that the digits are in the right columns. Seven million, four hundred and fifty-six thousand, three hundred and twenty-two. M 1 000 000 ................

H. Th 100 000

T. Th 10 000

Th 1000

H 100

T 10

0 1

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................

...............

................

1. Show these numbers on the table below 100 000

10 000

1000

5 498 765 2 098 634 4 200 049 187 685

280 097

100

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1 000 000

3 487 978 = (3 x 1 000 000) + (4 x 100 000) + (8 x 10 000) + (7 x 1000) + (9 x 100)

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+ (7 x 10) + (8 x 1).

2 876 543 = ...............................................................................................................................

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7 653 012 = ............................................................................................................................... .................................................................................................................................................. 3. Write the place value and the face value for the underlined numbers below. 3 425 643 = ten thousands = 20 000

3 298 765 = .......................

=.....................

5 364 243 = ...................... = ....................... 2 509 345 = ......................... =.....................

Challenge: Write this number in digits: Six million, two hundred thousand and fourteen hundred.

Exploring place value and face value to 1000 000. Writing in expanded notation.

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Addition Revision Set 1. 23 + 26

35 + 23

64 + 15

74 + 22

83 + 12

92 + 8

53 + 34

44 + 35

22 + 37

55 +34

Set 2. 51 + 87

62 + 76

73 + 35

84 + 42

94 + 34

63 + 74

64 + 82

32 + 94

41 + 72

54 +73

45 + 38

37 + 29

84 + 48

95 + 18

38 + 27

84 + 17

54 + 36

78 +27

46 + 89

10 + 97

39 + 86

74 + 75

62 + 48

84 + 97

Set 4. 68 + 87

57 + 56

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57 + 36

92 + 87

52 +52

Set 6. 412 + 243

46 31 + 12

68 11 + 21

97 32 + 31

75 13 + 10

35 11 + 14

46 13 + 42

68 32 + 71

847 + 352

928 + 422

787 + 232

849 + 451

903 + 546

783 + 545

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75 72 + 21

65 72 +20

673 + 345

832 + 437

734 +452

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Set 5. 67 12 + 10

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Set 3. 48 + 22 70

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Set 7. 573 + 493

575 + 465

464 + 687

686 + 909

989 + 787

454 + 567

778 + 544

898 + 465

562 + 345

535 +792

Set 8. 243 573 + 412

352 575 + 847

422 464 + 928

232 686 + 787

451 989 + 849

546 454 + 903

545 777 + 783

345 898 + 673

437 562 + 832

687 698 +734

Score =

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/80

Adding with regrouping

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Addition : Place V alue 1 Value Thousands

Hundreds

Tens

Ones

a. b. c. d. e.

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Place these numbers into the table. Make sure the numbers are in the right columns. a. 253

b. 6789

c. 56

d. 9

e. 79

f. 869

g. 60

If you were to add 56 and 253 you need to make sure they are set out correctly before you start. For example, you cannot add a number from the tens column to a number from the ones column.

1. Circle the sums below that show the correct setting out. a. 345 + 67

b. 67 + 87

2. Add these sets of numbers by first setting them out correctly.

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a. 678 + 8794 + 4 + 68 = 678 8794 4 + 68

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c. 2 + 2098 +132 + 75 =

d. 142 + 5 + 364 + 5409 =

3. Add these amounts to find the total sum. a. $32.78 + $987.89 + $0.53

b. $65 + $35.20 + 76c + $1001.00

Setting out addition sums.

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Subtraction with Regrouping Complete the subtraction sums below. Set 1. 65 − 32

87 − 42

576 − 132

698 − 253

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Set 2.

39 − 13

47 − 24

38 − 15

57 − 23

46 − 42

35 − 24

53 − 12

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587 − 432

465 − 143

536 − 432

879 − 523

676 − 532

575 − 532

48 − 24

334 − 322

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To complete Set 3 and 4 you will need to regroup. Remember that if you borrow from the tens you must cross out the ten that you borrowed. For example: 6 cannot be taken away from 4 so we borrow a 10 from the tens column. To show a 10 has been borrowed, we cross out the three, and mark 2 in the tens column, and 1 (one ten) in front of the ones column. Now we can take 6 from 14 which will leave 8. The 1 is then taken away from 2. H T O

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Set 3. Complete these, marking your regrouping as shown above. 84 − 47

74 − 57

37 − 29

58 − 29

75 − 28

68 − 59

53 − 37

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Set 4. Complete these, marking your regrouping as shown above. 423 − 217

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21 − 17

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687 − 629

745 − 326

747 − 239

844 − 327

45 − 28

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63 − 39

634 − 416

796 − 718

523 − 219

564 − 247

764 − 469

854 − 379

932 − 838

845 − 298

Set 5. In these sums you will need to regroup twice. 148 − 89

237 − 98

458 − 359

342 − 249

984 − 399

765 − 679

Check your answers to the above sums by adding your answer to the amount being taken away. For example, in the first sum of Set 5, add your answer to 89. If you regrouped correctly you should get 148 as your answer, which is the number you started from. Subtracting whole numbers with a minuend to 1000 with regrouping.

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Decimals: Place V alue 1 Value A decimal represents part of a whole. A decimal point separates the whole number and the fraction left over. For example the shaded blocks below show three wholes and one half of a block. We write this as 3.5. The 3 represents the complete blocks and the .5 represents the half block. = 3.5

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Look at the shaded areas below and write the decimal amount next to each one.

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..............................................

The left over amount is represented as tenths, hundredths and thousandths of one unit. Look at this example. Express the amount as a fraction.

© ReadyEdPubl i cat i ons We can say that the amount left over is equal to six tenths. This is shown in the table below. •f o rr ev i ew. p1/tenth ur posesonl y• Hundreds Tens Ones 25.6 = .......................................

1/hundredth 1/thousandth

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Tens

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1/tenth

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1. Record the following decimal amounts into the table: 36.7 23.5 12.52 525.3 0.755 1/hundredth 1/thousandth

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2. Write the place value represented by the underlined number. a. 156.2 ................................................

e. 56.38 .................................................

c. 68.2 ..................................................

d. 56.87 ................................................

g. 2.36 ...................................................

236.87 ...............................................

Introduction to decimals - exploring place value.

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Decimals: Place V alue 2 Value 1. Complete the following: 67.9

= six tens, seven ones and nine tenths.

99.4

= ........................tens,

12.3

= .................................................................................................................................

42.75

= .................................................................................................................................

........................ ones and ........................ tenths.

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45. 98 = .................................................................................................................................

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364.68 = .................................................................................................................................

Hundreds

Tens

Ones

1/tenth

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Where there is no number in a column a zero is used to hold the value. Look at the example below. 1/hundredth 1/thousandth

Represents 405.307 and not 45.37

2. Write the numbers represented in the table below.

©Tens Read yEd P ubl i cat i ons Ones . 1/tenth 1 2 1 . 2 1 2 •f or r e v i e w p u r p o s e s o n l y • 4 . 3 5 9

Hundreds

f. g.

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1/hundredth 1/thousandth

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.........................................................

b. ..........................................................

.........................................................

d. ..........................................................

.........................................................

..........................................................

Challenge: Which is the greater number 601.01 or 601.001? Writing decimals in expanded form to the 1 /1000 place.

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Decimals: Place V alue 3 Value 1. Write the following numbers in expanded form. the first one has been done for you. 234.35 = (2 x 100) + (3 x 10) + (4 x 1) + (3 x 1/10) + (5 x 1/100). 13.356 = .................................................................................................................................... 57.108 = ....................................................................................................................................

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29.998 = .................................................................................................................................... 2. What is the face value of the underlined digits below. 56.758 =

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35.424

3.222

132.1

..................................................................................................................................................

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3. Write these numbers in words. 289.78 = two hundred and eighty-nine point seven eight.

301.203 = ..................................................................................................................................

1345.2 = ....................................................................................................................................

1.298 = ...................................................................................................................................... 4. Order these numbers starting from the least. 1.9

..................................................................................................................................................

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1.9

1.99

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5. Use < or > to complete these. 4.23

4.023

5.155

1.5

3.00

13.1

18.2

182

49.5

49.7

64.8

64.09

75.6

7.56

3001

3001.9

203.4

204.3

46.003

46.03

21.003

21.333

234.05,

234.005.

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6. Write these numbers in order starting with the least. 2345,

2.345,

234.5,

23.45,

2.543,

2543.1,

..................................................................................................................................................

Challenge: Which is greater - 0.0005 or 0.003?

Ordering decimals and decimal inequalities.

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Word Problems 1. Tiffany spent $1.30 at the lolly shop and Jacinta spent $6.55. What was the total amount spent? ........................................... 2. Jake had $364 dollars saved in the bank. He also had $28.75 in his pocket and $3.80 in his car. How much money did he have altogether? ................................................

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3. Brad ran 6.23 km on Sunday afternoon and then 5.79 km on Monday. On Tuesday he jogged a distance of 24.4 km. What

was the total distance he ran over the three days? ..........................

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Which is the least expensive package? ...................................

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4. Alison and Matt were comparing prices for computers and printers. They were shown three separate deals. The first deal included a printer costing $989 and a computer costing $2899. The second deal involved a second-hand printer at $755 and a computer marked at $2995 and the third deal had a printer for $905 and a computer for $2795.

5. Chrissie and Shane were painting the lounge room. They used 395 mL of paint on the first coat and then another 275 mL touching up the corners. They then coated the walls another time and used up 455 mL.

How much paint did they use altogether? .................................... 6.

23, 855, 125, 122. How many pages did she read altogether? .....................................

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7. Tarlie grows sunflowers in her garden. Last year she counted 276 flowers and this year she counted 452 flowers. What is the total amount of sunflowers she has grown? .......................................

8. Billy had 657 jellybeans in a jar. He gave some to Samantha, and he now has 534 left.

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How many jellybeans did he give to Samantha?........................................... 9. Kyle weighed 97.54 kg. After taking up exercise he lost 13.85 kg. What is his current weight? ........................................

10. Amanda and Taylor spent most of the weekend doing assignments. On Saturday they worked for 5 hours and 15 minutes. On Sunday morning they worked 3 hours and 10 minutes and in the evening they spent another 3 hours and 35 minutes studying. What was the total amount of time they spent studying? ....................................... 11. In a game of cricket, Michael scored 143 runs, Kimberly scored 167 runs and Megan scored 25 runs. What was their combined score? ........................................

Addition and subtraction using decimals and units of measure with regrouping.

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Money The decimal system is used for measurement units and money. Our dollars and cents are based on units of 1, 10 and 100. Complete the following to get a better understanding of how the decimal system is used to write amounts of money. 1. How many cents in $1? .......................................................... 2. How many cents in $5? ..........................................................

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3. How many 10 c pieces are needed to make $1? ....................

4. How many dollars are there in 100 c? .....................................

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5. 46 cents is equal to 0.46 of $1. It is written as $0.46. Write these amounts below in numbers: a. 3 dollars and 45 cents .............................. b. 9 dollars and 59 cents ................................ c. 67 dollars and 6 cents .............................. d. 12 dollars and 23 cents .............................. e. 14 dollars and 5 cents .............................. f.

45 dollars and 50 cents ..............................

g. 143 dollars and 3 cents ............................ h. 20 dollars and 20 cents .............................. 6. Express these amounts in dollars.

© ReadyEdPubl i ca t i o ns 2090 cents ......................... 354 cents ......................... e. 2001 cents ...................... f. 15 cents .............................. •f orr evi ew pur posesonl y•

a. 3573 cents ....................... b. 2894 cents ...................... c. d.

g. 16 cents ........................... h. 235 cents ........................ i.

5 cents ................................

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45.3 = $45.30

a. 21.2 ......................

b. 367.6 ...................

d. 34 .......................... e. 245.08 ..................

f. 32.32 ...................

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c. 354.2 ................... g. 200.06 .................

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8. Round these amounts to the nearest dollar. $54.35 ≈ $54.00

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7. Express these decimal amounts as dollars and cents. The first one has been done for you.

a. $23.27≈ ................

b. $98.87≈ .................

c. $35.68≈

d. $87.02 ≈ .................. e. $3.89 ≈ ...................

f. $20.05 ≈ ................

g. $62.55 ≈ ................

h. $3234.45 ≈ ............. i. $0.96 ≈ ...................

j. $1.05 ≈ ..................

k. $57.62 ≈ ................

Challenge: Bindi has 30.2 dollars and Sean has $30.20. Who has the most money?

Exploring the decimal system using money.

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Adding and Subtracting Money Money:: 1.

Add these amounts. Take care to place the decimal points in the correct spot in each sum.

$57.00 + $32.00

$23.50 + $52.50

$35.25 + $ 0.10

$ 2.95 + $34.05

$251.00 + $736.50

$363.20 + $372.80

$12.15 + $25.55

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$278.10 + $200.45

$0.75 + $9.35

$253.50 + $6.90 + $24.10 + $534.45

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2. Add the following amounts by first setting them out correctly. =

$287.45 + $273.85 + $34 + $0.95

$25.25 − $22.00

$10.75 − $ 0.75

$42.00 − $36.00

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$578.50 − $345.50

$235.00 − $124.50

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3. Complete the following subtractions. Some of these sums need regrouping. Decimal amounts are regrouped in the same way as whole number amounts. $53.50 − $24.50

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$29.85 − $12.95

$300.00 − $243.65

$402.30 − $241.55

$39.40 − $19.55

4. Subtract the following amounts.

Take $35.78 from $199.99. ............................................................... Take 57c from $65.62. ...................................................................... Take $24.69 from $203.00. ............................................................... Take $143.37 from $200.00 .............................................................. Adding and subtracting decimals with regrouping using correct setting out.

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Rounding Whole Numbers 1 Rounding numbers allows us to make estimations to which we can compare our answer. To round a number we look in the ones column. Remember these rules for rounding numbers: 1. If the number of ones is greater than 5 round the number up to the next ten.

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2. If the number is less than 5 round the number down to the next ten.

3. If the number of ones equals 5 round the number to the nearest even number.

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1. Round these numbers to the nearest ten. 24 ≈ 20

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For example, if we have 47 stamps and are given another 34 we can quickly estimate how much we should have altogether. 47 is rounded to the nearest ten which is 50, and 34 is rounded to 30. 50 + 30 = 80 Therefore, we should have approximately 80 stamps. 47 + 34 = 81.

89 ≈ ............... 68 ≈ ................ 63 ≈ ............... 45 ≈ ............... 71 ≈ ...............

134 ≈ ............. 765 ≈ ............. 98 ≈ ................ 877 ≈ ............. 55 ≈ ............... 105 ≈ .............

To round numbers to the nearest hundred we follow the same rules, except this time we focus on the tens column and not the ones. If the number in the tens column is a five we then look to the ones. For example, 753 would be rounded up to 800 because 53 is closer to 800 than 700. 2. Round these numbers to the nearest hundred. 598 ≈ ............. 796 ≈ ............. 687 ≈ ............. 465 ≈.............

602 ≈ .............

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437 ≈ 400

355 ≈ ............. 505 ≈ ............. 12 ≈ ................ 245 ≈ ............. 865 ≈.............

857 ≈ .............

1354 ≈ ........... 9786 ≈ ........... 6355 ≈ ........... 2098 ≈ ........... 555 ≈.............

2674 ≈ ...........

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o c . che e r o t r s super

3. Use the skills that you have learnt to round these numbers to the nearest thousand. 2356 ≈2000

4698 ≈ ........... 8765 ≈ ........... 9089 ≈ ........... 9889 ≈ .........

876 ≈ .............

13 425 ≈ ........ 9855 ≈ ........... 2576 ≈ ........... 5555 ≈ ........... 5005 ≈ ..........

4501 ≈ ...........

4. Round the numbers below before completing the sums. The first one has been done for you. 36 23 63 + 17

≈ ≈ ≈ ≈

40 20 60 20 140

58 97 46 + 36

22 29 82 + 38

18 98 57 + 84

Rounding whole numbers to nearest 10, 100 and 1000.

Ready-Ed Publications

Page 17

Rounding Whole Numbers 2 1. Round these numbers to the nearest ten before subtracting. Check your estimate against the real answer. 354 ≈ 350 − 267 ≈ 270 87

959 − 354

576 − 423

837 − 487

r o e t s Bo r e p ok u S

2. Round these numbers to the nearest thousand and then subtract. Check your answer against the real answers. 8765 ≈ − 7823 ≈

5877 ≈ − 4653 ≈

3545 ≈ − 2363 ≈

ew i ev Pr

Teac he r

2456 ≈ − 1357 ≈

3. Round the numbers to the nearest 10 to work out the answers to the multiplication problems below. 47 x 86 ≈ 50 x 90 = 4500

32 x 28 ≈ .................................

97 x 56 ≈ ..............................

26 x 11 ≈ .................................

82 x 37 ≈ .................................

28 x 63 ≈ ..............................

4. Complete the division problems below by rounding the large numbers to the nearest hundred.

© ReadyEd355P ubl i cat i ons ÷ 2 ≈ .................... 951÷5 ≈ ........................ •f o rr e e w ten, pu r po s eson y• Round these numbers tov thei nearest hundred and thousand. Thel first one has

776 ÷ 4 ≈ 800 ÷ 4 = 200 875 ÷3 ≈ ..................... 5.

been done for you.

3876 2546 1209

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989 5541

hundred

8720

8700

thousand

m . u

w ww

8723

ten

9000

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Challenge: A cricket match was held over four days. On Sunday 2543 people attended the match. On Monday another 4678 people attended and the final two days saw crowds of 2123 and 6159 respectively. Approximately how many people attended the match overall? Round your answer to the nearest thousand. Making estimations for mathematical problems.

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Ready-Ed Publications

Rounding Decimals 1 Look at the number line below.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.510

1. Round these decimals to the nearest whole number. 3.6 ≈ 4

r o e t s Bo r e p ok u S

2.8 ≈ ............... 9.1 ≈ ............... 5.6 ≈ ............... 2.3 ≈ ............... 7.8 ≈ ................

3.1 ≈ ................. 4.7 ≈ ............... 9.8 ≈ ............... 6.4 ≈ ............... 1.7 ≈ ............... 2.9 ≈ ................

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Teac he r

2. Remember if the decimal ends in 5 (such as 2.5), it is rounded to the nearest even whole number. Complete these following the rule. 3.5 ≈ ................. 1.5 ≈ ............... 6.5 ≈ ............... 5.5 ≈ ............... 7.5 ≈ ............... 9.5 ≈ ................ 3. Round these decimals to the nearest whole number.

25.7 ≈ ............... 89.5 ≈ ............. 24.4 ≈ ............ 27.6 ≈ ............. 38.7 ≈............. 12.3 ≈ ..............

4. These decimals have two decimal places. Round them to the nearest whole number.

26.78 ≈ 27

36.35 ≈ ...............

19.18 ≈ ...............

87.94 ≈ ...............

84.32 ≈ ..................

13.245 ≈ .............

24.865 ≈ ............

2.367 ≈ ...............

25.895 ≈ ...............

4.111 ≈ ................ 5.555 ≈ ...............

53.455 ≈ ............

7.001 ≈ ...............

2.457 ≈ ..................

56.789 ≈ 57

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63.11 ≈ ................ 28.97 ≈ ...............

6. Estimate the sum of these decimals by rounding each decimal to the nearest whole number. 3.42 ≈

4.67 ≈

2.69 ≈

5.54 ≈

. te

≈ 17

3.56 ≈

2.56 ≈

2.79 ≈

8.98 ≈

8.74 ≈

6.54 ≈

7.43 ≈

2.53 ≈

3.53 ≈

2.41 ≈

5.32 ≈

2.42 ≈

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Challenge: Renee decided to put new carpet throughout the house. She worked out the measurements and found she needed 78.51 square metres (m2) for the lounge room and 43.24 m2 for each of the two bedrooms. How much carpet to the nearest square metre should she buy? Rounding decimals with up to three decimal places to nearest whole number.

Ready-Ed Publications

Page 19

Rounding Decimals 2 1. Round these decimals to the nearest decimal place. For example 3.54 ≈ 3.5 4.78 ≈ ............... 2.34 ≈ ............. 7.23 ≈ ............ 3.57 ≈ ............. 6.89 ≈ ............. 4.53 ≈ .............. 4.57 ≈ ............... 9.51 ≈ ............. 5.51 ≈ ............ 2.42 ≈ ............. 7.64 ≈ ............. 9.54 ≈ .............. 2. Round these decimals to two decimal places. For example 2.344 » 2.34

r o e t s Bo r e p ok u S

3.423 ≈ ............. 2.234 ≈ ........... 6.342 ≈ .......... 5.782 ≈ ........... 9.878 ≈ .......... 6.689 ≈ ............ 5.459 ≈ ............. 4.253 ≈ ........... 3.324 ≈ .......... 5.551 ≈ ........... 9.999 ≈ .......... 1.959 ≈ ...........

Teac he r

3. Use < or > to complete the following. 1.99

4.23

4.023

5.155

1.5

3.00

13.1

18.2

182

49.5

49.7

64.8

64.09

75.6

7.56

3001

3001.9

203.4

204.3

46.003

46.03

21.003

21.333

ew i ev Pr

1.9

4. Round these decimals to the nearest whole number and complete the sum. ≈ 3 + 5 + 8 + 3 = 19

© Rea yEdPubl i cat i ons ≈d ........................................................................................................... 2.67 + 5.645• + 9.001 3.424 ≈ ........................................................................................................... f o+r r ev i ew pur posesonl y• 3.45 + 4.67 + 7.58 + 3.22

2.34 + 3.456 + 5.645 + 4.37

≈ ...........................................................................................................

1.243 + 5.558 + 4.534 + 3.7

≈ ...............................................................................................

m . u

7.58 + 0.987 + 2.456 + 1.23

w ww

5. Round these amounts to the nearest ten cents. For example $5.76 ≈ $5.80

$3.42 ≈ ............. $4.56 ≈ ........... $7.89 ≈ .......... $5.42 ≈ ........... $0.98 ≈ .......... $7.79 ≈ ............

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Sometimes we may have an amount which does not divide evenly. For example if we share $35 between 8 students each student will get $4.375. This must then be rounded to $4.38. 6.

Round these amounts to the nearest cent.

$5.567 ≈ .............. $6.543 ≈ ................... $2.246 ≈ ................... $7.892 ≈ ................. $2.785 ≈ .............. $3.658 ≈ ................... $5.782 ≈ ................... $3.542 ≈ ................. $9.863 ≈ .............. $9.001 ≈ ................... $7.602 ≈ ................... $5.637 ≈ .................

Remember: Money is expressed in decimal form. For example 76 c is equal to $0.76. Rounding decimals with more than two decimal places back to two decimal places as in money.

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Ready-Ed Publications

Adding and Subtracting Decimals 1 1. Add the following decimals. 23.1 + 13.2

34.3 + 54.4

52.3 + 34.5

45.2 + 31.4

65.2 + 32.1

98.6 + 11.3

2. Add these decimals. Regrouping is the same as with whole numbers. ¹ 25.7 ¹ +24.6

r o e t s Bo r e p ok u S

24.9 + 74.3

Teac he r

50.3

65.6 + 73.4

46.8 + 83.3

37.8 + 79.5

64.3 + 46.9

3. Complete the following subtraction problems. 24.6 − 21.3

62.3 − 42.2

63.8 − 41.2

47.8 − 31.7

ew i ev Pr

46.8 − 23.4

74.9 − 64.2

4. This time you will need to borrow from the ones and tens columns. ³¹ 24.6 37.8 53.7 37.4 63.8 − 13.7 − 21.9 − 23.8 − 18.6 − 26.9

24.53 + 25.47

78.76 + 36.54

35.57 + 34.86

73.46 + 33.57

63.36 + 58.96

w ww

6. Subtract these decimals by first setting them out correctly. 23.45 − 12.56 =

. te

23.45 − 12.56

65.46 − 23.56 =

67.89 − 45.67 =

45.65 + 44.36

m . u

10.9 5.

63.4 − 59.9

o c . che e r o t r s super −

98.43 − 25.46 =

−

Challenge: Antonio went shopping with $36.85. He returned with $12.96. How much did he spend? Adding and subtracting decimals with up to two decimal places with regrouping.

Ready-Ed Publications

Page 21

Adding and Subtracting Decimals 2 So far we have added and subtracted decimals to and from other decimals with the same amount of decimal places. In all of the problems the decimal points have been placed in a line. This is because the decimal point is always after the number of ones. If we were to add 4.567 to 12.3 it would be set out like this.

4.567 + 12.3 16.867

r o e t s Bo r e p ok u S

1. Complete only the sums below that show the correct setting out. b.

24.243 + 2.73

2.4 + 256.3

532.5 + 24.56

643.7 + 32.53

7457.8 + 35.7

45.456 + 0.57

7.45 + 1.2

79.98 + 12.3

6.98 + 1.22

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Teac he r

2. Add these decimals. +

234 2.3

23.45 3.5 + 12.3

56 + 2.1

2.3 + 1.23

34.25 64.7 + 23.44

85.87 4.7 + 234.67

54.75 4.8 + 364.78

33.6 3.52 + 364.43

56.89 km + 13.5 km

23.12 cm + 54.6 cm

3. Add the following amounts. 3.75 kg + 19.5 kg

w ww

. te

43.2 mL + 3.55 mL

4. Complete the subtraction problems that are set out correctly. a.

24.564 − 2.462

3.789 − 23.45

$3.56 + 47c

m . u

4.99 m + 1.2 m

o c . che e r o t r s super c.

4.574 − 3.54

253.5 − 2.342

36.434 − 23.1

3.456 − 2.78

23.87 km − 19.9 km

87.65 cm − 34.3 cm

−

5. Subtract the following amounts. 5.99 m − 2.5 m

23.55 kg − 12.7 kg

45.75 mL − 34.8 mL

$6.25 78c

Challenge: On camp the following distances were travelled by bus. Monday - 24.3 km, Tuesday - 7.65 km and Wednesday - 46.53 km. What was the total distance travelled? Adding and subtracting decimals with an unlike number of decimal places.

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Ready-Ed Publications

Adding and Subtracting Decimals 3 1. Add the following decimals by setting them out correctly. 24.567 + 23.45 + 3.46

4.56 + 46.78 + 356.7

= +

r o e t s Bo r e p ok u S

1.009 + 456.7 + 4.302

23.01 + 345.6 + 45.643 =

2 .456 + 456.7 + 4.302 =

24. 56 + 35.3 + 245.63

ew i ev Pr

Teac he r

= 24.567 23.45 + 3.46

2. Subtract the following amounts.

24.567 = l © ReadyEd- 12.324 Pub i cat i ons •f orr evi ew pur p−osesonl y•

4578.7 - 32.3 = 4578.7 − 32.3

97.85 - 3.79 =

w ww −

567.9 - 29.8

. te =

−

m . u

35.687 - 2.54 =

o c . che e r o t r s super 116.34 - 35.76

−

Challenge: Emily picked three crates of apples and packed them into six boxes. The boxes had a total weight of 14.75 kg. Three of the boxes, weighing a total of 6.5 kg, were sold at the markets. What is the weight of the remaining boxes? Setting out addition and subtraction sums where numbers have a different number of decimal places.

Ready-Ed Publications

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Subtracting Decimals What happens if we need to subtract a number with more decimal places than the number we are subtracting it from? We use zeros. For example

25.3 - 16.27 =

²¹ 25.30 − 16.27 9.03

It is now possible to borrow from the tenths column to take 7 from 10.

r o e t s Bo r e p ok u S

We can add as many zeros as is needed. They do not change the value of the number. 1. Complete the following by adding zeros where necessary. 9.35 − 3.432

2.003 − 0.009

4.6 − 2.546

45.6 − 2.356

367.8 − 12.35

45.63 − 0.73

243.54 − 32.574

3.4 − 0.54

345.6 − 23.64

2.3 − 2.12

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Teac he r

24.56 − 12.322

6.37 − 2.647

2. Set out and solve the subtraction problems, adding zeros where necessary. 4.65 - 3.234

254.3 - 1.987

53.57 - 4.634

234.35 - 7.677

34.34 - 6.352

443.34 - 63.366

w ww

−

. te Word Problems

−

m . u

o c . che e r o t r s super

1. Jacinta put 35.7 litres of petrol in her car to fill the tank up. She knew that the petrol tank held exactly 50 litres. What amount of petrol was already in the tank? ................. 2. Pete was baking a cake. He needed 25 g of butter. He had exactly 14.75 g in the old container and 250 g in a fresh container. If he uses all the butter in the old container, how much will he need to use from the new container to make a total of 25 g? ............ 3. Irene bought 12 metres of material to make a quilt cover. She found she only needed 8.55 m of the fabric. How much material did she have left over? .................................. Subtracting decimals where minuend has less decimal places than the subtrahend.

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Ready-Ed Publications

Basic FFacts acts 1 Complete the following grids. Record how long it takes you to fill in each grid, and how many you get right out of 100. 1

Time Taken: ............................

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Accuracy: ................................

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5 6 7 8 9

w ww

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5 6

Date: ........................................ Time Taken: ............................

2 3

Date: ........................................

m . u

Accuracy: ................................

o c . che e r o t r s super

7 8 9 10 1. Adding and multiplying whole numbers up to 10. 2. Identifying patterns.

Ready-Ed Publications

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Basic FFacts acts 2 Complete the following grids. Record how long it takes you to fill in each grid, and how many you get right out of 100.

Time Taken: ............................

r o e t s Bo r e p ok u S

Accuracy: ................................

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Teac he r

9 3 2 5

w ww

8 9

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Date: ........................................

m . u

Date: ........................................

Time Taken: ............................ Accuracy: ................................

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3 2 5 4 1. Adding whole numbers up to 10. 2. Multiplying whole numbers up to 10.

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Ready-Ed Publications

Basic FFacts acts - Multiplication Complete the 9 x tables below. 1 x 9 = .................

Look down the column

1 x 4 = ............. 1 x 11 = ............

2 x 9 = .................

of your answers.

2 x 4 = ............. 2 x 11 = ............

3 x 9 = .................

What patterns can you find?

3 x 4 = ............. 3 x 11 = ............

r o e t s Bo r e p ok u S

4 x 9 = ................. 5 x 9 = ................. 6 x 9 = .................

4 x 4 = ............. 4 x 11 = ............

....................................................

5 x 4 = ............. 5 x 11 = ............

....................................................

6 x 4 = ............. 6 x 11 = ............

....................................................

7 x 4 = ............. 7 x 11 = ............

9 x 9 = ................. 10 x 9 = ...............

8 x 4 = ............. 8 x 11 = ............

ew i ev Pr

8 x 9 = ................. Can you find a pattern for these?

Teac he r

7 x 9 = .................

Describe your pattern here.

9 x 4 = ............. 9 x 11 = ............

10 x 4 = ........... 10 x 11 = ..........

Did you know there is a quick and easy way to work out your 9 x tables? Place your hands on the desk and number each finger 1 - 10 like below. 2 3 4

7 8 91 0

4 5 67

x3= © ReadyEd9P ubl i cat i ons = 27 •9f ev i e wunder. pu r pnow os e s2o nl y To multiply xo 3, r tuckr your third finger You are left with (before) and • 7 fingers 1

(after) = 27. Try this by multiplying 9 with other numbers. Does it work every time?

m . u

1. Multiply these whole numbers by 10. 45 x 10 = ........... 32 x 10 = ............

234 x 10 = ......... 536 x 10 = ......... 654 x 10 = ........

357 x 10 = ......... 279 x 10 = ..........

w ww

2 x 10 = ............. 14 x 10 = ........... 23 x 10 = ..........

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2. Multiply these multiples of 10.

o c . che e r o t r s super

20 x 30 = ........... 40 x 60 = ........... 30 x 50 = ..........

40 x 50 = ........... 80 x 20 = ............

20 x 40 = ........... 50 x 60 = ........... 70 x 90 = ..........

30 x 80 = ........... 60 x 70 = ............

3. Now try these.

300 x 20 = ......... 600 x 40 = ......... 200 x 80 = ........

700 x 30 = ......... 900 x 40 = ..........

30 x 200 = ......... 50 x 700 = ......... 600 x 80 = ........

800 x 30 = ......... 20 x 700 = ..........

4. Complete these equalities by filling in the missing number. 40 x 60 = 30 x 80

20 x 60 = 30 x

90 x 10 = 30 x

50 x 40 = 20 x

40 x 40 = 80 x

50 x 60 = 100 x

1. Identifying patterns. 2. Multiplying whole numbers to 1000 by 10. 3. Multiplying whole multiples of ten.

Ready-Ed Publications

Page 27

Mixed Basic FFacts acts 1. Make these number sentences true by adding the right number to the box. 5 x 6 = 25 +

7 x 6 = 40 +

8 x 7 = 50 +

9 x 5 = 50 -

4 x 8 = 16 +

3 x 9 = 30 -

25 - 5 = 10 x

7 x 7 = 40 +

56 ÷ 7 = 2 x

12 ÷ 4 = 9 ÷

18 ÷ 6 = 4 -

50 x 2 = 10 x

3x2=6x

r o e t s Bo r e p ok u S 6 x 4 = 20 +

5 x 6 = 10 x

8x9=9x

2. Time yourself on these.

A B C D E F 4 x 3 = ........... 5 x 7 = .......... 2 x 6 = .......... 5 x 8 = .......... 2 x 8 = .......... 1 x 6 = ............

ew i ev Pr

Teac he r

3 x 9 = ........... 5 x 4 = .......... 8 x 9 = .......... 8 x 5 = .......... 6 x 4 = .......... 3 x 5 = ............ 0 x 6 = ........... 5 x 9 = .......... 3 x 4 = .......... 5 x 3 = .......... 6 x 3 = .......... 2 x 7 = ............ 8 x 6 = ........... 6 x 7 = .......... 9 x 8 = .......... 7 x 5 = .......... 4 x 6 = .......... 7 x 3 = ............ 5 x 2 = ........... 8 x 3 = .......... 9 x 3 = .......... 2 x 3 = .......... 7 x 4 = .......... 4 x 8 = ............ 8 x 1 = ........... 6 x 9 = .......... 9 x 9 = .......... 8 x 8 = .......... 4 x 4 = .......... 0 x 5 = ............ 7 x 2 = ........... 2 x 1 = .......... 6 x 0 = .......... 8 x 7 = .......... 5 x 9 = .......... 6 x 8 = ............ 5 x 1 = ........... 2 x 9 = .......... 8 x 4 = .......... 9 x 5 = .......... 3 x 6 = .......... 4 x 7 = ............

© ReadyEdPubl i cat i ons 10 x 5 = ......... 10 x 7 = ........ 4 x 10 = ........ 9 x 7 = .......... 3 x 8 = .......... 5 x 10 = .......... •f orr evi ew pur posesonl y• 2 x 5 = ........... 1 x 7 = .......... 7 x 0 = .......... 6 x 5 = .......... 4 x 9 = .......... 2 x 4 = ............

Date: .......................... Time Taken: .......................... Accuracy: ..........................

m . u

G H I J K L 24 ÷ 3 = ......... 35 ÷ 7 =........ 12 ÷ 6 = ........ 40 ÷ 8 = ........ 24 ÷ 8 = ........ 12 ÷ 6 = ..........

w ww

36 ÷ 9 = ......... 20 ÷ 4 =........ 18 ÷ 9 = ........ 40 ÷ 5 = ........ 16 ÷ 4 = ........ 30 ÷ 5 = .......... 30 ÷ 6 = ......... 45 ÷ 9 =........ 24 ÷ 4 = ........ 15 ÷ 3 = ........ 18 ÷ 3 = ........ 21 ÷ 7 = ..........

. te

48 ÷ 6 = ......... 42 ÷ 7 =........ 24 ÷ 8 = ........ 35 ÷ 5 = ........ 24 ÷ 6 = ........ 21 ÷ 3 = ..........

o c . che e r o t r s super

20 ÷ 2 = ......... 27 ÷ 3 =........ 9 ÷ 3 = .......... 12 ÷ 3 = ........ 28 ÷ 4 = ........ 16 ÷ 8 = .......... 8 ÷ 1 = ......... 63 ÷ 9 =........ 90 ÷ 9 = ........ 80 ÷ 8 = ........ 36 ÷ 4 = ........ 10 ÷ 5 = .......... 14 ÷ 2 = ......... 20 ÷ 10 =...... 6 ÷ 2 = .......... 56 ÷ 8 = ........ 54 ÷ 9 = ........ 32 ÷ 8 = .......... 15 ÷ 5 = ......... 27 ÷ 9 =........ 8 ÷ 4 = .......... 25 ÷ 5 = ........ 24 ÷ 6 = ........ 81 ÷ 9 = .......... 20 ÷ 5 = ......... 70 ÷ 7 =........ 7 ÷ 1 = .......... 45 ÷ 5 = ........ 54 ÷ 6 = ........ 32 ÷ 4 = .......... 10 ÷2 = .......... 10 ÷ 1 =........ 40 ÷ 10 = ...... 42 ÷ 6 = ........ 8 ÷ 8 = .......... 80 ÷ 10 = ........ Date: .......................... Time Taken: .......................... Accuracy: .......................... Challenge: List all of the whole numbers that can evenly go into these numbers. 36 - .......................... 24 - .......................... 48 - ........................... 60 - ............................ 1. Revising basic multiplication and division facts through equalities in number sentences. 2. Dividing whole numbers evenly be a whole number up to nine.

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Ready-Ed Publications

Multiplying Whole Numbers 1 1. Multiply the following numbers, keeping the ones and tens in their right column. 3 x4

5 x7

7 x6

8 x5

9 x8

5 x4

7 x5

3 x3

2 x4

5 x5

6 x3

12 2. Try these by first multiplying the ones column and then multiplying the tens column. 14 x 2

r o e t s Bo r e p ok u S

30 x 5

15 x 1

73 x 3

82 x 4

34 x 2

Regrouping 18 x4 32 - ones 40 - tens 72

ew i ev Pr

Teac he r

3. This time you will need to regroup. Look carefully at the setting out below.

To multiply 18 x 4 we first multiply the ones by 4. 8 x 4 = 32 Next we need to multiply the tens by 4. The one in 18 represents a ten. 10 x 4 = 40. 32 + 40 = 72.

19 2

w ww

m . u

Try these problems setting your work out as above.

Shorter way: Carry the tens over into the tens column. For example: 3 18 x4 8 x 4 = 32. Write down the 2 in the ones column and carry 72 the 3 over to the tens column. 1 x 4 = 4 plus the 3 = 7 which is then written in the tens column.

. te

o c . che e r o t r s super

Solve these problems using the shorter method. x

24 4

16 3

17 2

19 4

27 3

38 2

Multiplying whole numbers up to 100 by whole numbers up to 9 using regrouping (long algorithm).

Ready-Ed Publications

Page 29

Multiplying Whole Numbers 2 1. Find answers to these multiplication problems. 23 56 78 97 34 x 5 x 4 x 3 x 2 x 9 15 100

2. a.

56 x 4

24 x 7

r o e t s Bo r e p ok u S

Now try the shorter way to solve the problems below.

15 x 4

23 x 6

56 x 6

87 x 4

64 x 5

35 x 3

46 x 6

$26 4

$45 6

$67 7

$78 5

$32 2

$104

97 x 4

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Teac he r

54 x 4

$24 8

3. Complete the following. Remember that the amount of cents is equal to a decimal. For example, 86c is equal to $0.86. 86c 75c 56c 33c 76c 27c x 4 x 3 x 7 x 8 x 3 x 5 $3.44

Word

1. Denis takes tour groups rock climbing on the weekend. If there are 16 people in the group and each person pays $9, how much money will Denis receive? ...........................................

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2. Sarah hosted a party for her friends. 36 people were at the party and the cost of the food

was $8 per head. How much was spent on food altogether? .............................................

. te

3. Jacinta bought 4 metres of material at a cost of $19 a metre. How much did the material

o c . che e r o t r s super

cost altogether? .......................................

4. Carl went surfing 7 times over the weekend and each time he caught 15 waves. How many waves did he catch altogether? .........................................

5. Chrissie planted 16 boxes of seedlings. If each box contained 8 seedlings, how many seedlings did she plant altogether? .......................................

6. Shane mowed 14 tennis courts. Each court took 9 minutes to mow. How much time did he take to mow all the courts? ........................................ 7. Irene bought 27 books at the second-hand book store. Each book cost $7. How much did she spend altogether? ........................................ Multiplying whole numbers up to 100 by whole numbers up to 9 using the short algorithm.

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Ready-Ed Publications

Mental Multiplication 1 1. Time yourself on these. A.

10 x 10 = ................... 20 x 10 = ................... 40 x 10 = ................... 60 x 10 = .................... 25 x 10 = ................... 34 x 10 = ................... 56 x 10 = ................... 69 x 10 = ....................

r o e t s Bo r e p ok u S

10 x 48 = ................... 25 x 10 = ................... 10 x 24 = ................... 38 x 10 = .................... 100 x 9 = ................... 100 x 4 = ................... 100 x 5 = ................... 100 x 6 = ....................

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8 x 100 = ................... 3 x 100 = ................... 100 x 3 = ................... 4 x 100 = .................... 340 x 10 = ................. 250 x 10 = ................. 380 x 10 = ................. 280 x 10 = ..................

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250 x 10 = ................. 260 x 10 = ................. 980 x 10 = ................. 10 x 350 = .................. 135 x 10 = ................. 246 x 10 = ................. 356 x 10 = ................. 257 x 10 = .................. 748 x 10 = ................. 298 x 10 = ................. 874 x 10 = ................. 239 x 10 = .................. 10 x 369 = ................. 203 x 10 = ................. 286 x 10 = ................. 296 x 10 = ..................

424 x 10 = ................. 245 x 10 = ................. 570 x 10 = ................. 897 x 10 = .................. 333 x 10 = ................. 23 x 100 = ................. 35 x 100 = ................. 100 x 56 = ..................

280 = 28 x 13 x

560 = 56 x = 130

w ww

24 x 10 =

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x 233 = 2330

100 x 54 x

= 700 = 540

= 33 x 10

34 x

=340

x 5 = 500

200 x

= 2000

35 x 10 =

m . u

= 46 x 10

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432 x

= 4320

240 x 10 =

379 x 10 =

3. Complete these number sentences by filling in the box. 40 x 3 = 4 x 30

2 x 30 = 20 x

30 x 5 = 3 x

60 x 8 = 6 x

3 x 70 = 30 x

5 x 30 = 50 x

70 x 6 = 7 x

2 x 50 = 20 x

40 x 5 = 4 x

3 x 70 = 30 x

20 x 7 = 2 x

60 x 5 = 6 x

Multiplying 100 by a number less than 10, multiplying 10 by a number less than 1000.

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Multiplying Whole Numbers 3 1. Complete these using only one line to work out your answer. 23 x 6

56 x 9

89 x 7

78 x 8

65 x 5

54 x 10

138 2. To multiply a number by a three digit number we follow the same steps, remembering to write the numbers in the correct column. 321 x 2 642

922 2

732 3

334 x 2

824 2

132 x 3

921 4

432 x 2

233 x 3

730 3

832 x 10

1844

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Teac he r

3. Complete these. x

r o e t s Bo r e p ok u S

440 x 2

4. This time you will need to regroup. Carry the ones over to the tens column. 1

236 x 2 472

217 4

429 2

129 3

328 3

149 3

447 2

5. Here you need to regroup the tens and the hundreds. x

802 x 4

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509 x 2

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Word Problems

299 x 3

905 x 5

860 x 10

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6. Complete these. 803 x 7

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Six people were organising a cruise holiday. The fare for each person was $989. How much money did they need altogether? .............................................................................. Every morning Tim runs 850 metres. How much will he run in one week? ............................ Tarnie types 135 words per minute. How many words would she type in 7 minutes? .......................................................................................................................................... Max was acting in a play that is 125 minutes long. If the play runs for 9 nights how many minutes will this be altogether? ........................................................................................... How many hours will this be? .............................................................................................. Multiplying numbers up to 1000 by a number up to 10 with regrouping.

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Ready-Ed Publications

Multiplying Whole Numbers 4 1. Complete the following. 46 x 10

35 x 10

87 x 20

67 x 30

54 x 20

32 x 50

460 In the above examples you will notice that the number being multiplied (the multiplier) was a multiple of 10. In this case we can complete the problem with only one line of working.

r o e t s Bo r e p ok u S

Where a multiplier is not a multiple of 10 we need to use two or more lines. 21 x 13 63 210 273

(21 x 3) (21 x 10)

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Teac he r

For example 21 x 13 is set out as

The first step involves multiplying 21 (the multiplicand) by the number of ones (3) and the next step involves multiplying 21 by 10 as there is one 10 in 13. It is very important that the numbers are written in the correct column. When multiplying by the digit in the tens column simply add a 0 on the end to hold the place and then multiply the numbers as normal. The final step is to add the two answers together to find the product.

33 x 12

29 x 11

23 x 13

66 330

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396

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43 x 22

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3. You will need to regroup to find answers to these. The first one has been done for you. 1 1

56 32

112 1680 1792

76 56

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23 24

83 46

24 34

28 36

74 39

24 96

Multiplying any two numbers each less than 100, with regrouping.

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Page 33

Multiplying Decimals 1 1. Complete the following sets of multiplication problems. $454 x 3

$354 x 4

$786 x 7

$576 x 5

$709 x 8

$903 x 6

$1362 2. x

$3.00 2

$6.00 3.

$7.00 6

$6.00 8

$2.00 4

$3.90 x 6

$2.80 x 7

$7.50 x 6

$8.39 x 6

$2.39 x 4

$8.05 x 7

$3.01 x 8

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$5.60 x 4

$18.00 4.

$3.87 x 10 $38.70 5. x

67.3 m 4

269.2 m

$9.00 7

$3.20 x 10

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$4.50 x 4

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$8.00 5

$6.32 x 5

35.4R cme 25.4 kg 46.9 mLb 35.7 12.8 mm © a d y Ed P u l i c a t i on s 3 x 5 x 4 x 3 x 3 •f orr evi ew pur posesonl y• x

Word Problems.

m . u

Use the back of this sheet for your working out.

w ww

Every day Kelli rode 5.25 km on her horse. How far would she ride in one week? ......................... Jess paid $3.95 for 8 books. How much did she pay altogether? ..................................................

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Peter bought 10 computer disks for $9.95 each. How much did he spend altogether?

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.............................................

Joe has 8 boxes of tomatoes, each weighing 12.7 kg. What is the total weight of the boxes? .............................................

Donelle swam 720 metres a day. How much would she swim in one week? .................................. Chrissie sold 6 airline tickets for $765 each. How much did she sell the tickets for altogether? ............................................. Tarlie bought 5 CDs at $24.95 each. How much did she pay altogether? ......................................

Multiplying numbers up to 1000 by a number up to 10 including money and other decimal measurements.

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Multiplying Decimals 2 1. Complete the following. Try to keep your working to just one line. $3.25 x 9

$5.78 x 4

$3.86 x 3

$2.31 x 5

$29.25 2. Multiply these decimals. x

0.3 2

0.6

r o e t s Bo r e p ok u S 0.7 4

1.2 2

3.4 6

4.5 3

5.3 4

3.8 x 4 ≈ 4 x 4 = 16 x

3.8 4

2.3 7

4.6 8

8.9 2

7.6 6

15.2

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Teac he r

3. Estimate the answer before completing these. The first one has been done for you.

3.5 3

4. Complete these. Make sure your answer has the same number of decimal places as the multiplicand.

5. x

0.24 0.19 0.47 0.84 © ad dxP0.87 u l i c t ons x R 4e x y 6E 5b xa 7i x 6 2.56 •f orr evi ew pur posesonl y• Find the product of these numbers using two lines for working out. 0.32 8

2.3 32

5.6 43

4.5 63

7.3 32

3.6 98

w ww

690

73.6

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6.8 57

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o c . che e r o t r s super

6. Complete the following problems by first estimating your answer. Leave the decimal point out while working out the problem and then add it at the end. 1 1 2 1

3.76 23

3.203 x 44

1128

5.61 x 76

3.57 98

8.97 x 83

5.43 x 72

7520 86.48

Challenge: A class of 43 students went to the museum. The entrance fee was $4.75. What was the total cost for the class? Multiplying decimals with up to two decimal places by whole numbers less than 100.

Ready-Ed Publications

Page 35

Multiplication Grids There are a number of ways of working out multiplication problems. This grid works by multiplying the two numbers for each square and then adding the numbers diagonally. For example to calculate 358 x 74:

Step 1

Step 2 3

3 1

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r o e t s Bo r e p ok u S 5

3 2

7 6

4 2

1. Try these grids using the same steps as above. 4

7 6

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4 9 2 In Step 1 the individual numbers are multiplied and written in the appropriate box. For example, 3 x 7 = 21. The two goes into the first half and the one is in the second half. In Step 2 all numbers are added in the direction of the arrows. The answer is 26 492.

w ww

Word Problems. Draw your own grids to find answers for these.

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Answer = .............................

m . u

Answer = ...........................

1. Lesley bought 25 metres of material at a cost of $3.25 a metre. What was the total cost of the material?

o c . che e r o t r s super

2. Carl runs 15.4 km each day to prepare for the cross country run. How far will he run over 15 days? 3. At Christmas Marie bought the same present for each of her brothers and sisters. Each present cost $8.59 and she has five brothers and seven sisters. How much did she spend altogether?

Using alternative methods for calculating multiplication problems.

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Ready-Ed Publications

Mental Multiplication 2 Some multiplication problems can easily be worked out mentally, whereas other require full working out or a calculator. 1. Complete the following mental problems. 20 x 40 = .................. 30 x 400 = ................ 40 x 600 = ................

2000 x 3 = .................

r o e t s Bo r e p ok u S

200 x 400 = .............. 10 x 500 = ................ 50 x 700 = ................

3 x 9000 = .................

2. To multiply the following, round the answer to the nearest ten and then add on the ones.

Teac he r

For example 4 x 21 ≈ 4 x 20 = 80 + (4 x 1) = 84.

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3 x 23 = ......... 2 x 41 = ........ 5 x 31 =......... 3 x 92 = ........ 4 x 52 = ........ 3 x 72 = ......... 3. In this row round the answer to the nearest ten and subtract the ones. For example 3 x 78 ≈ 3 x 80 = 240 - (3 x 2) = 240 - 6 = 234

39 x 3 = .......... 28 x 4 = ........ 29 x 5 =......... 37 x 2 = ........ 48 x 3 = ........ 66 x 2 = ......... 4. Find answers to these using the methods above.

421 x 3 = .................. © R e a d y E d P u b l i c a t i ons b. 42 x 4 = ................ 53 x 2 = .................... 64 x 3 = .................... 35 x 3 = ..................... f orr exv w pu r p seso nxl • c. 202 x 2• = ............... 203 3i =e .................. 404 x 2o = .................. 303 3y = ................... a. 321 x 3 = .............. 233 x 2 = .................. 112 x 2 = ..................

424 x 2 = ...................

e. 999 x 4 = .............. 998 x 3 = .................. 1002 x 4 = ................

1050 x 2 = .................

w ww

f. 499 x 7 = ............... 399 x 6 = .................. 299 x 8 = ..................

m . u

d. 505 x 2 = .............. 212 x 4 = .................. 313 x 2 = ..................

799 x 7 = ...................

5. Write six multiplication number sentences for each of these numbers. The first one has been done for you. 24 = 2 x 12,

24 = 2 x 3 x 4 =2x6x2

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24 x 1,

o c . che e r o t r s super 4 x 6,

2x2x3x2 2x2x6

6 x 4,

3 x 8,

8x 3, 12 x 2,

1 x 24.

2x2x6x1 1x3x2x4

36 = ...............................................................

48 = ..............................................................

......................................................................

.....................................................................

50 = ...............................................................

40 = ..............................................................

......................................................................

.....................................................................

60 = ...............................................................

100 = ............................................................

......................................................................

.....................................................................

Multiplying a whole number to 1000 by a whole number to 10.

Ready-Ed Publications

Page 37

Multiplying FFractions ractions and Whole Numbers 1 Example 1: Tim ate half a banana every day. How many bananas would he eat in one week? 1 ⁄2 x 7 = 0.5 x 7 = 3.5 = 3 1⁄2

r o e t s Bo r e p ok u S

We can also work this out by multiplying 1⁄2 x 7. 1 ⁄2 x 7 = 1 x 7 = 7 = 3 1⁄2 2 2

⁄2 x 4 = .................... 3 x 1⁄2 = .................... 5 x 1⁄2 = ....................

⁄2 x 6 = ......................

ew i ev Pr

Teac he r

1. Work out the following.

Example 2: There are 9 students in a class and a 1⁄3 of them wear glasses. To find the number of students wearing glasses we need to find a 1⁄3 of 9. How many times does 3 go into 9? The answer is3 times. So one third of 9 = 3. 1 This may be written as: 1⁄3 of 9 or ⁄3 x 9

© ReadyEdPubl i cat i ons xe 12v = ................... ⁄ xr 18p = ................... ⁄ xn 3 =l ...................... a. ⁄ x 6 = .................. •f or⁄ r i ew pu oseso y• 2. Find the answers to these using the method above. 1

⁄4 x 8 = ....................

c. 1⁄5 x 5 = ..................

⁄5 x 10 = ..................

d. 1⁄6 x 6 = .................

⁄6 x 12 = .................

w ww

b. 1⁄4 x 4 = ..................

⁄4 x 12 = ..................

⁄5 x 50 = ..................

⁄6 x 24 = .................

⁄4 x 20 = ................... ⁄5 x 100 = ................. ⁄6 x 36 = ..................

We know that 1⁄3 of 9 is equal to 3. So 2⁄3 of 9 must be equal to 2 x 3 because 2⁄3 = 2 x 1/3 Therefore 2⁄3 x 9 = 6

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m . u

o c . che e r o t r s super

3. Find the fractions of these whole numbers. Follow the example. ⁄3 x 12 = 9

⁄4 x 8 = 6

⁄5 x 20 = 16

⁄6 x 12 = 2

⁄3 x 18 = .....................

⁄3 x 30 = ..................

⁄4 x 12 = .....................

⁄5 x 10 = .....................

⁄6 x 18 = .....................

⁄3 x 90 = ..................

⁄4 x 100 = ...............

⁄5 x 100 = ................

⁄6 x 600 = ...............

⁄4 x 40 = ................... ⁄5 x 50 = ................... ⁄6 x 30 = ...................

Multiplying fractions with a denominator up to 10 by a whole number.

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Ready-Ed Publications

Multiplying FFractions ractions and Whole Numbers 2 1. Find 1⁄10 of these numbers. The first one has been done for you. 20 = 2

30 = .............. 40 = .............. 100 = ............ 200 = ............ 300 = .............

2. Find 3⁄5 of these numbers.

r o e t s Bo r e p ok u S

(Hint: Find 1⁄5 first and then multiply by 3.)

20 = .......................... 40 = ..........................

100 = ........................

25 = .......................... 35 = .......................... 200 = ........................

50 = ..........................

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30 = 18

36 = 12

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3. Find 2⁄6 of these numbers.

18 = .......................... 42 = ..........................

60 = ..........................

600 = ........................ 6000 = ...................... 6 = ............................

24 = ..........................

4. Find 1⁄2 of these numbers. 42 = 21

50 = .......................... 250 = ........................

44 = ..........................

2 = ............................ © R e a d y E d P u b l i c a t i ons 5. Complete the following. orr i ew pu p...................... oseso⁄ n l y • ⁄ x 8 = 2 •f 3e x ⁄v ........................ ⁄ r x 12 x 24 ....................... 14 = .......................... 80 = .......................... 1000 = ......................

⁄4 x 100..................... 27 x 2⁄9 ...................... 21 x 2⁄7 ......................

⁄7 x 28 .......................

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6. Convert these fractions to decimals to complete the problem, then write the answer as a fraction. a. 7⁄10 x 5 = 0.7 x 5 = 3.5 = 3 1⁄2

. te

b. 1⁄5 x 6 = ......................................................

c. 4⁄5 x 9 = ......................................................

d. ⁄10 x 8 = .....................................................

e. 1⁄4 x 7 = .....................................................

f. 3⁄5 x 6 = .......................................................

g. 8⁄10 x 4 = ....................................................

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7. Find the answers to these using your calculator. ⁄6 x 762 = 635

⁄25 x 75 = ..................

⁄20 x 1000 = ...............

⁄4 x 53 = ...................

⁄8 x 7 = .....................

⁄8 x 45 = ....................

⁄7 x 854 = .................

432 x 1⁄4 = ..................

Multiplying fractions with a denominator up to 10 and of 20 and 25 by whole numbers.

Ready-Ed Publications

Page 39

Division - Revision 1. Complete the following division problems. 4 ) 24

5 ) 35

6 ) 30

9 ) 72

7 ) 63

2. Complete the following problems and circle the twin division facts in each line. The first pair has been done for you.

r o e t s Bo r e p ok u S 6 8 ) 48

3 ) 27

7 ) 21

b. 9 ) 54

8 ) 64

4 ) 32

6 ) 42

7 ) 42 8 ) 72

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7 ) 56

c. 3 )21

6 ) 54

9 ) 72

4 ) 36

d. 3 ) 18

6 ) 30

8 ) 56

7 ) 49

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8 a. 6 ) 48

5 ) 30

3. Find the answer to the following division problems. Follow the first example. 9r2 5 ) 47 8 ) 58 3 ) 26 9 ) 68 7 ) 48

4. Complete the following problems. 8 ) $32

Word

1. If you share 36 peanuts between four students, how many does each student receive?

m . u

.........................................................

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2. Eight children went to the zoo. It cost a total of $56 for their entry. What is the admission cost for one child? .................................................

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3. Chrissie bought $35 worth of material. If each metre costs $7 how many metres did she buy? ....................................................

4. Jason, Patrick and Brad went fishing on the weekend and each caught the same amount of fish. If the total number of fish caught was 48, how many fish did each boy catch? ...................................................

5. If 6 children have 42 one dollar coins to share, how much money would each child receive? ................................................... 6. 8 children have 60 oranges to share. How many oranges will each child receive and how many will be left over? ........................................................ Revision of basic division facts including money.

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Ready-Ed Publications

Division - Basic FFacts acts 1. Divide the following. 80 ÷ 4 = 20

60 ÷ 3 = .................... 40 ÷ 2 = ....................

100 ÷ 5 = ...................

120 ÷ 4 = .................. 160 ÷ 8 = .................. 270 ÷ 9 = ..................

450 ÷ 5 = ...................

300 ÷ 6 = .................. 480 ÷ 6 = .................. 420 ÷ 7 = ..................

240 ÷ 2 = ...................

r o e t s Bo r e p ok u S

400 ÷ 2 = .................. 630 ÷ 7 = .................. 320 ÷ 8 = ..................

540 ÷ 9 = ...................

6000 ÷ 3 = ................ 4000 ÷ 5 = ................ 9000 ÷ 3 = ................

3200 ÷ 4 = .................

32 ÷ 4 = 320 ÷ 40 420 ÷ 70 =

÷7

63 ÷ 9 = 630 ÷

54 ÷ 9 =

÷ 90

48 ÷

= 480 ÷ 80

270 ÷ 30 = 27 ÷

81 ÷ 9 =

÷ 90

240 ÷ 60 = 24 ÷

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2. Complete the following by filling in the missing number.

3. Complete the problems below. 8 ÷ 4 = ...................... 80 ÷ 40 = .................. 800 ÷ 400 = ..............

8000 ÷ 4000 = ...........

6 ÷ 3 = ...................... 60 ÷ 3 = .................... 600 ÷ 3 = ..................

6000 ÷ 3 = .................

240 ÷ 40 = ................. © ReadyEdPubl i cat i on s 3600 ÷ 4 = ................ 360 ÷ 4 = .................. 36 ÷ 4 = .................... 360 ÷ 40 = ................. •f orr evi ew pur posesonl y• 4. Use = or ≠ to make these number sentences true.

24 ÷ 4 = .................... 240 ÷ 4 = .................. 2400 ÷ 4 = ................

180 ÷ 60

180 ÷ 6

320 ÷ 40

90 ÷ 3

9000 ÷ 3

6000 ÷ 100

600 ÷ 10

420 ÷ 7

4200 ÷ 70

720 ÷ 80

72 ÷ 8

5400 ÷ 900

540 ÷ 9

240 ÷ 60

240 ÷ 6

400 ÷ 8 640 ÷ 8

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o c . che e r o t r s super

4000 ÷ 80

1500 ÷ 300

15 ÷ 3

45 ÷ 9

640 ÷ 80

350 ÷ 7

3500 ÷ 70

56 ÷ 8

Challenge:

3200 ÷ 400

m . u

12 ÷ 4

w ww

120 ÷ 40

450 ÷ 90 5600 ÷ 80

Two Lotto syndicates win first and second division in the weekly draw. The first division winners share $48 000 and there are 80 people in the syndicate. The second division winners must share $4800 between 60. What amount would the following winners receive? First division winner :..............................

Second division winner: .............................

Applying basic division facts to multiples of 10, 100 and 1000.

Ready-Ed Publications

Page 41

Division of Whole Numbers 1 Look at the division problems below. We need to divide the number outside of the division bracket into each of the numbers inside the division bracket to calculate the answer. 3 ) 69 First we divide 3 into the number of tens (6) which equals 2 tens. The number 2 is placed directly above the 6 and represents 2 tens. Next we divide the 3 into the number of ones - 9. 3 goes into 9 three times and we write the 3 directly above the 9. 23 The answer is 23. 3 ) 69

r o e t s Bo r e p ok u S

1. Use the setting out shown above to complete the following problems. 4 ) 84

3 ) 93

4 ) 88

3 ) 63

You will need to regroup in the problems below. Follow the example.

1 7 3 ) 5 21

2 ) 82

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Teac he r

5 ) 55

3 goes into 5 once with 2 left over. The 5 represents the tens column so the 2 is carried over to the ones column making 21. 3 goes into 21 seven times and so the answer is 17.

2. Complete the following by using the steps above.

3 ) 42

6 ) 84

5 ) 95

4 ) 96

3 ) 87

7 ) 91

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4 ) 64

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3. Find answers for these problems. The first one has been done for you. 1 1r4 a. 7 ) 841 b. 5 ) 64

2 ) 35

) . t e ) 2 47

c. 5 ) 76

3 97

d. 3 ) 52

6 ) 81

e. 7 ) 36

4 ) 91

4 ) 73

8 ) 98

6 ) 77

3 ) 53

o ) c . che e r ) ) ) ) o r st super ) ) ) ) 3 ) 83

7 ) 83

4 ) 77

9 ) 94

2 ) 49

4 ) 75

6 ) 99

10 78

8 47

3 89

4 31

6 59

5 93

8 49

6 75

7 90

Dividing whole numbers with the dividend less than 100 and the divisor to 10.

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Ready-Ed Publications

Mixed Division Problems To calculate the number of times 4 will divide into 236 we set the problem out as follows. 4 will not go into 2 so we move onto the next number. We do not need to write a zero above the 2. 5 9 4 goes into 23 five times with 3 left over. 4 goes into 36 nine times. 4 ) 2336 The answer is 59. 1. Complete the following. 7 ) 623

r o e t s Bo r e p ok u S

5 )240

8 ) 600

9 )414

6 ) 468

4 ) 368

8 ) 864

a. 3 ) 246

6 ) 642

4 ) 832

9 ) 963

7 ) 756

b. 6 ) 345

5 ) 987

7 ) 864

8 )765

4 ) 433

c. 7 ) 707

8 ) 888

9 ) 918

4 ) 424

6 ) 636

d. 6 ) 354

7 ) 245

8 ) 356

2 )367

5 ) 678

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2. Find the answers to the following.

5 ) 524

7 ) 147

9 ) 432

8 ) $64.80

8 ) $32.56

9 ) $27.81

203 c. 8 ) 1624

5 ) 1525

3 ) 2730

9 ) 8127

6 ) 3624

d. 4 ) 2356

3 ) 1767

5 ) 4825

7 ) 4606

9 ) 2322

e. 7 ) 4569

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3 4687

Challenge:

5 ) $35.75

m . u

9 ) $54.00

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b. 6 ) $18.12

8 ) 5648

6 ) 2868

o c . che e r o t r s super 5 ) 5342

8 ) 4523

7 ) 3574

9 ) 7864

Sam spent $45.85 while on holiday. He was away for 7 days and spent exactly the same amount each day. How much money did Sam spend each day? .....................................................................

Dividing whole numbers, money and decimals by whole numbers to ten.

Ready-Ed Publications

Page 43

Expressing Remainders 1 So far we have expressed remainders as whole numbers; however, there are other ways of expressing remainders depending on the problem. Look at the examples below to see where different methods are used. Example 1 : If there were 68 students and 5 teams were formed, how many students would there be in each team? 1 3r3 5 ) 618 68 ÷ 5 =

r o e t s Bo r e p ok u S

There would be 13 students in each team and 3 students left over.

Teac he r 68 ÷ 5 =

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Example 2: Maddy used 68 cm of string to hang 5 mobiles from the ceiling. Each piece of string was exactly the same length. How long was each piece of string? 13.6 5 ) 618 .3 0

Maddy used 13.6 cm of string for each mobile. Note: The decimal point is placed after the ones. Example 3:

68 cakes were shared equally between 5 classes. How many cakes did each class receive? 3 1 3 r ⁄5 5 ) 618

Example 4:

68 students watched a play at the theatre. They sat five to a row. How many rows were used? 13r3 5 ) 618

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68 ÷ 5 =

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They used 14 rows (even though one row only had three students).

Exercises

m . u

68 ÷ 5 =

Complete the problems below and express the remainder in the most appropriate form. 1. Share 37 bananas among 8 people. ...................................................

2. Share $56 dollars among 5 students. ................................................. 3. How many cars are needed to transport 89 people if there are 5 people to a car? .............................................................................. 4. Share 68 pizzas among 7 classes. ..................................................... 5. Share 25 kg of ice-cream among 4 families. ...................................... Exploring the different forms of expressing remainders in division problems.

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Ready-Ed Publications

Expressing Remainders 2 Complete the following expressing remainders as decimals. The first problem in each set has been done for you. (Hint: estimate your answers first.) =

5 ) 536 2 ) 159

4 ) 4738 .2 0

r o e t s Bo r e p ok u S =

8 ) 362

3. 4 ) 4569

4 ) 286

6 ) 537

8 ) 380

8 ) 636

4 ) 394

6 ) 429

8 ) 394

8 ) 638

4 ) 3159

5 ) 2296

8 ) $42

5 ) $48

61. 2 5 4 ) 245.1020

4 ) 315 1142. 2 5

5 ) 1234

4 ) 4569.1020 8 ) 3722

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2. 4 ) 245

6 ) $87

4 ) $78

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5. 4 ) $30.70 4 ) $23.14

≈

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≈ ..........................

Word Problems

$7. 6 7 5 ≈ $7.68 4 ) $30.730 20

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Note: The decimal point always follows the number in the ones column.

119 . 5

1. 4 ) 478

8 ) $50.04

4 ) $21.10

6 ) $35.25

≈ ...........................

≈ ..............................

≈ ..........................

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Share $77 among 8 people. Approximately how much will each person receive?......................... Share $49.54 among four people. What amount to the nearest whole cent should each person receive? ............................................. Share $68 among 6 people. What will each person receive? Round your answer to the nearest whole cent. ........................................

Exploring the different forms of expressing remainders in everyday problems.

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Page 45

Division of Decimals When we divide money we are dividing with decimals. In the working out, the decimal place in the answer must go directly over the decimal places within the division bracket. 0.9 For example 7) 6.3

and

4.2 3 ) 12.6

1. Complete the following divisions of decimals.

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9 ) 8.1

4 ) 3.2

6 ) 3.6

8 ) 6.4

3 ) 2.7

5 ) 4.5

3 ) 9.6

5 ) 7.5

4 ) 7.2

2 ) 9.8

7 ) 5.6

4 ) 9.2

8.1 4 ) 32.4

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divisor

For example 32.4 ÷ 4 ≈ 32 ÷ 4 = 8

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It is best to make an estimate of the answer by rounding the decimals so that you know roughly what the answer should be. dividend

Instead of rounding the dividend to the nearest whole number, round it to the nearest multiple of the divisor. Complete the following by first making an estimate. 2. Show how you would estimate the answers to these, then complete the original problem to see how close your estimate was.

4 63.2

c. 7 ) 43.4 ≈

6 ) 29.4 ≈

7 ) 40.6 ≈

3) 46.8 ≈

d. 2 ) 24.8 ≈

7 ) 14.7 ≈

5 ) 35.5 ≈

8) 72.8 ≈

e. 4 ) 12.8 ≈

6 ) 66.6 ≈

8 ) 32.8 ≈

4) 37.6

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≈

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4 36.8 ≈

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b. 3 24.9 ≈

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3. Complete the following by first making an estimate. 19.74 For example 78.96 ÷ 4 ≈ 80 ÷ 4 = 20. 4 ) 78.96

a. 4 ) 22.48

6 ) 274.8

7 ) 298.2

8 ) 27.68

9 ) 511.2

3 ) 230.4

b. 4 ) 315.2

6 ) 577.2

3 ) 78.6

9 ) 86.22

5 ) 38.5

6 ) 45.36

Division of decimals by a whole number up to 10, expressing remainders as decimals.

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Division - Recurring Decimals When we divide a whole number by another number we may have to add extra zeros on the end to calculate the exact answer. For example $98 shared among four people can be shown as 24. 50 4) $98.200

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Zeros are also added to normal whole numbers in order to calculate the answer. 76 ÷ 5 = 15. 2 5 ) 76.10

For example

35 ÷ 4 = 8. 7 5 4 ) 35. 3020

0.6666

2.0 ÷ 3 = 3 )2.0202020

The answer is expressed as a recurring decimal = 0.66

Another example: 44 ÷ 7 = 6.2 8 5 7 1 4 2 8 5 7 1 4 ) 44.206040501030206040501030 and so on .....Answer ≈ 6.28 7

In this case the answer would be rounded to two decimal places.

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If we divide certain numbers we will end up with a recurring decimal. For example:

6 )1.0

9 )3.0

9 ) 6.2

9 )5.0

9 )4.0

3 ) 7.0

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3 )1.0

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3 ) 8.0

2. Calculate answers to the following rounding your answer to the second decimal place.

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3.142857 7 ) 22.00000 ≈ 7 ) 9.3

≈

6 ) 7.9

≈

7 ) 59

≈

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3.14

) 7 83

≈

14 7.8

) 6 5.0

)13 12

≈

Exploring the concept of recurring decimals.

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Page 47

Expressing FFractions ractions as Decimals You will need a calculator to complete this page. Work out the answer to this division problem. Express the remainder in the form of a fraction. 7 ) 69

= .................................................

Now use your calculator to find the answer in decimal form. Round the answer to three

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decimal places. .........................................

The numbers that come after the decimal point are equivalent to the fraction in the first answer. Therefore we can say that 6⁄7 ≈ 0.857.

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1. Use your calculator to convert these fractions to a decimal. Round your answer to three decimal places. 1

⁄3 = ...........................

⁄3 = ..........................

⁄6 = ..........................

⁄8 = ...........................

⁄9 = ...........................

⁄7 = ..........................

⁄8 = ..........................

⁄7 = ...........................

⁄8 = ...........................

⁄9 = ..........................

⁄7 = ..........................

⁄9 = ...........................

2. Use your calculator to help you fill in the correct sign in the boxes below. Use =, ≈ or ≠ to make the sentence true.

⁄5

⁄3

0.222

⁄6

0.833

0.625

⁄8

⁄7

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Decimal Patterns 3. Use your calculator to investigate these number patterns.

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0.572

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⁄4

0.75

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Convert these fractions into decimals. Round your answers to the third decimal place. 1

⁄9 = 1 ÷ 9 = 0.1111

⁄9 = ......................................

⁄7 = ......................................

= ......................................

⁄8 = ......................................

⁄8 = ........................................

⁄3 = ......................................

⁄3 = ........................................

⁄6 = ......................................

⁄6 = ........................................

⁄9 = ........................................ 7

= ........................................

Investigating relationships between decimal remainders and fractional remainders; Exploring number patterns with calculators.

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Ready-Ed Publications

Percentages 1 Decimals and fractions can also be expressed as percentages. Percentages are another way of representing a part of a whole. Percentages are expressed as a fraction with a denominator of 100, as per cent means ‘for each hundred’. 1. Convert the percentages below to a fraction. 35% = 35⁄100

56% = ............... 98% = ................ 87% = ............... 50% = ................

100% = .............

105% = ............. 765% = .............. 0% = ................. 12% = ................

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2. Change these decimals to a percentage.

0.56 =................ 0.99 = ................ 0.27 = ............... 0.5 = ...................

0.7 = .................

0.25 =................ 0.3 = .................. 0.55 = ............... 0.2 = ...................

3. Change these fractions to a percentage.

⁄100 = 20% ......

⁄100 = ...............

254

⁄100 = .............

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0.23 = 23%

⁄100 =..................

4. If a fraction has a denominator which is not equal to 100 an equivalent fraction with a denominator of 100 must be found. Look at the examples below and complete the rest of the line.

⁄ a = ......................... ⁄ =u ......................... ⁄n = .................... © Re dyEdP bl i cat i o s = 5% ⁄ = ......................... ⁄ = ......................... ⁄ = .......................... • f orr evi ew pur posesonl y• 4

⁄20 = 5⁄100

⁄50 = 20⁄100 = 20%

⁄5 = 20⁄100 = 20%

10 20

500

⁄50 = .........................

⁄5 = ..........................

1000

⁄50 =........................

⁄5 = ..........................

⁄50 = ........................

⁄5 = ...........................

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⁄10 = 10⁄100 = 10 %

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Another way to convert fractions to a percentage is to multiply the fraction by 100. For example

⁄4 x 100 =

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⁄2 x 100 =

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300 4

100 2

4 300

50 = 50%

75 = 75%

5. Change these fractions into percentages.

⁄4 = ...........................

⁄5 = ..........................

⁄20 = .........................

⁄50 = .........................

⁄20 = ......................... ⁄50 =........................

⁄10 = ..........................

154

⁄200 = ......................

Converting fractions and decimals to a percentage where the denominator is a factor of 100.

Ready-Ed Publications

Page 49

Percentages 2 1. Match the percentage on the left by circling the equivalent fraction and decimal on the right. There may be more than one answer.

⁄10

a. 4 % =

b. 12% =

1.2

4.5

0.72

⁄100

⁄200

⁄100

0.45

⁄100

720

⁄1000

0.25

⁄100

0.12

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c. 45% = d. 72% =

e. 25% =

⁄4

⁄10

72.0

0.4

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0.04

Another way to calculate percentages is to multiply the fraction by 100. Cancel the fractions to simplify the problem. For example

⁄20 =

ii) 5

15 x 100 = 75 = 75% 20 1

⁄16

12 x 100 = 75 = 75% 16 1 4 1

© ReadyEdPubl i cat i ons 12 out of 24• = ................................................ 9 out of o 27 =s ................................................ f orr evi ew pu r p esonl y• 2. Use this method to calculate the following percentages.

20 out of 32 = ..............................................

16 out of 25 = ................................................

50 out of 500 = ............................................

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Word Problems

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15 out of 60 = ................................................

a. Emily received 35 out of 50 in a test. What percentage did she score? ..............................

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b. On Saturday Denis climbed 40 metres up a rock face. The next day he climbed 10%

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further. How far did he climb up the rock face on Sunday? ................................................. c. Lesley played in a tennis tournament and won 80% of her games. Overall she played 20 games. How many games did she win? .............................................................................. d. Noel read 18 chapters of a book.

The book contained 24 chapters altogether. What percentage has he read? ............................

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Ready-Ed Publications

Mixed W ord Problems Word 1.

At the town fair the following crowds were recorded: Saturday 976, Sunday 1089, Monday 675 and Tuesday 232. What was the average attendance number over the four days? ............................................

Denis drove 48.8 km on Tuesday, 54.7 km on Wednesday morning, 123.6 km on

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Wednesday afternoon and 320 km on Thursday.

What was the total distance covered? .................................................................................. Noel scored the following number of runs in a cricket test series - 121, 29, 98, 57, 145.

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What was his average score?..............................................................................................

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Samantha jogged 19.8 km on Friday and 23.4 km on Saturday. How much further did she

run on Saturday than Friday? ...............................................................................................

Sarah bought 17 CDs at the second-hand shop. If each CD was $9.95, how much did

she pay altogether? .............................................................................................................

© ReadyEdPubl i cat i ons f o r ev i e wp ur p se s1o nl y • Three• brands ofr chocolate have different amounts ofo sugar. Brand contains 56% sugar, On the coldest day in winter 20% of the class were absent. What fraction of the class

made it to school? ............................................................................................................... 7.

Brand 2 is 3⁄5 sugar and in Brand 3 sugar makes up 0.62 of the chocolate. Which of the 3

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brands contains the most sugar? ......................................................................................... Eight school students paid $67 each to attend the school camp. What was the total

amount paid by the students? ..............................................................................................

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A man left $9853 to his four children. If it is divided evenly among them how much will

each person receive? .......................................................................................................... 10. A washing machine was priced at $315. It was then reduced by 20%. What is the reduced price? .................................................................................................................................. 11. On his 15th birthday Dan weighed 65 kg. On his 16th birthday his weight had increased by 15%. What did he weigh on his 16th birthday? ................................................................ 12. What percentage of an hour is 42 minutes? .........................................................................

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Page 51

Answers All answers are given in row order: left to right.

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Page 5 Addition 1. 46, 45, 57, 50, 27, 346, 745, 957, 450, 627. 2. 65, 45, 69, 65, 41, 906, 483, 757, 348, 980. 3. 63, 43, 52, 100, 75, 338, 764, 233, 684, 402. 4. 48, 33, 63, 53, 51, 146, 869, 247, 985, 630. Subtraction 1. 41, 51, 34, 51, 43, 538, 684, 561, 734, 919. 2. 37, 41, 45, 51, 34, 863, 547, 315, 248, 121. 3. 80, 90, 88, 67, 61, 136, 572, 328, 219, 534. 4. 38, 15, 53, 45, 43, 327, 685, 844, 688, 524. Multiplication 18, 24, 16, 40, 54, 45, 35, 8, 27, 36, 21, 20. Division 3, 9, 3, 9, 7, 6, 6, 10, 8, 4, 5, 6. Page 6 1 - Ones, tens, hundreds, tens; 2 - 800, 80, 8000, 8, 500; 3 - b. 3000 + 900 + 40 + 7; c. 3000 + 800 + 70 + 6; d. 7000 + 700 + 60 + 4. 4 - 5376, 7839, 8064, 9206, 3017. 5 - 2, 6, 7, 4, 3, 3. 6 - 2, 1, 1, 7, 4, 6. 7 - 8, 800, 8, 8000. Page 7 7 456 322. 1. Show teacher. 2 - (2 x 1000 000) + (8 x 100 000) + (7 x 10 000) + (6 x 1000) + (5 x 100) + (4 x 10) + (3 x 1); (7 x 1 000 000) + (6 x 100 000) + (5 x 10 000) + (3 x 1000) + (1 x 10) + (2 x 1). 3 - Millions = 3 000 000, thousands = 4000; hundred thousands = 500 000. Challenge - 6 201 400. Page 8 1 - 49, 58, 79, 96, 95, 100, 87, 79, 59, 89. 2 - 138, 138, 108, 126, 128, 137, 146, 126, 113, 127. 3 - 70, 93, 83, 66, 132, 113, 65, 101, 90, 105. 4 - 155, 113, 135, 107, 125, 149, 110, 181, 179, 104. 5 - 89, 89, 100, 160, 98, 60, 101, 171, 168, 157. 6 - 655, 1199, 1350, 1019, 1300, 1449, 1328, 1018, 1269, 1186. 7 - 1066, 1040, 1151, 1595, 1776, 1021, 1322, 1363, 907, 1327. 8 - 1228, 1774, 1814, 1705, 2289, 1903, 2105, 1916, 1831, 2119. Page 9 1 - b, e, g, h. 2 - a. 9544, b. 1701, c. 2307, d. 5920, 3 - a. $1021.20, b. $1101.96. Page 10 1 - 33, 45, 26, 23, 23, 34, 4, 11, 41, 24. 2 - 444, 445, 623, 155, 322, 104, 356, 144, 43, 12. 3 - 24, 37, 17, 8, 29, 47, 9, 16, 4, 17. 4 - 206, 527, 58, 419, 508, 517, 218, 78, 304, 317. 5 - 59, 139, 99, 93, 585, 86, 295, 475, 94, 547. Page 11 3.4, 4.5, 2.6; 25 6⁄10; 1. Check table. 2 - a. tens, b. tenths, c. tenths, d. hundreds, e. hundredths, f. tenths.

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Page 12 1-

9 tens 9 ones 4 tenths 1 ten 2 ones 3 tenths 4 tens 2 ones 7 tenths 5 hundredths 4 tens 5 ones 9 tenths 8 hundredths 3 hundreds 6 tens 4 ones 6 tenths 8 hundredths 2 - a. 121.212, b. 40.359, c. 201.003, d. 146.524, e. 3.4, f. 20.377, g. 420.004; Challenge - 601.01.

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All answers are given in row order: left to right.

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Page 13 1 - (1 x 10) + (3 x 1) + (3 x 1/10) + (5 x 1/100) + (6 x 1/1000); (5 x 10) + (7 x 1) + (1 x 1/10) + (8 x 1/1000); (2 x 10) + (9 x 1) + (9 x 1/10) + (9 x 1/100) + (8 x 1/1000). 2 - 5/100; 4/10, 2/1000, 1/10. 3 - Three hundred and one point two zero three; One thousand, three hundred and forty five point two; One point two nine eight. 4 - 1.23, 1.234, 1.9, 2.013, 2.13, 21.13, 210.103, 1234.12. 5 - <,>, >, <, <, <, >, >, <, <, <, <. 6 - 2.345, 2.543, 23.45, 234.005, 234.05, 234.5, 2345, 2543.1. Page 14 1 - $7.85. 2 - $396.55. 3 - 36.42 km. 4 - Third deal. 5 - 1125 mL or 1.125 L. 6 - 2112. 7 - 728. 8 - 123. 9 - 83.69 kg. 10 - 12 hours. 11 - 335. Page 15 1 - 100, 2 - 500, 3 - 10, 4 - 1, 5 - a. $3.45, b. $9.59, c. $67.06, d. $12.23, e. $14.05, f. $45.50, g. $143.03, h. $20.20. 6 - a. $35.73, b. $28.94, c. $20.90, d. $3.54, e. $20.01, f. $0.15, g. $0.16, h. $2.35, i. $0.05. 7 - a. $21.20, b. $367.60, c. $354.20, d. $34.00, e. $245.08, f. $32.32, g. $200.06. 8 - a. $23, b. $99, c. $36, d. $87, e. $4, f. $20, g. $63, h. $3234, i. $1, j. $1, k. $58. Challenge - They have the same amount. Page 16 1 - $89.00, $76.00, $987.50, $736.00, $37.10, $35.35, $37.00, $403.83, $478.55, $10.10; 2 - $818.95, $596.25; 3 - $3.25, $6.00, $233.00, $110.50, $29.00, $10.00, $16.90, $56.35, $160.75, $19.85; 4 - $164.21, $65.05, $178.31, $56.63. Page 17 1 - 90, 70, 60, 40, 70, 130, 760, 100, 880, 60, 100. 2 - 600, 800, 700, 500, 600, 400, 500, 0, 200, 900, 900, 1400, 9800, 6400, 2100, 600, 2700. 3 - 5000, 9000, 9000, 10 000, 900, 13000, 10 000, 3000, 6000, 5000, 5000; 4 - 250, 170, 260. Page 18 1 - 605/610, 153/160, 350/350; 2 - 700/1099,1000/942, 1000/1224, 200/1182; 3 - 30 x 30 = 900; 100 x 60 = 6000; 30 x 10 = 300; 80 x 40 = 3200; 30 x 60 = 1800; 4 - 900 ÷ 3 = 300; 400 ÷ 2 = 200; 100 ÷ 5 = 250; 5 - 3876 - 3880, 3900, 4000; 2546 - 2550, 2600, 3000; 989 - 990, 1000, 1000; 5541 - 5540, 5500, 6000; Challenge - 16 000. Page 19 1 - 3, 9, 6, 2, 8, 3, 5, 10, 6, 2; 3; 2 - 4, 2, 6, 6, 8,10; 3 - 26, 89 or 90, 24, 28, 39, 12; 4 - 36, 19, 88, 84, 63, 29, 25, 55, 72; 5 - 13, 25, 2, 26, 4, 6, 53, 7, 2; 6 - 22, 20, 16; Challenge - 165m2. Page 20 1 - 4.8, 2.3, 7.2, 3.6, 6.9, 4.5, 9.5, 3.6, 5.5, 2.4, 7.6, 9.5. 2 - 3.42, 2.23, 6.34, 5.78, 9.88, 6.69, 5.46, 4.25, 3.32, 5.55, 10.00, 1.96. 3 - <, >, >, <, >, <, <, >, <, <, <. ; 4 - 2 + 3 + 6 + 4 =15; 3 + 6 + 9 + 3 = 21; 8 +1 + 2 + 1 =12; 1 + 6 + 5 + 4 =16. 5 - $3.40, $4.60, $7.90, $5.40, $1.00, $7.80. 6 - $5.57, $6.54, $2.25, $7.89, $2.78, $3.66, $5.78, $3.54, $9.86, $9.00, $7.60, $5.64. Page 21 1 - 36.3, 88.7, 86.8, 76.6, 97.3, 109.9; 2. 99.2, 139.0, 130.1, 117.3, 111.2; 3 - 23.4, 3.3, 20.1, 22.6, 16.1, 10.7; 4. 15.9, 29.9, 18.8, 36.9, 3.5; 5 - 50, 115.30, 70.43, 107.03, 122.32, 90.01; 6 - 10.89, 22.22, 41.9, 72.97. Challenge - $23.89 Page 22 1 - a -26.973, c - 557.06, e - 7493.5, f - 46.026; 2 - 236.3, 58.1, 8.65, 92.28, 8.2, 3.53; 39.25, 193.62, 122.39, 325.24, 424.33, 401.55; 3 - 6.19 m, 23.25 kg, 46.75 mL, 70.39 km, 77.72 cm, $4.03; 4 - a - 22.102, c - 1.034, e - 13.334, f - 0.676; 5. 3.49 m, 10.85 kg, 10.95 mL, 3.97 km, 53.35 cm, $5.47. Challenge - 78.48 km. Page 23 1 - 51.477, 408.04, 462.011, 414.253, 463.458, 305.49. 2 - 4546.4, 12.243, 33.147, 94.06, 538.1, 80.58. Challenge - 8.25 kg. Page 24 1 - 12.238, 5.918, 43.244, 355.45, 44.90, 0.18, 1.994, 2.054, 210.966, 2.86, 321.96, 3.723. 2 - 1.416, 252.313, 48.936, 226.673, 27.988, 379.974.

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Word Problems: 1. 14.3 L, 2. 10.25 g, 3. 3.45 m.

All answers are given in row order: left to right. 2 3 4 5 6 7 8 9 10 11 12

x 1 2 3 4 5 6 7 8 9 10

2 2 4 6 8 10 12 14 16 18 20

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x 10 6 7 1 8 9 3 2 5 4

7 70 42 49 7 56 63 21 14 35 28

5 6 7 8 9 10 11 12 13 14 15

6 7 8 9 10 11 12 13 14 15 16

7 8 9 10 11 12 13 14 15 16 17

8 9 10 11 12 13 14 15 16 17 18

9 10 11 12 13 14 15 16 17 18 19

10 11 12 13 14 15 16 17 18 19 20

3 3 6 9 12 15 18 21 24 27 30

4 4 8 12 16 20 24 28 32 36 40

5 5 10 15 20 25 30 35 40 45 50

6 6 12 18 24 30 36 42 48 54 60

7 7 14 21 28 35 42 49 56 63 70

8 8 16 24 32 40 48 56 64 72 80

9 9 18 27 36 45 54 63 72 81 90

10 10 20 30 40 50 60 70 80 90 100

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Page 26 + 7 10 17 6 13 7 14 1 8 8 15 9 16 3 10 2 9 5 12 4 11

4 5 6 7 8 9 10 11 12 13 14

6 16 12 13 7 14 15 9 8 11 10

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9 90 54 63 9 72 81 27 18 45 36

6 60 36 42 6 48 54 18 12 30 24

4 14 10 11 5 12 13 7 6 9 8

8 18 14 15 9 16 17 11 10 13 12

5 15 11 12 6 13 14 8 7 10 9

3 13 9 10 4 11 12 6 5 8 7

2 12 8 9 3 10 11 5 4 7 6

1 11 7 8 2 9 10 4 3 6 5

4 40 24 28 4 32 36 12 8 20 16

8 80 48 56 8 64 72 24 16 40 32

5 50 30 35 5 40 45 15 10 25 20

3 30 18 21 3 24 27 9 6 15 12

2 20 12 14 2 16 18 6 4 10 8

1 10 6 7 1 8 9 3 2 5 4

10 20 16 17 11 18 19 13 12 15 14

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1 1 2 3 4 5 6 7 8 9 10

3 4 5 6 7 8 9 10 11 12 13

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Page 25 + 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11

10 100 60 70 10 80 30 30 20 50 40

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Page 27 1 - 20, 140, 230, 450, 320, 2340, 5360, 6450, 3570, 2790. 2 - 600, 2400, 1500, 2000, 1600, 800, 3000, 6300, 2400, 4200.

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All answers are given in row order: left to right.

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3 - 6000, 24 000, 16 000, 21 000, 36 000, 6000, 35 000, 48 000, 24 000, 14 000; 4 - 40, 30, 100, 20, 30. Page 28 1 - 5, 2, 6, 5, 16, 3, 2, 9, 4, 3, 1, 10, 1, 4, 3, 8. 2 - A - 12, 27, 0, 48, 10, 8, 14, 5, 10, 50; B - 35, 20, 45, 42, 24, 54, 2, 18, 7, 70; C- 12, 72, 12, 72, 27, 81, 0, 32, 0, 40; D - 40, 40, 15, 35, 6, 64, 56, 45, 30, 63; E - 16, 24, 18, 24, 28, 16, 45, 18, 36, 24; F - 6, 15, 14, 21, 32, 0, 48, 28, 8, 50; G- 8, 4, 5, 8, 10, 8, 7, 3, 4, 5; H- 5, 5, 5, 6, 9, 7, 2, 3, 10, 10; I- 2, 2, 6, 3, 3, 10, 3, 2, 7, 4; J - 5, 8, 5, 7, 4, 10, 7, 5, 9, 7; K - 3, 4, 6, 4, 7, 9, 6, 4, 9, 1; L - 2, 6, 3, 7, 2, 2, 4, 9, 8, 8. Challenge - 36: 1, 2, 3, 4, 6, 9, 12, 18, 36; 24: 1, 2, 3, 4, 6, 8, 12, 24; 48 - 1, 2, 3, 4. 6, 8, 12, 16, 24, 48; 60 - 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. Page 29 1 - 35, 42, 40, 72, 20, 35, 9, 8, 25, 18. 2 - 150, 15, 219, 328, 68. 3 - 38, 104, 76, 224, 81, 56. 4. 48, 34, 76, 81, 76. Page 30 1 - 224, 234, 194, 306, 224, 168, 216. 2 - a. 138, 336, 348,320, 105, 276, 388. b. $270, $469, $390, $64, $192. 3. $2.25, $3.92, $2.64, $2.28, $1.35. Word Problems - $144, $288, $76, 105, 128, 126, $189. Page 31 1 - A - 100, 250, 480, 900, 800, 3400, 2500, 1350, 7480, 3690, 4240, 3330; B - 200, 340, 250, 400, 300, 2500, 2600, 2460, 2980, 2030, 2450, 2300; C - 400, 560, 240, 500, 300, 3800, 9800, 3560, 8740, 2860, 5700, 3500; D - 600, 690, 380, 600, 400, 2800, 3500, 2570, 2390, 2960, 8970, 5600. 2 - 10, 10, 330, 10, 10, 7, 100, 10, 240, 10, 350, 460, 10, 10, 2400, 3790. 3 - 3, 50, 80, 7, 3, 60, 5, 50, 7, 70, 50. Page 32 1 - 504, 623, 624, 325, 540; 2 - 880, 668, 396, 864, 699; 3 - 2196, 1648, 3684, 2190, 8320; 4 - 868, 858, 387, 984, 894; 5 - 447, 1968, 2268, 1947, 1516, 2760; 6 - 1018, 3208, 897, 4525, 8600, 5621. Word Problems - $5934, 5950 m or 5.95 km, 945, 1125 min or 18 hours and 45 minutes. Page 33 1 - 350, 1740, 2010, 1080, 1600; 2 - 319, 299, 946; 3 - 552, 816, 1008, 4256, 3818, 2886, 2304. Page 34 1 - $1416, $5502, $2880, $5672, $5418; 2 - $40.00, $42.00, $48.00, $8.00, $63.00; 3 - $22.40, $23.40, $19.60, $45.00, $32.00; 4 - $50.34, $9.56, $56.35, $24.08, $31.60; 5 - 106.2 cm, 127 kg, 187.6 mL, 107.1, 38.4 mm. Word Problems - 36.75 km, $31.60, $99.50, 101.60 kg, 5040 m, $4950, $124.75. Page 35 1 - $23.12, $11.58, $11.55; 2. 2.8, 2.4, 20.4, 13.5, 21.2. 3 - 14/16. 1, 40/36.8, 18/17.8, 56/45.6, 12/10.5. 4 - 0.96, 1.14, 4.35, 3.29, 5.04. 5 - 240.8, 283.5, 233.6, 352.8, 387.6. 6 - 132/142.12, 456/426.36, 392/349.86, 747/744.51, 360/390.96. Page 36 1 - 16 286, 56 259, 33 570, 28 348, 16 008, 60 921. Word Problems - $81.25, 231 km, $103.08. Page 37 1 - 800, 12 000, 24 000, 6000, 80 000, 5000, 35 000, 27 000; 2 - 69, 82, 155, 276, 208, 216; 3 - 117, 112, 145, 74, 144, 132; 4 - a. 963, 466, 224, 1263, b. 168, 106, 192, 105,c. 404, 609, 808, 909, d. 1010, 848, 626, 848, e. 3996, 2994, 4008, 2100, f. 3493, 2394, 2392, 5593. 5 - Answers will vary. Page 38 1 - 2, 11⁄2, 21⁄2, 3; 2 - a - 2, 4, 6, 1; b - 1, 2, 3, 5; c - 1, 2, 10, 20; d - 1, 2, 4, 6; 3 - 12, 20, 60, 9, 75, 30, 4, 20, 30, 12, 100, 10. Page 39 1 - 3, 4, 10, 20, 30; 2 - 12, 24, 60, 15, 21, 120, 30; 3 - 6, 14, 20, 200, 2000, 2, 8; 4 - 25, 125, 22, 7, 40, 500, 1; 5 11⁄2, 4, 16, 75, 6, 6, 16; 6 - b. 0.2 x 6 = 1.2 = 11⁄5 c. 0.8 x 9 = 7.2 = 71⁄5, d. 0.6 x 8 = 4.8 = 48⁄10, e. 0.25 x 7 = 1.75 = 13⁄4, f. 0.6 x 6 = 3.6 = 36⁄10, g. 0.8 x 4 = 3.2 =

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32⁄10. 7 - 50, 39.75, 33.75, 3, 4.375, 487.99, 108.

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Page 40 1 - 6, 7, 5, 8, 9; 2- a. 1st and 3rd - 8, 8, 6, 9, 3; b. 4th and 5th - 6, 8, 8, 7, 6; c. 3rd and 5th - 7, 9, 8, 9, 9; d. 2nd and 5th - 6, 5, 7, 7, 6. 3 - 7 r 2, 8 r 2, 7 r 5, 6 r 6, $4, 6c, 7 cm, $6, 12c. Word Problems - 12, $7, 8 m, 16, $7, 7 and 4 leftover. Page 41 1 - 20, 20, 20, 30, 20, 30, 90, 50, 80, 60, 120, 200, 90, 40, 60, 2000, 800, 3000, 800; 2 - 90, 540, 8, 42, 3, 810, 6; 3 - 2, 2, 2, 2, 2, 20, 200, 2000, 6, 60, 600, 6, 900, 90, 9, 9; 4 - =, ≠, =, ≠, =, =, =, ≠, ≠, =, =, =, ≠, =, ≠. Challenge -1st Division - $600, 2nd Division - $80. Page 42 1 - 21, 11, 31, 22, 21, 41; 2 - 16, 12, 12, 25, 17, 12, 14, 14, 19, 24, 29, 13; 3 - 17 r 1, 18 r 1, 12 r 2, 12 r 5, 17 r 2, b.12 r 4, 23 r 1, 27 r 2, 11 r 6, 19 r 1, 10 r 4, c. 15 r 1, 32 r 1, 24 r 1, 18 r 3, 16 r 3, 7 r 8, d.17 r 1, 13 r 3, 5 r 7, 29 r 2, 7 r 3, 9 r 5, e.5 r 1, 22 r 3, 18 r 3, 6 r 1, 12 r 3, 12 r 6. Page 43 1 - 89, 48, 75, 46, 78, 92; 2 -a. 82, 107, 208, 107, 108, 108, b. 57 r 3, 197 r 2, 123 r 3, 95 r 5, 108 r 1, 104 r 4, c. 101, 111, 102, 106, 21, d. 59, 35, 44 r 4, 183 r 1, 135 r 3, 48; 3 - a. $3.11, $1.02, $1.06, $1.07, $1.71, $1.08; b. $3.02, $6.00, $8.10, $4.07, $3.09, $7.15; c. 203, 305, 910, 903, 604, 706; d. 589, 589, 965, 658, 258, 478; e. 652 r 5, 1562 r 1, 1068 r 2, 565 r 3, 510 r 4, 873 r 7. Challenge - $6.55. Page 44 1 - 4 5⁄8, 2 - $11.20, 3 - 18 cars, 4 - 9 5⁄8, 5 - 6.25 kg. Page 45 1 - a. 107.2, 71.5, 89.5, 47.5, 79.5, 79.5, 98.5, 71.5; b. 45.25, 78.75, 49.25, 79.75; c. 246.8, 465.25, 789.75, 459.2; d. $14.50, $19.50, $5.25, $9.60; e. $5.78, $6.26, $5.28, $5.88. Problems - $9.62, $12.38, $11.33. Page 46 1 - 0.9, 0.8, 0.6, 0.8, 0.9, 0.9, 3.2, 1.5, 1.8, 4.9, 0.8, 2.3; 2 - a. 6/6.1, 8/8.1, 7/7.1; b. 8/8.3, 9/9.2, 9/8.9, 16/15.8; c. 6/6.2, 5/4.9, 6/5.8, 15/15.6; c. 12/12.4, 2/2.1, 7/7.1, 9/9.1; e. 3/3.2, 11/11.1, 4/4.1, 9/9.4; 3 - a. 5/5.62, 50/45.8, 30/42.6, 3/3.46, 60/56.8, 80/76.8; b. 80/78.95, 100/96.2, 25/26.2, 10/9.58, 7/7.7. . . . . . . . . Page 47

1 - 2.66, 0.33, 0.166, 0.33, 0.68, 0.55, 0.44, 2.33. 2 - 11.86, 1.33, 0.56, 1.32, 0.83, 8.43, 0.92.

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Page 48 9 6/7, 9.857; 1 - 0.333, 0.666, 0.833, 0.875, 0.222, 0.571, 0.375, 0.286, 0.625, 0.889, 0.143, 0.111; 2 - =, =, ≈, ≈, ≠, ≈, ≈, ≈,≠, ≈, ≠, ≈. 3 - 0.222, 0.333, 0.143, 0.286, 0.428, 0.125, 0.25, 0.375, 0.333, 0.666, 1.333, 0.166, 0.333, 0.666. Page 49 1 - 56⁄100, 98⁄100, 87⁄100, 50⁄100, 100⁄100, 105⁄100, 765⁄100, 0, 12⁄100; 2 - 23%, 56%, 99%, 27%, 50%, 70%, 25%, 30%, 55%, 20%. 3 - 67%, 52%, 254%, 1%. 4 - 40%, 70%, 50%, 25%, 4%, 45%, 8%, 32%, 70%, 60%, 80%, 100%. 5 - 25%, 40%, 15%, 70%, 25%, 6%, 52%, 77%. Page 50 1 - a. 0.04, 4/100; b. 12/100, 0.12; c. 45/100, 0.45; d. 0.72, 72/100; e. 1/4, 0.25. 2 - 50%, 33 1⁄3%, 25%, 62 1⁄2%, 64%, 10%; Word Problems - a. 70%, b. 44 m, c. 16 games, d. 75%

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Page 51 1 - 743, 2 - 547.1 km, 3 - 90, 4- 3.6 km, 5 - $169.15, 6 - 4⁄5, 7 - Brand 3, 8 - $536, 9 - $2463.25, 10 - $252, 11 74.75 kg, 12 - 70%.

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