Striving to Improve: Mathematics - Fractions, Decimals & Percentages by Teacher Superstore

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Acknowledgements i. i-stock Photos. ii. Clip art images have been obtained from Microsoft Design Gallery Live and are used under the terms of the End User License Agreement for Microsoft Word 2000. Please refer to www.microsoft.com/permission.

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o c . che e r o t r s super Published by: Ready-Ed Publications PO Box 276 Greenwood WA 6024 www.readyed.net info@readyed.com.au

ISBN: 978 186 397 852 1 2

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Any copying of this book by an educational institution or its staff outside of this blackline master licence may fall within the educational statutory licence under the Act.

Reproduction and Communication by others

Contents Teachers’ Notes Curriculum Links

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6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

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Skills With Decimals – Teachers’ Notes Decimal Place Value 1 Decimal Place Value 2 Decimal Place Value 3 Greater Than/Less Than Rounding Decimals 1 Rounding Decimals 2 Decimal Addition 1 Decimal Addition 2 Decimal Subtraction 1 Decimal Subtraction 2 Adding And Subtracting Decimals 1 Adding And Subtracting Decimals 2 Adding And Subtracting Decimals 3 Adding And Subtracting Decimals 4 Multiplying Decimals 1 Multiplying Decimals 2 Dividing Decimals Recurring Decimals

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Answers

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

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Fractions, Decimals And Percentages – Teachers’ Notes Shading Decimal And Fraction Quantities 1 Shading Decimal And Fraction Quantities 2 Shading Decimal And Fraction Quantities 3 Expressing Fractions as Decimals Expressing Decimals as Fractions Fraction and Decimal Conversions 1 Fraction and Decimal Conversions 2 Fraction and Decimal Conversions 3 Decimals And Equivalent Fractions Fractions Into Decimals: Word Problems Percentages 1 Percentages 2 Percentages 3 Percentages 4 Decimal And Percentage Conversions Fraction And Percentage Conversions Fractions, Decimals And Percentages 1 Fractions, Decimals And Percentages 2 Fractions, Decimals And Percentages 3 What Is My Test Score As A Percentage? Percentage Of An Amount What’s The Discount? Mixed Word Problems 1 Mixed Word Problems 2 Mixed Word Problems 3

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51-55

Teachers’ Notes This resource is focused on the Number and Algebra Strand of the Australian Curriculum for lower ability students and those who need further opportunity to consolidate these core areas in Mathematics.

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Each section provides students with the opportunity to consolidate written and mental methods of calculation, with an emphasis on process and understanding.

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The section entitled Skills With Decimals enables students to re-encounter ideas in decimal place value, calculations with decimals, comparing decimal quantities and rounding decimal amounts. These activities are a useful way to scaffold a new unit of Mathematics and will help build confidence for lower ability students to attempt more challenging problems at their year level. The section entitled Fractions, Decimals And Percentages walks students through conversions between fractions, decimals and percentages. The activities are designed to guide student learning with minimal input from the teacher and there is a strong emphasis on process and understanding. Students explore mental and written methods for performing conversion calculations. Attention is also given to real world applications and uses of these different representations, with an emphasis on understanding and using percentages.

© ReadyEdPubl i cat i ons The activities can be used for individual students needing further consolidation •f orr evi ew pur posesonl y• in a mainstream classroom or as instructional worksheets for a whole class of

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lower ability students. The activities are tied to Curriculum Links in the Australian Curriculum ranging from grade levels of Year 5 through to Year 7 and are appropriate for students requiring extra support in Years 7, 8 and 9. It is hoped that Fractions, Decimals And Percentages will be used to help teachers provide appropriate resources and support to those students in greatest need. The book as a whole can be used as a programme of work for those students on a Modified Course or Independent Learning Programme. Activities are sufficiently guided so that students can work independently and at their own pace without constant supervision and guidance from the teacher.

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Curriculum Links Compare, order and represent decimals (ACMNA105) Investigate strategies to solve problems involving addition and subtraction of fractions with the same denominator (ACMNA103)

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Solve problems involving addition and subtraction of fractions with the same or related denominators (ACMNA126)

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Find a simple fraction of a quantity where the result is a whole number, with and without digital technologies (ACMNA127)

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Add and subtract decimals, with and without digital technologies, and use estimation and rounding to check the reasonableness of answers (ACMNA128)

Multiply decimals by whole numbers and perform divisions by non-zero whole numbers where the results are terminating decimals, with and without digital technologies (ACMNA129) Multiply and divide decimals by powers of 10 (ACMNA130)

© ReadyEdPubl i cat i ons •f o rdivide r ev i ew ur p os eswritten onstrategies l y•and Multiply and fractions andp decimals using efficient Make connections between equivalent fractions, decimals and percentages (ACMNA131) digital technologies (ACMNA154)

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Express one quantity as a fraction of another, with and without the use of digital technologies (ACMNA155) Round decimals to a specified number of decimal places (ACMNA156)

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Connect fractions, decimals and percentages and carry out simple conversions (ACMNA157)

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Find percentages of quantities and express one quantity as a percentage of another, with and without digital technologies. (ACMNA158)

Teachers’ Notes

Skills With Decimals The activities in this section allow students to revise many of the core Number properties and ideas that are involved when working with decimal numbers. Before introducing lower ability students to new work and applications involving decimals and percentages, these activities will encourage students to consolidate concepts from previous years.

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Place Value

Students have the opportunity to explore what they know about place value for integers and extend this understanding to decimal place value. These activities are particularly useful before moving on to calculations and applications.

Rounding

Estimation

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The concepts covered include:

To assist students with building their appreciation and understanding of working with numbers, estimation is a core skill. These activities will encourage students to reflect on whether their calculations are providing reasonable solutions.

Addition, Subtraction, © ReadyEdP ubl i cat i ons Multiplication And Division These activities are designed to develop •f orr evi ew pu r p o s e s o n l y • the mental and written learning processes

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of students. It may be useful to encourage students to check their answers with a calculator or appropriate technology. Full engagement with these core skills is also useful to prepare students for NAPLAN requirements.

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As a concept with which many students experience difficulty, it is important to allow for a thorough consolidation of rounding decimals to specified place values. This is important work to include prior to work on scientific notation and significant figures.

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* Decimal Place Value 1 * Task a

Complete the following.

67.9

e.g. six tens, seven ones and nine tenths. = .............................................................................................................................................

99.4

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

12.3

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

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42.75 = .............................................................................................................................................

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

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

zz Where there is no number in a column a zero is used to hold the value. Look at the example below. The table represents the number 405.307 NOT 45.37.

Example

Hundreds

Tens

Ones

1/tenth

1/hundredth 1/thousandth

Tens

Ones

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e. f. g.

2 4

1/tenth

1/hundredth 1/thousandth

405.307

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task c: Challenge * Which is the greater number – 601.01 or 601.001? 7

* Task a

* Decimal Place Value 2 Write the following numbers in expanded form.

e.g. (2 x 100) + (3 x 10) + (4 x 1) + (3 x 1/10) + (5 x 1/100) 234.35 = ................................................................................................................................................... 13.356 = ................................................................................................................................................... 57.108 =....................................................................................................................................................

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

56.758 =

* Task c

35.424

3.222

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* Task b

132.1

Write these numbers in words.

289.78 = two hundred and eighty-nine point seven eight.

© ReadyEdPubl i cat i ons 1345.2 =................................................................................................................................................... •f orr evi ew pur posesonl y• 1.298 =...................................................................................................................................................... 301.203 =.................................................................................................................................................

1.9

1.234

210.103

2.013

21.13

1.23

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Order each set of numbers starting from the least.

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* Task d

1234.12

2.13

. te o 2345 2.345 234.5 23.45 2.543 2543.1 234.05 234.005 c . che e r ................................................................................................................................................................... o r st super ...................................................................................................................................................................

* Task e

Use < or > to complete these.

1.9

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

* Decimal Place Value 3 zz Look at the numbers 5432 and 62.45. Four represents a different value for each number even though it is the same digit.

* Task a

5432 = 4 x 100 = 400

62.45 = 4 x 1⁄10 = 4⁄10

Example

What value does each underlined number represent below?

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9675..................... 29.38 ..................... 1.987...................... 135.3...................... 209.08................. 24.34 .................. 147.2...................... 100.333 . .............. 24.24 . ................... 999.99.................

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24.35 = 20 + 4 +

3 10

5 + 100

(2 x 10) + (4 x 1) + (3 x

Write these decimals in expanded form.

1 1 10 ) + (5 x 100 )

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zz Look at the decimal number 24.35 in expanded form.

a. 136.57 =...............................................................................................................................................

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

b. 26.987 = ..............................................................................................................................................

© ReadyEdPubl i cat i ons c. 35.57 . ............................................................................................................................................... •=f orr evi ew pur posesonl y•

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

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

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d. 49.08 = . ............................................................................................................................................... e. 765.297 = . ..........................................................................................................................................

. te o Task c Use < or > to make these true. c . * che e r o t r 3.546 35.46 1.256 125.6 24.78 s2.478 1000 s r upe

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

2.002

2.2

980

9.8

860.086 12

860.068

2.3

3.2

0.12

154.3

134.5

1.000

56.65

65.56

264.1

264.9

* Challenge Andrew is putting petrol into Dad’s car. The litre gauge has stopped and reads 40.72 litres. What value in litres does the 7 represent?

* Greater Than/Less Than > means “greater than”; < means “less than”. zz Look at the examples below and compare the numbers. If two numbers have the same number of place values, start comparing from the left until you find the number that has the FIRST largest place value. Example

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Compare 4.570 and 4.507.

Which number has MORE place values (before the decimal point)? Ones .

Same

1/hundredth 1/thousandth

Same

Larger

Ones 4

Same

1/tenth

1/hundredth 1/thousandth

Same

Smaller

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1/tenth

The first number to have a larger digit is 4.570. This is written as 4.570 > 4.507. Example

Compare 0.09 and 0.55.

Which number has MORE place values (before the decimal point)? Ones 0

Same

©R eadyEdP ubl i cat i ons 1/hundredth Ones 1/tenth 1/hundredth 9 0 . 5 5 •0f orr evi ew pur po se son l y• 1/tenth

Smaller

Same

Larger

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Task a *

4.8 _____ < 5.8

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The first number to have a larger digit is 0.55. This is written as 0.09 < 0.55. Place the symbols in between these sets of numbers to show which is greater.

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4.90 _____ > 4.09

5.8 _____ 8.5

13.4 _____ 11.9

3.99 _____ 3.09

6.35 _____ 6.53

8.35 _____ 3.99

7.38 _____ 3.87

8 _____ 7.99

1 _____ 0.008

3.987 _____ 11.002

20.67 _____ 26.6

8.227 _____ 8.12

11.87 _____ 7.912

6.022 _____ 6.020

4.80 _____ 4.8

What is the trick in the last pair of numbers, 4.80 and 4.8 ? ............................................................................................................................................................. Use a separate piece of paper to write your own.

* Rounding Decimals 1 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 9.5 10

* Task a

Round these decimals to the nearest whole number.

3.6 ≈ 4 2.8 ≈................. 9.1 ≈................. 5.6 ≈................. 2.3 ≈................ 7.8 ≈..............

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

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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.

* Task b

Complete the following.

Round these decimals to the nearest whole number.

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3.5 ≈................... 1.5 ≈................. 6.5 ≈................. 5.5 ≈................. 7.5 ≈................ 9.5 ≈..............

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

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

Round these decimals to the nearest whole number.

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63.11 ≈.................. 28.97 ≈................. 24.65 ≈................ 55.34 ≈................ 72.43 ≈...............

56.789 ≈ 57 13.245 ≈.............. 24.865 ≈.............. 2.367 ≈................ 25.895 ≈.............

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4.111 ≈.................. 5.555 ≈................. 53.455 ≈.............. 7.001 ≈................ 2.457 ≈...............

Task c *

o c . Estimate the sum of these decimals by rounding each decimal c e her r to the nearest whole number. o t s super

3.42 ≈ 3

3.56 ≈ __

2.56 ≈ __

2.79 ≈ __

4.67 ≈ 5

8.98 ≈ __

8.74 ≈ __

6.54 ≈ __

2.69 ≈ 3

7.43 ≈ __

2.53 ≈ __

3.53 ≈ __

+ 5.54 ≈ 6

+ 2.41 ≈ __

+ 5.32 ≈ __

+ 2.42 ≈ __

≈ 17

* Rounding Decimals 2

Task a Complete the following. * 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 ≈............

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2. Round these decimals to two decimal places. For example 2.344 ≈ 2.34. 3.423 ≈.............. 2.234 ≈.......... 6.342 ≈............ 5.782 ≈............ 9.878 ≈.......... 6.689 ≈..........

Task b Complete the following. * 1. Use < or > to complete the following.

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5.459 ≈.............. 4.253 ≈.......... 3.324 ≈.......... 5.551 ≈......... 9.999 ≈.......... 1.959 ≈..........

1.9

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

3001.9

203.4

204.3

46.003

46.03

21.003

21.333

2. Round these decimals to the nearest whole number and complete the sum.

2.34 + 3.456 + 5.645 + 4.37 ≈................................................................................................................

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2.67 + 5.645 + 9.001 + 3.424 ≈................................................................................................................ 7.58 + 0.987 + 2.456 + 1.23 ≈................................................................................................................

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

o c . c e Sometimes we may have an amount which does not divide evenly. For example ifr we share $35 between 8 h e o t r students each student will get $4.375. This must then be rounded tos $4.38. Remember: Money is expressed in s r u e p decimal form. For example 76 c is equal to $0.76.

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

* Task c

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 ≈................... 12

* Decimal Addition 1 zz Adding decimals is like regular adding. You regroup the same way. Just remember to keep the decimal point in the same place.

Examples

3. 45 + 5. 22

5. 79 + 4. 15

8. 39 + 1. 78

9. 94

10. 17

Regrouping one column

Regrouping two columns

8. 67

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* Task a

Try these sums with no regrouping.

2. 25 + 5. 32

4. 43 + 3. 14

4. 34 + 3. 31

3. 66 + 5. 22

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WORK FROM RIGHT TO LEFT

6. 28 + 1. 60

4. 36 + 3. 51

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5. 27 + 2. 13

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5. 37 + 2. 24

* Task c

3. 58 + 4. 13

6. 47 + 2. 38

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* Task b

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4. 27 + 4. 65

Try these sums regrouping two columns.

$4. 46 + $1. 85

$6. 79 + $2. 55

$4. 48 + $2. 87

* Decimal Addition 2 zz Adding decimals is like regular adding. You regroup the same way. Just remember to keep the decimal point in the same place.

Examples

5. 79 + 4. 3

10. 09

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WORK FROM RIGHT TO LEFT

Try these sums. Hint: Put 0 in the gaps to help.

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* Task a

8. 65

No regrouping

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3. 45 + 5. 2

1. 40 + 4. 12

5. 6 + 4. 14

3. 4 + 1. 59

3. 47 + 5. 8

4. 8 + 5. 95

1. 9 + 5. 89

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Example

Task b *

Wrong: 2.45 3.6 0.78 + 5

Right: 2. 45 3. 60 0. 78 + 5. 00

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zz When you write the decimals for a sum, make sure the decimal point is lined up. Look at the sum 2.45 + 3.6 + 0.78 + 5 below. Putting 0 into the gaps helps neat setting out!

o c . c e her r Try lining the sum up in the space. o t s super 5.37 + .4 + 23.55 + 7

* Decimal Subtraction 1 zz Subtracting decimals is like regular subtraction. You regroup the same way. Just remember to keep the decimal point in the correct place so it lines up and down the column. 5. 45 – 3. 22

Examples

7 12

2. 23

No regrouping

8. 36 – 1. 78

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5. 74 – 4. 15 1. 59

Regrouping one column

6. 58

Regrouping two columns

* Task a

Try these sums with no regrouping.

7. 55 – 2. 24

5. 28 – 2. 23

7. 43 – 3. 12

8. 89 – 2. 63

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WORK FROM RIGHT TO LEFT

9. 67 – 1. 50

2. 87 – 1. 23

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8. 47 – 2. 19

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8. 42 – 3. 17

* Task c

5. 74 – 2. 26

6. 76 – 1. 39

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* Task b

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7. 36 – 3. 28

Try these sums regrouping two columns.

$7. 52 – $1. 86

$8. 32 – $4. 57

$6. 56 – $2. 79

* Decimal Subtraction 2 zz Subtracting decimals is like regular subtraction. You regroup the same way. Just remember to keep the decimal point in the correct place so it lines up and down the column.

Examples

5 14

5. 39 – 4. 7

6. 50 – 3. 73

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No regrouping

0. 69

Regrouping one column

2. 77

Regrouping two columns

WORK FROM RIGHT TO LEFT

Try these sums. Hint: Put 0 in the gaps to help.

7. 30 – 5. 12

8. 6 – 3. 13

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* Task a

5. 45 – 3. 2

9. 6 – 1. 28

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zz When you write the decimals for a sum, make sure the decimal point is lined up. Look at the sum 8.45 – 5 below. Putting 0 into the gaps helps neat setting out!

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b: Challenge * 7task – 4.59

Hint: Make 7 into 7.00.

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–

8.45 5

Right:

8. 45 – 5. 00

* Adding And Subtracting Decimals 1 Task a Try these sums. *Add the following decimals. 23.1 34.3 52.3 45.2 65.2 98.6 + 13.2 + 54.4 + 34.5 + 31.4 + 32.1 + 11.3

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Add these decimals. Regrouping is the same as with whole numbers. ¹25.7 ¹ 24.9 65.6 46.8 37.8 64.3

+24.6

+ 74.3

+ 83.3

+ 79.5

+ 46.9

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50.3

+ 73.4

Task b Try these sums. *Complete the following subtraction problems.

46.8 24.6 62.3 63.8 47.8 74.9 − 23.4 − 21.3 − 42.2 − 41.2 − 31.7 − 64.2

This time you will need to borrow from the ones and tens columns. 3

− 13.7

− 21.9

− 23.8

− 18.6

− 26.9

− 59.9

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10.9

* Task c

Try these sums.

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Add these decimals. 24.53 78.76 35.57 73.46 63.36 45.65 + 25.47 + 36.54 + 34.86 + 33.57 + 58.96 + 44.36

o c . che e r o t r s ssetting r pe Subtract these decimals by firstu them out correctly. 23.45 − 12.56 =

67.89 − 45.67 =

65.46 − 23.56 = 98.43 − 25.46 =

Adding And Subtracting Decimals 2 * zz 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. Look at how the sum 4.567 + 12.3 is set out.

Task a * a.

Example

4.567 + 12.3 16.867

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* Task b

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Complete only the sums below that show the correct setting out. b. c. d. e. f. 24.243 2.4 532.5 643.7 7457.8 45.456 + 2.73 + 256.3 + 24.56 + 32.53 + 35.7 + 0.57

Add these decimals.

234 56 7.45 79.98 6.98 2.3 + 2.3 + 2.1 + 1.2 + 12.3 + 1.22 + 1.23

23.45 46.78 34.25 85.87 54.75 33.6 3.5 23.3 64.7 4.7 4.8 3.52 + 12.3 + 123.54 + 23.44 + 234.67 + 364.78 + 364.43

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Add the following amounts.

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4.99 m 3.75 kg 43.2 mL 56.89 km 23.12 cm $3.56 + 1.2 m + 19.5 kg + 3.55 mL + 13.5 km + 54.6 cm + 47c

. te o c the subtraction problems that are set out correctly. . c *a. Task c Complete e hc. er d. st b. e. r f. o s up253.5 er 36.434 3.456 24.564 3.789 4.574

− 2.462

− 23.45

− 3.54

− 2.342

− 23.1

− 2.78

d: Challenge *On taskcamp 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?

* Task a

* Adding And Subtracting Decimals 3 Add the following decimals by setting them out correctly.

24.567 + 23.45 + 3.46 =

24.567 4.56 + 46.78 + 356.7 23.45 3.46 +

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1.009 + 456.7 + 4.302 =

23.01 + 345.6 + 45.643 =

2 .456 + 456.7 + 4.302 =

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24. 56 + 35.3 + 245.63 =

©Subtract Rea dyEdPubl i cat i ons the following amounts. * •f rr evi ew pur pos eson y• 4578.7 - 32.3 o = 24.567 - 12.324 =l 4578.7 Task b

32.3 −

−

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35.687 - 2.54

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567.9 - 29.8

= −

97.85 - 3.79

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−

o c . c e her 116.34s r = -t 35.76 = o super −

−

task c: 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?

* Adding And Subtracting Decimals 4

zz What happens if we need to subtract a number with more decimal places than the number we are subtracting it from? We use zeros. ²¹ 25.30 Look at the example 25.3 - 16.27. It is now possible to − 16.27 Example borrow from the tenths column to take 7 from 10. 9.03

* Task a

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Complete the following by adding zeros where necessary.

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24.56 9.35 45.6 367.8 45.63 2.3 − 12.322 − 3.432 − 2.356 − 12.35 − 0.73 − 2.12

2.003 4.6 243.54 3.4 345.6 6.37 − 0.009 − 2.546 − 32.574 − 0.54 − 23.64 − 2.647

Task b Set out and solve the subtraction problems, adding zeros where * © ReadyEdPubl i cat i ons necessary. 4.65 - 3.234 = 254.3 - 1.987 = 53.57 - 4.634 = •f orr evi ew pur posesonl y•

w ww

234.35 - 7.677 = − . te

−

34.34 - 6.352 =

−

m . u

−

443.34 - 63.366 =

o c . che e r o t task c: word Problems 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?

* Multiplying Decimals 1 * Task a

Complete the following sets of multiplication problems.

Set 1

$454 $354 $786 $576 $709 $903 x 3 x 4 x 7 x 5 x 8 x 6 $1362 Set 2

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$3.00 $8.00 $7.00 $6.00 $2.00 $9.00 x 2 x 5 x 6 x 8 x 4 x 7

Set 3

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$6.00

$4.50 $5.60 $3.90 $2.80 $7.50 $3.20 x 4 x 4 x 6 x 7 x 6 x 10 $18.00

Set 4

$3.87 $8.39 $2.39 $8.05 $3.01 $6.32 x 10 x 6 x 4 x 7 x 8 x 5

$38.70 Set 5

269.2 m

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* task b: word Problems

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67.3 m 35.4 cm 25.4 kg 46.9 mL 35.7 12.8 mm x 4 x 3 x 5 x 4 x 3 x 3

. te o c 2. Jess paid $3.95 for 8 books. How much did she pay altogether? . c e her r 3. Peter bought 10 computer disks for $9.95 each. t How much did he spend o s s uper altogether?

Use the back of this sheet for your working out. 1. Every day Kelli rode 5.25 km on her horse. How far would she ride in one week?

4. Joe has 8 boxes of tomatoes, each weighing 12.7 kg. What is the total weight of the boxes? 5. Donelle swam 720 metres a day. How much would she swim in one week? 6. Chrissie sold 6 airline tickets for $765 each. How much did she sell the tickets for altogether? 7. Tarlie bought 5 CDs at $24.95 each. How much did she pay altogether? 21

* Multiplying Decimals 2

* Task a

1. Complete the following. Try to keep your working to just one line. $3.25 $5.78 $3.86 $2.31 x 9 x 4 x 3 x 5 $29.25

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2. Multiply these decimals.

0.6

3.4 4.5 5.3 6 x 3 x 4

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0.3 0.7 1.2 x 2 x 4 x 2 x

3. Estimate the answer before completing these. 3.8 x 4 ≈ 4 x 4 = 16

3.8 2.3 4.6 4 x 7 x 8 x

15.2

8.9 7.6 3.5 2 x 6 x 3

2.56

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

w ww

2.3 5.6 4.5 32 x 43 x 63 x

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5. Find the product of these numbers using two lines for working out.

7.3 3.6 6.8 32 x 98 x 57

o c . 73.6 che e r o t r s your answer. Leave the s 6. Complete the following problems byp first estimating r u e decimal point out while working out the problem and then add it at the end.

690

1 2

1 1

3.76 3.203 5.61 3.57 8.97 5.43 x 23 x 44 x 76 x 98 x 83 x 72 1128 7520 86.48 22

Dividing Decimals * zz 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. 4.2 0.9 Example ) ) 7 6.3 and 3 12.6

Task a *

Complete the following divisions of decimals. Remember to place the decimal point in the correct place.

9 ) 8.1

4 ) 3.2

6 ) 3.6

8 ) 6.4

3 ) 2.7

5 ) 4.5

5 ) 7.5

4 ) 7.2

2 ) 9.8

7 ) 5.6

4 ) 9.2

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3 ) 9.6

r o e t s Bo r e p ok u S 



zz It is best to make an estimate of the answer by rounding the decimals so that you know roughly what the answer should be. 8.1 divisor 4 ) 32.4 dividend Example 32.4 ÷ 4 ≈ 32 ÷ 4 = 8 Instead of rounding the dividend to the nearest whole number, round it to the nearest multiple of the divisor.

8 ) 64.8 ≈

7 ) 49.7≈

set 2

3 ) 24.9 ≈

4 ) 36.8 ≈

3 ) 26.7 ≈

4 ) 63.2≈

set 3

7 ) 43.4 ≈

6 ) 29.4 ≈

7 ) 40.6 ≈

. te )

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5 ) 45.5 ≈ 5 ) 45

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set 1

3 ) 46.8 ≈

o c 4 12.8 ≈ 4 ) 37.6 ≈ . che e r o t r s s r u e p Task c Complete the following by first making an estimate.

set 4

2 ) 24.8 ≈

set 5

7 ) 14.7 ≈

5 ) 35.5 ≈

6 ) 66.6 ≈

8 ) 32.8 ≈

For example 78.96 ÷ 4 ≈ 80 ÷ 4 = 20.

8 ) 72.8 ≈

19.74 4 ) 78.96

set 1

4 ) 22.48

6 ) 274.8

7 ) 298.2

8 ) 27.68

9 ) 511.2

set 2

4 ) 315.2

6 ) 577.2

3 ) 78.6

9 ) 86.22

5 ) 38.5 23

Recurring Decimals * zz When we divide a whole number by another number we may have to add extra zeros on the end to calculate the exact answer. $98 shared among four people can be shown as: Example 24. 50 ) 4 $98.200 Zeros are also added to normal whole numbers in order to calculate the answer.

r o e t s Bo r e p ok u S 76 ÷ 5 = 15. 2 5 ) 76.10

Example

35 ÷ 4 = 8. 7 5 ) 4 35. 3020

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If we divide certain numbers we will end up with a recurring decimal. Example 0.6666 2.0 ÷ 3 = 3 2.0202020 The answer is expressed as a recurring decimal = 0.66

44 ÷ 7 = Example 6.2 8 5 7 1 4 2 8 5 7 1 4 7 ) 44.206040501030206040501030 and so on … Answer ≈ 6.28 In this case the answer would be rounded to two decimal places.

6 ) 1.0

9 ) 6.2

9 ) 5.0

9 ) 4.0

9 ) 3.0

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3 ) 1.0

w ww

3 ) 8.0

3 ) 7.0

. Calculate answers to the following. Round your answer to the t * e o second decimal place. c . c e h r 3.142857 e o t r s ≈ 7 ) 22.00000 ≈ 3.14 s 7 ) 83 up er Task b

7 ) 9.3

≈

14 ) 7.8

≈

6 ) 7.9

≈

6 ) 5.0

≈

7 ) 59

≈

13 ) 12

≈

Teachers’ Notes

Fractions, Decimals And Percentages The activities in this section allow students to revise basic ideas involving fractions and percentages and to further extend their understanding of the relationships between the three numerical representations.

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

The concepts covered include:

Students begin by examining percentages as visual fractional quantities, enabling them to draw parallels between percentages as being fractions out of one hundred.

Conversions

The emphasis on this section is students being able to convert between fractions, decimals and percentages using various mental and written strategies. A few different options are presented and explained and teacher discretion can be used to determine which strategies will be most useful for students.

Percentage Applications

A few of the core applications of percentages are given in this section which align closely with the topics in the Australian Curriculum for this age group. These are presented with mental and written strategies for understanding and engaging with the real-life applications.

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Visual Representation

Mixed Applications

finall activities ini this section will © ReadyEdPThe u b i c a t o n s be useful in determining the fluency of students with relation to their ability to •f orr evi ew pur posesonl y• work easily with fractions, decimals and

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w ww

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percentages and with their ability to work with short applications.

o c . che e r o t r s super

* Task a

0.1

0.23

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0.7

0.26

0.69

0.6

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* Task b

Write the decimal that shows the shaded area.

w ww

m . u

Shade in the correct amounts.

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* Shading Decimal And Fraction Quantities 1

. te ............................... ................................ ............................... .............................. o c . c e h r and the decimal for each Task c Write the fraction e o t r * s of the shaded areas. super

0.6 = 6⁄10

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

task d: Challenge *Decimals are used to show amounts of money. How would you express a dollar coin and a twenty cent piece as a decimal?

* Shading Decimal And Fraction Quantities 2 The grids below have been divided into 100 units. Shade the amount shown underneath.

0.2

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0.96

0.45

0.01

0.05

0.68

0.86

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Task a *

0.8

What fraction of the above grids have you shaded? Express in the simplest form. 20 = 15 100 a.....................................

.................................. c. ................................... d. ................................ © Reb.a dyEdPubl i cat i ons e. . ................................. f. . .................................. g. .................................. h. ................................ •f orr evi ew pur posesonl y•

w ww

3 4

Complete these using = or ≠. 0.75

. te

4 8

0.6

* Task c 1

3 4

9 108

2 6

0.4

8 10

0.8

1 3

0.3

4 8

0.6

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* Task b

2 3

0.3

2 5

0.25

o c . e Use =,c <h or > to complete these. r er o t s s r u e p 1.75 2 2.4 4 8

9.8

5 6 100

6.5

task d: Challenge * Bridget has painted 0.75 of the garage door. What fraction does she still need to paint?

* Shading Decimal And Fraction Quantities 3 * Task a

Shade the amounts shown below. How many squares are shaded in each box? a.______

Use the grids below to complete the amounts shown. Add =, < or > for each pair.

⁄2

0.84

⁄10

0.35

⁄5

0.69

w ww 0.15

Task c *

. te

⁄4

o c . c e he Complete these number sentences usingo =, r < or >. t r s s uper Use squared paper if needed.

3 10

0.13

6.32

2 5

Challenge *Which is longer:

3 4

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0.47

By looking at the boxes we can see that 0.73 is less than 34 .

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Task b *

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a. 0.73

b.______

5 6

⁄20

0.4

5 20

0.5

7.85

7 17 20

3 5

2.65

0.35

3 5

sticks of liquorice or 2.56 sticks of liquorice?

2 5

3.16

⁄20

0.4

3 16 20

* Expressing Fractions As Decimals zz Sometimes we want to express as a fraction, rather than a decimal, to make some calculations easier. The easiest form is to change the denominator to a 10, 100 or 1000 where possible.

Example 1

Convert

2 to a decimal. 5

Convert

We can since 5 divides into 10 without a remainder. So to make the 5 into a 10 we need to multiply by 2.

If we want to change ¾ to a decimal we change the denominator to 100 (not 10, since 4 doesn’t divide into 10 evenly). We do this by multiplying top and bottom by 25. So ¾ = 75/100 So we have a 7 in the tenths column and a 5 in the hundredths column. So ¾ =0.75

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Whatever we do to the bottom we do to the top so the 2 becomes 4. 2/5 = 4/10 This means we have a 4 in the tenths column. So 2/5 = 0.4

Task a * a.

32 50

Convert each of the following to a decimal. b.

1E 14 © Readyd P u b l i c a t i ons 5 20 •f orr evi e w pur poses onl y• e. f. 17 25

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zz If we can’t change the denominator into 10, 100 or 1000, then we can change a fraction to a decimal by using short division.

* a.

Task b

2 9

5 15

Example

3/8 = 3÷8 = 0.375

. t Convert e each of the following to a decimal. co . che e r o t r s super b.

1 6

7 20

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6 10

3 to a decimal. 4

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If we want to change 2/5 to a decimal we first want to see if we can change the denominator to a 10.

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Example 2

5 8

2 7

5 7

2 3

3 40

11 15 29

* Expressing Decimals As Fractions zz To convert a decimal to a fraction we simply need to look at the place value of the last decimal digit.

Example

Convert 0.24 to a fraction. Look at the decimal 0.24; we see that the last digit is in the hundredths column. So 0.24 = 24/100. We now simplify our answer by dividing top and bottom by 4 (the largest common denominator) and we have 6/25.

Teac he r

Convert each of the following decimals into fractions and simplify your answers where possible.

0.1

0.4

Task b * 0.25 d.

1.17 g.

0.345

0.8t © Read1.5yEdPubl i ca i ons •f orr evi ew pur posesonl y•

Convert each of the following decimals into fractions and simplify your answers where possible.

w ww

0.9

0.3

. te

0.32

0.95

m . u

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Task a *

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o c . che e r 0.53 2.48 o t r s super e.

0.852

0.655

* Fractions And Decimal Conversions 1 * Task a

2.05 = 2 100 = 2 20

Example

Express these decimals as simplified fractions.

3.2......................... 4.65...................... 5.25...................... 13.26.................... 7.8...........................

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623.02................. 0.5........................ 4.04...................... 6.008.................... 22.22......................

* Task b

Convert these fractions to decimals.

24 15 1000. ...................... 1000

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

12 57 350 3 23 100 100 1000 1000 1000 ........................ ........................ ....................... . ......................

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

10 ........................

49 100

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

50 30 100 ........................ 100

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7.75...................... 3.025................... 12.6...................... 10.42.................... 17.017...................

23 100

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

7 10

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

70 100

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

700 1000

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

39 10

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

143 100

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

198 100

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

25 10

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

43 10

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

656 100

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

11 10

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

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10 ........................

264 100

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

2795 3423 9098 3456 578 100 1000 100 1000 ........................ ........................ ....................... . ...................... 10

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

w ww

10 ........................

. t Write five equivalent fractions for each decimal below. o Task d e c * . c e her r 6.5 =............................................................................................................................ o t s super 2.25 =......................................................................................................................... 0.75 =......................................................................................................................... 3.6 =............................................................................................................................ 9.75 =.........................................................................................................................

task c: Challenge * Matthew is counting his savings and has calculated that he has 687 ¢. Express this amount as a decimal and also as a fraction.

* Fractions And Decimal Conversions 2 zz Fractions and decimals can Examples be used to express the same amounts. We use fractions for some objects and decimals for others. Consider the examples and circle the way you would describe them.

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Express the decimals below as fractions.

0.2 =

0.5 =

* Task b

Express the fractions below as decimals.

1 = 10

7 = 10

0.6 =

0.23 =

10 = 100

34 = 100

0.98 =

0.47 =

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* Task a

1 or 0.5 a glass of orange juice; 2 3 0.3 of a metre or of a metre; 10 1 of a sandwich or 0.25 of a sandwich; 4 3 0.75 or of a job finished. 4

28 = 100

567 = 1000

zz Fractions need to be expressed with denominations of 10, 100 or 1000 before being expressed as decimals.

* Task c

6 10

1 2

5 10

Express the fractions below as decimals. = ...............

1 5

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

8 20

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

6 20

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

10 50

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

10 = ................ 20

20 50

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

2 5

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

3 4

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

1 4

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

15 20

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

200 = ...............

* Task d 0.5 4 5

m . u

4 10

w ww

25 = ................

. = .............. = . ............ = ............... = ............... = . ............ te o c . c e r Use =, < or h > toe make the following true.o t r s super 300 600

20 2000

150 200

200 200

20 40

4 10

6 10

6.0

8 100

0.08

0.45

90 100

0.9

8 1000

0.08

task c: Challenge * Miles has collected 36 sports cards this year. If there are 200 in the set, what fraction has he collected so far? Express this fraction as a decimal.

* Fractions And Decimal Conversions 3 Task a Convert each decimal to a fraction. Be sure to simplify your answers.

The first one has been done for you.

0.42 =

42 21 = 100 50

0.05

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

1.1

0.82

a. 3 8

0.09

0.015

Convert each fraction to a decimal using short division. The first one has been done for you.

w ww

3 10

. te

f. 1 7

1 9

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Task b

0.004

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0.25

0.6

o c . che e r o t r s r u e p Task c: Investigative Challenge s * g.

1 3

5 8

5 6

Converting recurring decimals to fractions is difficult if you don’t Fraction = First Fraction 1 – Fraction Ratio just know the answer. We can use this formula to help us work it out: For example if we look at 0.111111111 We can see that this is 0.1 +0.01 + 0.001 + … Using the formula we would have:

1 1 10 = 1 10 1– 10

10 1 = 9 9

Use this formula to convert these recurring decimals to fractions: 0.666666666 0.4444444444 0.16161616161616 33

Decimals And Equivalent Fractions * zz So far the fractions we have changed to decimals have all had a denominator which is a multiple of 10, such as 10, 100 and 1000. Sometimes it is necessary to convert fractions that cannot evenly be divided into 100. 36 needs to be divided by 6 so that the denominator is 10. 60

Example

6 36 ÷ 6 = 6 = 0.6 10 60 ÷ 6 = 10

Divide the top number by 6 ... Divide the denominator by 6 ...

* Task a

= 8 = 0.8

24 30

35 70

64 80

42 60

81 90

56 70

14 20

48 80

36 40

63 90

28 70

Teac he r

Simplify the following fractions so that the denominator is 10.

Task b * 4

3 5

3 4

5 25

3 15

2 8

2 5

=e = =b =i 10 R 3y 6a 2 = © ad Ed4Pu l i c t ons •f orr evi ew pur posesonl y•

* Task c

a. 0.7 =

4 20

9 12

13 20

3 50

700

100

1000

100

1000

100

1000

100

1000

100

1000

w ww

. te c. 0.8 = 10

d. 1.0 = e. 1.5 =

3 100

Change these decimals to fractions by filling in the boxes below.

b. 0.2 =

o c . che e r o t r s super

d: Challenge * taskFiona buys her stamps in sets and there are twenty stamps to a set.

She has five complete sets and another set that contains only 12 stamps. Express the number of sets Fiona has as a decimal.

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2 5

Now try converting these fractions to a decimal. Some of them are quite tricky.

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32 40

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* Task a

* Fractions Into Decimals: Word Problems

Answer the following quick questions.

1. What is eight tenths as a decimal?...................................................................................... 2. Write five and nine tenths as a decimal............................................................................. 3. What is seven point four as a fraction?..............................................................................

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4. Write two point two five as a fraction................................................................................ 3 5. Which is greater: 0.60 or ?................................................................................................. 4

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6. If you have $10.00 pocket money and spend a quarter of it, how much would you have left?......................................................................................................................................

7. What is zero point two five as a fraction?.........................................................................

8. True or false: Six and three tenths is less than six and four fifths.............................

2 of a dollar is equal to how many cents?......................................................................... 5 1 of $2.00 is equal to how many cents?.......................................................................... 10. 4

© ReadyEdPubl i cat i ons orr vi ew pur posesonl y• 12. What• is af quarter ofe twenty?................................................................................................. 11. True or false: Zero point four five is the same as forty five over a hundred.........

13. Two thirds of nine is equal to................................................................................................

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3 4

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14. Express two and four fifths as a decimal........................................................................... 15. True or false: 3 is greater than 3.65.................................................................................. b: word Problems * 1. taskAnne . t fifteen bananas from the shop and gave five to her brother. bought

e o c What fraction does she still have?.......................................................................................... . c e r 2. Steve rode 6.75 kmh on e the weekend. o t r s super Express this amount as a fraction........................................................................................... 3. Suzy received $6 pocket money and spent two thirds of it on a book. How much did the book cost?................................................................................................. 4. Rebecca and Michael went fishing and caught 20 fish. Eight of the fish were undersized and so they threw them back. What fraction do they have left?............................................................................................ 35

Percentages 1 * zz Percent means “out of 100”, so if you get  in a test, you would get 75%. 75

* Task a

100

Use the grid and complete the following task. This grid has 100 squares in it.

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Colour in 20 squares green.This is 0.20 or 20 hundredths, or 20 100 or 20%.

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Colour in 2 squares red. This is 0.02, or 2 hundredths, or 2100, or 2%.

Remember that 0.2 is the same as 0.20.

© ReadyEdPubl i cat i ons Task b See if you can fill out this chart to compare fractions, decimals * •f o rr evi ewImagine puthat r peach os eso l yin• and percentages. fraction isn a score a test, e.g. 4/10 means you got 4 correct out of ten questions. Out of 100

310

w ww

Fractions 810

710

6.5

9.5

10

. te

10

100

Decimals

Percentages

0.3

30%

100

m . u

o c . ch e r  e o t r s super  100

65 95 73

0.65

100 100

0.12

0.85

20%

50%

* Percentages 2 zz Percent means “out of 100”, so if you get 75100 in a test, you would get 75%.

Task a *

Use these fractions and decimals to help you fill out the chart underneath.

2 = 510 = 0.5

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4 = 25100 = 0.25

5 = 210 = 0.2

1 1

4 = 50100 = 0.5

4 = 75100 = 0.75

5 = 410 = 0.4

5 = 610 = 0.6

5 = 810 = 0.8

Teac he r

Remember that 0.2 is the same as 0.20.

Out of 100

Decimals

Percentages

310

0.3

30%

810

100 100

710

10

0.65

10

0.95

6.5

100

9.5

100

95%

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Fraction

5

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m . u

zz Sometimes, it is too difficult to convert a fraction to be out of 100.

Use your calculator to divide the numerator by the denominator. Task b. t * e This will give you a decimal with hundredths, which oyou can then

c . che e r o t r s super

convert to a percentage.

e.g. 1840 on the calculator is 18 ÷ 40 = 0.45 or 45%.  Try these.

25 = 0.64 = ______%

70 = ______ = ______%

30 = ______ = ______% 52 = ______ = ______%

Hint: Round the decimal to 2 places.

Percentages 3 * zz So far we know that decimals and fractions can be used to represent the same amount. A percentage is another way of expressing a part of a whole. Per means ‘for every’ and cent means ‘100’ so it is easy to remember that percent means ‘for every 100’. For example, if we had 100 students playing on the school sports field and 56 of them were girls, we could say that 56 percent (56 out of 100) of the students playing are girls.

* Task a

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Complete the following.

1. We use the symbol % to express percentage. Name three everyday places where you might see this symbol.

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

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2. Look at the shaded amounts below. What percentage of each grid has been shaded?

© ReadyEdPubl i cat i ons ................................... .................................... ...................................... ..................................... •f orr evi ew pur posesonl y• 3. Convert these fractions to a percentage. The first one has been done for you. ....................... = 100 = 50%

3 100 .......................

15 170 100 ....................... 1000 . ......................

8 10

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

1 100

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

25 100 .......................

4 10

2 5

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

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

400 1000 . ......................

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55 10 10

4. Express these percentages as decimals and then simple fractions. 75% = 0.75 =

. te 75 3 100 = 4

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a. 60% =....................... b. 80% = . .................... c. 50% = ...................... d. 32% = ..................... e. 24% =....................... f. 40% = ....................... g. 90% = . .................... h. 25% = ..................... 5. Express these percentages as decimals.

35%........................................... 23%........................................... 89%.................................................. 67%........................................... 79%........................................... 100%................................................

task b: Challenge * Melanie scored 98% in a Maths test. If there were fifty questions, how many questions must Melanie have answered correctly?

Percentages 4 * zz In order to convert these fractions to percentages, we need to find an equivalent fraction with a denominator of 10, 100 or 1000.

Task a * 40

200 =

20 100

Look at these examples and then convert each fraction to a percentage.

= 20%

20 200

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

1 4

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

460 2000

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

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

40 800

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

15 20

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

40 60

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

30 40

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

300 400

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

600 800

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

300 3000

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

25 50

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

5 25

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

9 20

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

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

Task b *

a) 25%

b) 55%

Match the percentage on the left with the correct fraction and decimal. There may be more than two answers. 0.25

2.5 5 100 4

0.14

32 10

d) 80% 5

0.08

e) 15%

0.15 5

1.5

0.55 100 5 10

8.0 1

32 100

16 50

0.45

0.8

8 1000

0.015

5.1

15 100

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30 50

c: word Problems *1. task Sophie spent 10% of her pocket money on a new pencil. What percentage of her

. t e o is this? 2. Taylor spent ⁄ of his spare time reading. What percentage of time c . che ............................................................................................................................................................ e r o 3. Marcelle collected snails in r thes garden. 50% of them near the rose st r upShe efound pocket money does she have left?........................................................................................ 4

bushes, 15% of them near the hose and 25% around the clothes line. What percentage were found elsewhere?..........................................................................

4. Katie and Greg have 100 chocolates in a jar. If 37 of them have hard centres and the rest are soft centred, what percentage have soft centres?.................................... 5. Lilly had 10 000 Frequent Flyer points. She received a 10% bonus for reaching the 10 000 mark. How many points does she now have?............................................. 39

* Task a

* Decimal And Percentage Conversions

Convert each decimal to a percentages. The first one has been done for you.

0.03 × 100 = 0.03 = 3% d.

0.45

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2.04

0.105

0.01

0.002

0.067

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1.3

0.78

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2.1%

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0.4%

52%

107% g.

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each percentage to a decimal. The first one has been done for you. * Task b Convert © Read yEdPubl i c at i ons a. b. c. •f r evi ew pur pose4% sonl y• 24% = 24 ÷ 100 =o 24r = 0.24 95%

o c 33.3%. 0.15% che e r o r st super h.

c: Small Group Challenge * Task When we measure our Body Mass Index or BMI we use percentages. In a small group, each of you calculate your BMI using the formula: BMI =weight (kgs) ÷height2 (cms). Also in small groups choose three of your favourite foods that you can buy at the supermarket. Record the energy, sugar, protein and fat content that is found in each of these three products as a percentage.

* Fraction And Percentage Conversions

Task a Convert each of the following percentages to fractions. Be sure to simplify

your answers. The first one has been done for you.

85% =

85 ÷ 5 100 ÷ 5

17 20

20%

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100%

64%

130%

96%

86%

54%

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42%

Convert each fraction to a percentage. The first one has been done for you. * Task b © ReadyEdPubl i cat i ons c. b. a. •f orr evi ew pur poses3onl y• 2 1 × 100 = 2 × 20 = 40% 20

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3 50

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4 5

7 25

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1 3

2 3

c: Personal Challenge * Task To convert fractions whose denominator does not divide evenly into 100 we can use short division. See if you can use short division to convert each of the following fractions to percentages. 3 2 7 3 1 , , , , 8 15 8 14 24

Fractions, Decimals And Percentages 1 * zz 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’.

* Task a

Complete the following.

1. Convert the percentages below to fractions.

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35% = 35⁄100 56% =................... 98% =.................. 87% =................... 50% =..................... 100% =................ 105% =................ 765% =................ 0% =...................... 12% =.....................

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2. Change these decimals to percentages.

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0.23 = 23% 0.56 =................... 0.99 =................... 0.27 =................... 0.5 =........................

0.7 = .................... 0.25 =................... 0.3 =..................... 0.55 =................... 0.2 =........................ 3. Change these fractions to percentages. ⁄100 = 20%.......... 67⁄100 =................... 52⁄100 =...................

⁄100 =.................. 1⁄100 =.......................

254

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. 4

⁄20 = 5⁄100 = 5%

⁄50 =............................... 16⁄50 =..............................

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⁄5 = 20⁄100 = 20%

1000

10 1

500

⁄20 =............................... 1⁄25 =............................... 9⁄20 =................................

⁄50 = 20⁄100 = 20%

⁄50 =...............................

⁄5 =................................. 4⁄5 =................................. 5⁄5 =..................................

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⁄10 = 10⁄100

o c . che e r o t r s s r u e p )

zz Another way to convert a fraction to a percentage is to multiply the fraction by 100.

Example

⁄4 x 100 =

* Task b

300

⁄2 x 100 =

4 300

75 = 75%

100 2

50 = 50%

Change these fractions into percentages.

⁄4 =................................. 2⁄5 =................................. 3⁄20 =............................... 7⁄10 =...............................

⁄20 =............................... 3⁄50 =............................... 26⁄50 =..............................

⁄200 =...........................

154

* Task a

* Fractions, Decimals And Percentages 2 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 % =

0.04

b. 12% = c. 45% =

e. 25% =

⁄100

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0.12

⁄100

0.45

⁄100

720

72.0

⁄1000

0.25

0.4

1.2

4.5

0.72

⁄4

⁄200

⁄10

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d. 72% =

⁄100

zz Another way to calculate percentages is to multiply the fraction by 100. Cancel the fractions to simplify the problem. Example 1

Look at the fraction 15 20

Look at the fraction 12

Example 2

1 4

Use this method to calculate the following percentages.

12 out of 24 =........................................................

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

9 out of 27 =........................................................

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* Task b

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

50 out of 500 =................................................... . te o c task c: word Problems . *1. Emily received 35c e r outh ofe 50 in a test. What percentage did she score? o t r s s uper 2. On Saturday Denis climbed 40 metres up a rock face. The next day he climbed 16 out of 25 =........................................................

10% further. How far did he climb up the rock face on Sunday?

3. Lesley played in a tennis tournament and won 80% of her games. Overall she played 20 games. How many games did she win? 4. Noel read 18 chapters of a book. The book contained 24 chapters altogether. What percentage has he read? 43

* Task a

* Fractions, Decimals And Percentages 3 Complete the table below. The first one has been done for you.

Fraction

14 1

5 2 10

Decimal

Percentage

0.25

25%

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0.42

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36%

4 5

64%

3 20

0.95

4 200

175 1000

4.5

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20.5%

. t e= or ≠ in the boxes below. o Task b Use c * . che e r o t r 75% 34% 25% s 0.25 50% 0.75 sup er 3 4

0.8

80%

4 5

1 4

0.8

5 25

2 4

25%

7 25

0.28

17 20

5.0 0.59

task c: Challenge * Joey scored 65% on the Science test, Shelley got 0.75 of the questions correct and Matt answered 4⁄5 of the test correctly. Which student received the highest mark for the test?

* What Is My Test Score As A Percentage? How many times have you annoyed your teacher by asking them what your test score is as a percentage? Converting your test score to a percentage is exactly like converting a fraction to a percentage. We take our mark, divide it by the total number of marks in the test and then multiply by 100. For example, if I scored 45 marks out of 50 this is what I would do to change it to a percentage. 2 45 × 100 = 45 × 2 = 90% 50 1

* Task a

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Change each test score to a percentage. Check your answers with a calculator.

b. 8 out of 10

* Task b

c. 18 out of 20

e. 8 out of 15

d. 37 out of 40

f. 49 out of 60

Convert each of these quantities to a percentage.

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a. a. 15 out of 25

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b. There is 220 grams of sugar left in a 1 kilogram bag. What percentage of sugar is left?

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a. a. Three people in a class of 25 have red hair.

Sugar

o c . che e r o t r s sup er d. During a T.V. program that runs for an hour, there are 12 minutes of c. In a school of 1500 students, the 250 Year 11 students are going on camp. What percentage of students will remain at school?

commercials. What percentage of the program is television commercials?

c: Personal Challenge * Task Begin to record your test results for every subject this year as a percentage score. Also record the average mark for each test. Over time you will be able to see if your marks are improving.

* Percentage Of An Amount

zz We know that 10% means 10 for every 100, 20% means 20 for every 100 and so on. We also know that 10% of 200 is 20, 10% of 1000 is 100, 10% of 750 is 75 and so on.

* Task a

Complete the following.

1. Find 10% of the following amounts.

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$30................. $60.................. $130................ $290 .............. $400 .............. $2000 ...............

2. Find 50% of the following amounts.

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$25.................. $48.................. $120 . ............. $293 .............. $498 .............. $450 . ................

20..................... 30.................... 100.................. 150.................. 200.................. 1000...................

1200................ 64.................... 65..................... 250.................. 16.................... 17........................

44..................... 28.................... 350.................. 12.6................. 25.8................. 243.2..................

© ReadyEdPubl i cat i ons $3.00..................... $2.30.................... $1.20.................... $4.80..................... $9.60........................ •f orr evi ew pur posesonl y• 3. Find 20% of the following amounts.

$0.50..................... $25.50.................. $16.30.................. $29.80.................. $320.00...................

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4. Subtract 20% from each amount below. $9.60..................... $10.80.................. $4.00.................... $2.00..................... $150.........................

. te task b: word Problems *

$1000................... $3.50.................... $6.00.................... $7.20..................... $9.50........................

o c . e 1. Rick received a 10%c discount on his new basketball. Originally, the basketball h r e o cost $50.00. How much did Rick pay for the ball?s r s upert 2. In Ali’s class, 5 of the students are away sick. If there are normally 20 students in the class, what percentage of the students is absent? 3. Donelle sold 30 ice creams at the football. The following week she sold 10% more. What amount did she sell? 4. Tanya correctly answered 180 questions out of 200 in an exam. What percentage did she answer correctly?

* What’s The Discount? One of the most familiar areas where we use percentages every day is when we go shopping at the sales. You’ll see lots of signs telling you the percentage discounts available. For example, if you want to buy a pair of jeans that are on sale at 20% off the normal retail price of $180, we can work out the sale price like this: 20 × 180 = $36 100

Sale Price = 180 - 36 = $144

Task a r o e t s * Bo r e Calculate the discount available on the sale items below.

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a. 10% off $3000

b. 35% off $250

Calculate the sale price for the items below. c. 15% off $850

d. 8% off $400

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a. 5% of 200 grams

b. 10% of 54 km

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d. 12% of 3L

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c. 25% of 800 m

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o c . c e r f. 27% of 10 hours e. 84% of 5000 cm h er o t s super 2

* Task c: Partner Challenge

Create a mental maths quiz for your partner. The quiz should be fifteen questions long and should have a mix of questions using fractions, decimals and percentages. Make sure you work out the answer, without a calculator, before giving your quiz to your partner. If it’s too hard for you then it will be too hard for them!

quiz 47

* Mixed Word Problems 1

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? . .............................................................................................................................................. 2. 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?...................................................................................................................................................

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3. Noel scored the following number of runs in a cricket test series: 121, 29, 98, 57,

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

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

did she run on Saturday than Friday?............................................................................................

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

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

6. On the coldest day in winter 20% of the class were absent. What fraction of the

7. Three brands of chocolate have different amounts of sugar. Brand 1 contains 56%

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

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Which of the 3 brands contains the most sugar?...................................................................... 8. Eight school students paid $67 each to attend the school camp. What was the total

. t eto his four children. If it is divided evenly amongc o 9. A man left $9853 them how much . che e will each person receive?................................................................................................................... r o t r s s r u e p 10. A washing machine was priced at $315. It was then reduced by 20%. What is the amount paid by the students?.........................................................................................................

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?. ............................................................................ 48

* Mixed Word Problems 2

1. A bike is marked at $200.00. The retailer decides to mark the bike down by 10%. What will be the new cost of the bike?......................................................................................... 2. Each year Josh’s dad pays 10% of his salary into a superannuation fund. If he makes $35 000 a year, how much money will go into the fund each year?.................................. 3. Julia made a chocolate cake, and flour made up 65% of the mixture. What

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percentage of the cake is not flour?............................................................................................... 4. Sam is buying books on sale at the local newsagent. Each book is discounted by

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20% of what the marked price states. If he wants to buy a book marked at $20.00,

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what will he actually pay after the discount?.............................................................................

5. Jarrad took thirty seconds to brush his teeth. What fraction of a minute is this?

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

6. Helen took 45 minutes to walk to the beach. What percentage of an hour is this?

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

7. Claudia rode 2 km in an hour. This was 25% of the total amount she rode all day.

8. Billy had a bag of fruit. 50% of the fruit were bananas, 25% were apples, 10% were strawberries and the rest were peaches. What fraction of the bag did the peaches

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take up?.................................................................................................................................................... 9. Jeff spent 3⁄5 of his savings on some CDs. If each CD cost $20, and Jeff bought 3, how much money did Jeff start off with?.....................................................................................

. t ehave failed?............................................................................................................... o students must c . c e 11. Karen ran 2.46 km onh Wednesday. Express this distance r as a fraction............................ er o t s supone r 12. The bank is offering interest rates of 5% savings accounts. How many cents for 10. In the final exam, 30% of the students failed. If 140 students passed how many

each dollar will the bank pay?.......................................................................................................... 13. At the local mine 85% of the miners were under 30 years of age. What fraction of the miners were over thirty? Express this amount as a decimal.......................................... 14. Justin, Thomas and James had six ice creams to share. What is the ratio of boys to ice creams?.............................................................................................................................................. 49

* Mixed Word Problems 3 1. In Mario’s class one quarter of the students wear glasses. If there are 24 students in the class how many wear glasses?................................................................................................ 2. Leanna walked 3.56 km and Stephanie walked three and a half km. Who walked the furthest distance?........................................................................................................................

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3. The ratio of beachgoers to umbrellas was six to one. What fraction of beachgoers had an umbrella?................................................................................................................................. 4. The ratio of football spectators to raincoats was 20:1. Express this amount as a

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percentage.............................................................................................................................................

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5. Katrina took 40 minutes to complete her homework. What fraction of an hour is

this?..........................................................................................................................................................

6. Alex spent two hours a day practising the piano. What fraction of the day is this?

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

7. Lara spent two hours on homework each night. If 1⁄4 is spent on Maths and 50% is

© ReadyEdPubl i cat i ons a. How many minutes are spent on Maths?.............................................................................. •f orr evi ew pur posesonl y• b. How many minutes are spent on History?............................................................................ spent on History what is the decimal amount left for other subjects?............................

8. The football team won 80% of its matches during the last season. If twenty

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matches were played, what was the total number of games won?.................................. 9. The rowing team has won 0.65 of its total races. What fraction of races did it lose?

. te o played fifty games, how many has Bill won?............................................................................. c . c e h r 11. Sam and Tess are playing cards. They have played eighteen games and Tess has er o t s s up er won two thirds of the games. How many games has Sam won?.......................................

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

10. Bill and Ted are playing chess. Bill has beaten Ted 60% of the time. If they have

12. Maria invited 35 guests to her birthday party, however only 5⁄7 of the guests are able to come. How many of the guests will be able to attend?.......................................... 13. Marguerite spent $11.00 on a new hat. She now has 4⁄5 of her savings left. a. What percentage of her savings was spent on the hat?................................................... b. How much money did Marguerite start off with?.............................................................. 50

* Answers

Decimal Value 1 Page 7 Task A: 99.4 9 tens 9 ones 4 tenths 12.3 1 ten 2 ones 3 tenths 42.75 4 tens 2 ones 7 tenths 5 hundredths 45.98 4 tens 5 ones 9 tenths 8 hundredths 364.68 3 hundreds 6 tens 4 ones 6 tenths 8 hundredths Task b: a. 121.212, b. 40.359, c. 201.003, d. 146.524, e. 3.4, f. 20.377, g. 420.004 Task c: challenge - 601.01

Rounding Decimals 1 Page 11 Task A: 3, 9, 6, 2, 8, 3, 5, 10, 6, 2; 3; 4, 2, 6, 6, 8,10; Task b: 26, 89 or 90, 24, 28, 39, 12; 36, 19, 88, 84, 63, 29, 25, 55, 72; 13, 25, 2, 26, 4, 6, 53, 7, 2; Task c: 22, 20, 16;

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Decimal Value 2 Page 8 Task A: (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). Task b: 5/100; 4/10, 2/1000, 1/10. Task c: Three hundred and one point two zero three; One thousand, three hundred and forty five point two; One point two nine eight. Task d: 1.23, 1.234, 1.9, 2.013, 2.13, 21.13, 210.103, 1234.12; 2.345, 2.543, 23.45, 234.055, 234.05, 234.5, 2345, 2543.1. Task e: <,>, >, <, <, <, >, >, <, <, <, <.

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Greater Than Less Than Page 10 <,>; >,<,>,>; >,>,<,<; >,>,>,=

Rounding Decimals 2 Page 12 Task a: 1 - 4.8, 2.3, 7.2, 3.6, 6.9, 4.6, 4.6, 9.5, 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. Task b: 1 - <, >, >, <, <, <, >, >, <, <, <. 2 - 2 + 3 + 6 + 4 =15; 3 + 6 + 9 + 3 = 21; 8 +1 + 2 + 1 =12. 3 - $3.40, $4.60, $7.90, $5.40, $1.00, $7.80. Task c: $5.57, $6.54, $2.25, $7.89, $2.78, $3.66, $5.78, $3.54, $9.86, $9.00, $7.60, $5.64.

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Decimal Value 3 Page 9 Task a: 7 x 10, 8 x 1⁄100, 1 x 1, 3 x 10, 0 x 1⁄10, 4 x 1⁄100, 4 x 10, 3 x 1⁄1000, 4 x 1⁄100, 9 x 1⁄10; Task b: a. (1 x 100) + (3 x 10) + (6 x 1) + (5 x 1⁄10) + (7 x 1⁄100); b. (2 x 10) + (6 x 1) + (9 x 1⁄10) + (8 x 1⁄100) + (7 x 1⁄1000); c. (3 x 10) + (5 x 1) + (5 x 1⁄10) + (7 x 1⁄100); d. (4 x 10) + (9 x 1) + (0 x 1⁄10) + (8 x 1⁄100); e. (7 x 100) + (6 x 10) + (5 x 1) + (2 x 1⁄10) + (9 x 1⁄100) + (7 x 1⁄1000); Task c: >, <, >, >, <, >, <, <, >, >, >, <. Task d: challenge 7⁄10 of a litre.

Decimal Addition 1 Page 13 Task a: 7.57, 7.57, 7.88; 7.65, 8.88, 7.87; Task b: 7.40, 7.71, 8.85; 7.61, 5.87, 8.92; Task c: $6.31, $9.34, $7.35

o c . che e r o t r s super

Decimal Addition 2 Page 14 Task a: 5.52, 9.74, 4.99; 9.27, 10.75, 7.79; Task b: 11.83, 36.32 Decimal Subtraction 1 Page 15 Task a: 5.31, 3.05, 8.17; 4.31, 6.26, 1.64; 51

Task b: 6.28, 3.48, 5.37; 5.25, 3.15, 4.08; Task c: $5.66, $3.75, $3.77 Decimal Subtraction 2 Page 16 Task a: 2.18, 5.47, 8.32; 2.57, 4.45, 2.51; Challenge: 3.45, 2.41

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Adding And Subtracting Decimals 2 Page 18 Task a: 26.973, 557.06, 7493.5, 46.026; Task b: 236.3, 58.1, 8.65, 92.28, 8.2, 3.53; 39.25, 193.62, 122.39, 325.24, 424.33, 401.55; 6.19 m, 23.25 kg, 46.75 mL, 70.39 km, 77.72 cm, $4.03; Task c: 22.102, 1.034, 13.334, 0.676; Task d: challenge - 78.48 km.

Multiplying Decimals 2 Page 22 Task a: 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 - 132/140.932, 456/426.36, 392/349.86, 747/744.51, 360/390.96.

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Adding And Subtracting Decimals 1 Page 17 Task a: 36.3, 88.7, 86.8, 76.6, 97.3, 109.9; 99.2, 139.0, 130.1, 117.3, 111.2; Task b: 23.4, 3.3, 20.1, 22.6, 16.1, 10.7; 15.9, 29.9, 18.8, 36.9, 3.5; Task c: 50, 115.30, 70.43, 107.03, 122.32, 90.01; 10.89, 22.22, 41.9, 72.97.

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Multiplying Decimals 1 Page 21 Task a: Set 1 $1416, $5502, $2880, $5672, $5418; Set 2 $40.00, $42.00, $48.00, $8.00, $63.00; Set 3 $22.40, $23.40, $19.60, $45.00, $32.00; Set 4 $50.34, $9.56, $56.35, $24.08, $31.60; Set 5 106.2 cm, 127 kg, 187.6 mL, 107.1, 38.4 mm. Task b: Word Problems - 36.75 km, $31.60, $99.50, 101.60 kg, 5040 m, $4590, $124.75.

Dividing Decimals Page 23 Task a: 0.9, 0.8, 0.6, 0.8, 0.9, 0.9, 3.2, 1.5, 1.8, 4.9, 0.8, 2.3; Task b: Set 1 6/6.1, 8/8.1, 7/7.1; Set 2 8/8.3, 9/9.2, 9/8.9, 16/15.8; Set 3 6/6.2, 5/4.9, 6/5.8, 15/15.6; Set 4 12/12.4, 2/2.1, 7/7.1, 9/9.1; Set 5 3/3.2, 11/11.1, 4/4.1, 9/9.4; Task c: Set 1 5/5.62, 50/45.8, 30/42.6, 3/3.46, 60/56.8, 80/76.8; Set 2 80/78.80, 100/96.2, 25/26.2, 10/9.58, 7/7.7.

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Adding And Subtracting Decimals 3 Page 19 Task a: 51.477, 408.04, 462.011, 414.253, 463.458, 305.49. Task b: 4546.4, 12.243, 33.147, 94.06, 538.1, 80.58. Task c: task c: challenge - 8.25 kg.

Recurring Decimals Page 24 Task a: 2.66, 0.33, 0.166, 0.33, 0.68, 0.55, 0.44, 2.33. Task b: 11.86, 1.33, 0.56, 1.32, 0.83, 8.43, 0.92.

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Adding And Subtracting Decimals 4 Page 20 Task a: 12.238, 5.918, 43.244, 355.45, 44.90, 0.18, 1.994, 2.054, 210.966, 2.86, 321.96, 3.723. Task b: 1.416, 252.313, 48.936, 226.673, 27.988, 379.974. Task c: Word Problems: 1. 14.3 L, 2. 10.25 g, 3. 3.45 m. All answers are given in row order: left to right. 52

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Shading Decimal Quantities 1 Page 26 Task a: Check diagrams; Task b: 0.07, 0.3, 0.5, 0.95; Task c: 5 ⁄10 = 0.5, 6⁄10 = 0.6, 3⁄10 = 0.3. Task d: challenge -1.2. Shading Decimal Quantities 2 Page 27 Task a: Check diagrams.

b. 9⁄20; c. 1⁄100; d. 43⁄50; e. 24⁄25; f. 1⁄20; g. 17⁄25; h. 4⁄5; Task b: =, ≠, =, ≠, ≠, =, ≠, ≠; Task c: =, >, =, <. Task d: challenge - 1⁄4.

Fraction And Decimal Conversions 3 Page 33 Task a 1 1 9 e. 1 b. h. 20 10 100 3 1 3 c. f. i. 5 250 200 1 41 d. g. 4 50 Task b f. 0.1 b. 0.25 g. 0.3 c. 0.8 h. 0.625 d. 0.3 e. 0.142857 i. 0.83

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Expressing Fractions As Decimals Page 29 Task A: 0.6, 0.2, 0.7, 0.64, 0.68, 0.35 Task b: 0.167, 0.625, 0.67, 0.2222, 0.285714, 0.075, 0.33333, 0.714285, 0.7333 Expressing Decimals As Fractions Page 30 Task A: 1/10, 3/10, 9/10, 2/5, 3/2, 4/5 Task b: ¼, 19/20, 8/25, 1 17/100, 2 12/25, 53/100, 69/200, 213/250, 131/200

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Shading Decimal And Fraction Quantities 3 Page 28 Task a: Check diagrams; a. 73; b. 75; Task b: <, >, <, >, =, =; Task c: >, <, >, =, <, =, >, <. Task d: challenge - 25⁄6.

Task d: >, <, =, <, =, <. Task e: challenge - 0.18

Decimals And Equivalent Fractions Page 34 Task a: 0.5, 0.8, 0.7, 0.9, 0.8, 0.8, 0.7, 0.6, 0.9, 0.7, 0.4; Task b: 0.4, 3.75, 0.2, 0.2, 4.25, 9.4, 4.6, 10.2, 3.75, 4.65, 6.06, 2.03. Task c: b. 2, 20, 200, 1, 4; c. 8, 80, 800, 4, 32; d. 10, 100, 1000, 5, 9; e. 15, 150, 1500, 3, 9. Task d: challenge - 5.6.

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Fraction And Decimal Conversions 1 Page 31 Task a: 31⁄5, 413⁄20, 51⁄4, 1313⁄50, 74⁄5, 6231⁄50, 1⁄2, 41⁄25, 61⁄125, 2211⁄50, 73⁄4, 31⁄40, 123⁄5, 1021⁄50, 1717⁄1000; Task b: 0.3, 0.5, 0.3, 0.024, 0.015, 0.12, 0.57, 0.35, 0.35, 0.003, 0.023, 0.49, 0.23, 0.7, 0.7, 0.7; Task c: 1.6, 3.9, 1.43, 1.98, 1.1, 3.2, 2.5, 4.3, 6.56, 2.64, 27.95, 3.423, 90.98, 3.456, 57.8; Task d: Answers will vary. Task e: challenge - 6.87, 687⁄100.

Fractions Into Decimals: Word Problems Page 35 Task a: 1. 0.8; 2. 5.9; 3. 72⁄5; 4. 21⁄4; 5. 3⁄4; 6. $7.50; 7. 1⁄4; 8. True; 9. 40 c; 10. 50 c; 11. True; 12. 5; 13. 6; 14. 2.8; 15. True. Task b: Word Problems - 1. 2⁄3; 2. 63⁄4; 3. $4.00; 4. 3 ⁄5.

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Fraction And Decimal Conversions 2 Page 32 Task a: 2 ⁄10, 5⁄10, 6⁄10, 23⁄100, 98⁄100, 47⁄100; Task b: 0.1, 0.7, 0.1, 0.34, 0.28, 0.567; Task c: 0.4, 0.4, 0.2, 0.4, 0.3, 0.2, 0.5, 0.4, 0.4, 0.75, 0.25, 0.75, 0.2, 0.5, 0.01, 0.75, 1, 0.5;

Percentages 1 Page 36

Fractions

Out of 100

Decimals

Percent

10 10 6.5 10 9.5 10 7.3 10 1.2 10 8.5 10 2 10 5 10

0.80 0.70 0.65 0.95 0.73 0.12 0.85 0.20 0.50

80% 70% 65% 95% 73% 12% 85% 20% 50%

100 100 65 100 95 100 73 100 12 100 85 100 20 100 5 100

Percentages 2 Page 37 Fractions

Out of 100

Decimals

Percent

10 10 6.5 10 9.5 10 3 4 2 5 = 410 4 5 = 810 5 5 = 1010

0.80 0.70 0.65 0.95 0.75 0.40 0.80 1.00

80% 70% 65% 95% 75% 40% 80% 100%

100 100 65 100 95 100 75 100 40 100 80 100 100 100

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64%, 0.6 = 60%, 0.9 = 90%, 0.92 = 92%

Fraction, Decimals And Percentages 1 Page 42 Task a: 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%. Task b: 25%, 40%, 15%, 70%, 25%, 6%, 52%, 77%.

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Percentages 3 Page 38 Task a 1. Shop windows, Bank advertisements, newspaper advertisements, statistics; 2. 25%, 30%, 50%, 97%; 3. 50%, 3%, 15%, 17%, 80%, 1%, 25%, 40%, 40%, 40%; 4a. 0.6 = 3⁄5; b. 0.8 = 4⁄5; c. 0.5 = 1⁄2; d. 0.32 = 8⁄25; e. 0.24 = 6⁄25; f. 0.4 = 2⁄5; g. 0.9 = 9⁄10; h. 0.25 = 1⁄4; 5. 0.35, 0.23, 0.89, 0.67, 0.79, 1. Task b: challenge - 49

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Fraction And Percentage Conversions Page 41 Task a 1 16 43 b. e. h. 5 25 50 24 27 c. 1 f. i. 25 50 21 3 d. g. 1 50 10 Task b f. 28% b. 50% g. 6% c. 30% h. 33.3% d. 75% i. 66.6% e. 80%

Decimals And Percentages © ReadyEdFraction, Pub l i ca t i ons2 Page 43 Task a: a. 0.04, 4/100; b. 12/100, 0.12; c. 45/100, 0.45; d. •f orr evi ew pu r poe.s es nl y• 0.72, 72/100; 1/4, 0.25.o

Decimals And Percentages Conversions Page 40 Task a f. 1% b. 45% g. 10.5% c. 78% h. 0.2% d. 130% i. 6.7% e. 204%

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Task b b. 0.95 c. 0.04 d. 1.07 e. 0.52

f. g. h. i.

0.004 0.021 0.0015 0.333

Task b: 50%, 33 1⁄3%, 25%, 62 1⁄2%, 64%, 10%; Task c: Word Problems - a. 70%, b. 44 m, c. 16 games, d. 75%

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Percentages 4 Page 39 Task a: 10%, 25%, 23%, 60%, 10%, 5%, 75%, 66.6%, 75%, 75%, 75%, 10%, 50%, 20%, 45%; Task b: 0.55, 55⁄100, c. 0.32, 32⁄100, 16⁄50, 4⁄5, 0.8; e. 0.15, 15⁄100. Task c: Word Problems - 90%, 80%, 10%, 63%, 11 000.

Fraction, Decimals And Percentages 3 Page 44 Task a: Fraction Decimal Percentage 1 ⁄4 0.25 25% 1 ⁄5 0.2 20% 2 ⁄ 0.2 20% 10 36 ⁄100 0.36 36% 42 ⁄ 0.42 42% 100 4 ⁄5 0.8 80% 16 ⁄25 0.64 64% 3 ⁄ 0.15 15% 20 95 ⁄100 0.95 95% 28 ⁄ 0.28 28% 100 73 ⁄100 0.73 73% 4 ⁄200 0.02 2% 175 ⁄ 0.175 17.5% 1000 450 ⁄100 4.5 450% 205 ⁄ 0.205 20.5% 1000

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Task b: =, ≠, =, ≠, ≠, =, =, ≠, =, ≠. Task c: challenge - Matt. What Is My Test Score As A Percentage? Page 45 Task a a. 60% c. 90% e. 53.3% b. 80% d. 92.5% f. 81.6% Task b a.12% b.22% c.83.3% d.20%

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What’s The Discount? Page 47 Task a: a.$300 b.$87.50 c.$722.50 d.$368 Task b: a.10g b.5.4 km c.200 m d.0.36L e.4200cm2 f.2.7 hours

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Percentage Of An Amount Page 46 Task a: 1. $3, $6, $13, $29, $40, $200, $2.50, $4.80, $12.00, $29.30, $49.80, $45; 2. 10, 15, 50, 75, 100, 500, 600, 32, 32.5, 125, 8, 8.5, 22, 14, 175, 6.3, 12.9, 121.6; 3. 60%, 46 c, 24 c, 96 c, $1.92, 10 c, $5.10, $3.26, $5.96, $64; 4. $7.68, $8.64, $3.20, $1.60, $120, $800, $2.80, $4.80, $5.76, $7.60. Task B: Word Problems - $45.00, 25%, 33, 90%.

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Mixed Word Problems 1 Page 48 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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Mixed Word Problems 2 Page 49 1. $180.00; 2. $3 500; 3. 35%; 4. $16; 5. 1⁄2; 6. 75%; 7. 8 km; 8. 3⁄20; 9. $100; 10. 60; 11. 233⁄50; 12. 5; 13. 3⁄20, 0.15; 14. 1:2.

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Mixed Word Problems 3 Page 50 1. 6; 2. Leanna; 3. 1⁄6; 4. 5%; 5. 2⁄3; 6. 1⁄12; 7. 0.25; a. 30; b. 60; 8. 16; 9. 7⁄20; 10. 30; 11. 6; 12. 25; 13a. 20%, b. $55.00.