A&A
Maths English through Maths
5 HM Hison Josi Adu-mfum
PREISSMURPHY A&A
Education Group
PO Box 1529, Corvallis, OR, USA 97339 info@preissmurphy.com Text © HM Hison Josi adu-mfum PREISS MURPHY and PREISS MURPHY SCHOOL PUBLISHERS are trademarks of Preiss Murphy A&A Education Group. Database rights Preiss Murphy A&A Education Group (maker). First published 2019 2019 2020 2021 2022 2023 ISBN 978-9-95737-644-4
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Contents
5A Reading Numbers Everywhere!
Numbers Roman Numerals Powers of 10 Rounding Rounding and Estimating Adding Integers Prime Numbers Mean Degrees Celsius
5 6 7 8 9 10 11 12 13
5B Math Families Addition Subtraction Addition and Subtraction One-Digit Multiplication With Regrouping Two-Digit Multiplication With Regrouping Word Problems Three-Digit Multiplication With Regrouping Factor Trees Least Common Multiple Division Multiplication and Division Checking Division
14 15 16 17 19 20 21 22 23 24 25 26
5C Geometry: Figures, Objects and Angles Polygons Three-Dimensional Objects Geometric Patterns Similar, Congruent and Symmetrical Figures Volume Perimeter, Area and Volume Lines and Rays Triangle Angles Graphs Pie Graph Locating Points on a Grid Chances and Probability Review
28 29 30 31 32 33 34 35 36 37 38 39 40
Contents 5D Fractions and Decimal Facts Adding and Subtracting Fractions With Same Denominators Adding and Subtracting Fractions With Different Denominators Improper Fractions Mixed Numbers Caveman Pathway Subtracting Mixed Numbers Multiplying Fractions Multiplying Mixed Numbers Dividing Fractions Place Values and Decimals Decimal Puzzle Adding and Subtracting Decimals Multiplying Decimals Dividing With Decimals More Decimal Problems Changing Fractions to Decimals What Percent Is It? Percents Finding Percents 5E Lengths and Weights Length: Inches, Feet, Yards and Miles Lengths and Measurements Length: Centimetres, Metres and Kilometres Lengths and Measurements Weight: Metric Weights and Measurements Capacity: Metric
5A 5A Numbers
Read the words. Then write the numbers. 45 46 47 48 49 50 51 52 53 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71
5F Money Problems
Money Problems Max’s Sale Multiplying Money Ratios Review
Reading Numbers Everywhere!
72 73 74 75 76
Place value is where a digit is in a number. In the number 5,137, '5' is in the thousands place (or has the place value of thousands), '1 ' is in the hundreds place, '3' is in the tens place and '7' is in the ones place.
Example:
Read: Two billion, four hundred and sixty-three million Write: 2, 463 ,000,000
Billions h, t, o 2,
Millions h, t, o 4 6 3,
Thousands h, t, o 0 0 0,
Ones h, t, o 0 0 0
six billion, one hundred seventy-two million, three thousand, five hundred and eighty-one eight hundred sixty-five million, three thousand and twenty-eight five billion, four hundred million, nine hundred thousand, two hundred and thirteen three hundred forty-one billion, three million, six thousand and four hundred seven hundred ninety-five million, sixteen thousand, two hundred and thirty-seven eight hundred forty-six billion, nine hundred twenty-four million, twenty-eight thousand and twenty-two
55
5A Roman Numerals
5A Powers of 10
Read the rules of writing Roman numerals. Match each Roman numeral in Column A with its number in Column B. Fill in the letter in the blank. Roman Numerals
Value
Rules for Roman Numerals
I V X L C D M
1 5 10 50 100 500 1,000
• When a group of letters goes from a greater to a lesser value, then you add the numbers. • When a group of letters goes from a lesser to a greater value, then you subtract the numbers. • Don't repeat a number more than 3 times.
Match the number to the correct equation.
Example: A power of 10 equals the number 10 multiplied by itself a given number of times. 1 ,000,000 = 10 x 10 x 10 x 10 x 10 x 1 0 There are 6 zeros in 1 ,000,000, so 1 0 is multiplied by itself 6 times.
VIII 5+ 1 + 2 = 8 CCXXV 1 0 0 + 1 0 0 + 1 0 + 1 0 +5 =22 5 CD 500 - 100 = 400 XIX 1 0 + (1 0 - 1) = 1 0 + 9 = 1 9 MMCCXL 1,0 0 0 + 1,0 0 0 + 1 0 0 + 1 0 0 + (5 0 - 1 0) = 2, 2 40 Column A 1. 2. 3. 4. 5. 6. 7. 8. 9. 1 0. 1 1. 1 2.
66
VI CIV XXIX CMXCIX LXVII DCXLI XXLV MCCMLXII CCLXXV CDXLIV DCCLXXIII CCDXXCI
Column B a. 1 04 b. 1 ,8 6 2 c. 35 d. 6 4 1 e. 444 f. 773 g. 29 h. 3 8 1 i . 999 j. 6 k. 67 l. 2 75
1 0 x 10 x 10
1 ,0 0 0 ,0 00
1 0 x 10 x 10
1 0 0,000
l0 x l0 x 10
1,000
l0 x l0 x l0 x l0 x l 0 x 10 x l0 x 10
1 0, 000,000
1 0 x 10
1 00
l0 x l0 x l0 x l0 x 10
1 00,000,000
l0x l0x l0x l0x l0x 10x l 0
77
5A Rounding
5A Rounding and Estimating
Round each number to the given place.
Circle the correct answer.
Follow these steps to round numbers to a given place. Round 8 5,3 45 to the nearest thousand.
Example:
8 5 ,000
8 4 ,0 0 0
86 ,0 00
8 7 ,00 0
85 , 345
Find the digit in the thousands place: 8 5,3 47.
a. Find the digit that is to be rounded.
b. Look at the number to the right of that digit. If the number is 5 or more, then the digit should increase by 1 . If the number is 4 or less, then the digit remains the same.
Three is less than 5, so the digit to be rounded, should remain the same.
c. Write the new rounded number with the digit that is rounded up or down, and then change all the remaining digits on the right to zeros.
The rounded number is 85,0 0 0.
Round 667 to the nearest 1 0. 65 0
6 70
660 667
6 80
Round to the nearest ten: 60 66 52 70
50 60
35
30 40
70 90
80 90
26
20 30
600 7 00
426
400 50 0
300 400
55 8
50 0 60 0
85
82
Round to the nearest hundred: 2 00 2 43 691 300 792
700 800
333
Round to the nearest thousand: 2,386
Find the digit in the tens place: 6 6 7
Example:
You can estimate answers by rounding numbers first, and then adding or subtracting. Estimating is an easier way to find out an approximate amount.
2,000 3,000
34 ,560
34 ,000 35,000
5 2,3 9 5
5 2,00 0 5 3,0 00
Charlie wants to buy a new TV. He has about €1 ,700. Circle the TV he can afford to buy.
Seven is 5 or more, so round up and increase the tens digit by 1 . The rounded number is 6 70.
nearest 10:
965
42 4
nearest 100:
5,8 1 9 28,4 9 1 2 1,39 5 5 2 1,95 8
3,2 6 3 7,7 2 4 6 46,2 3 0 6 7 3 ,0 8 4
nearest 1 ,0 00: nearest 10,000:
88
nearest 100,00 0:
€1 ,759
€1 ,82 9
€1 , 5 39
Charlie wants a set of speakers for €2 08 and a new remote for €28. About how much more money does he need? ______________________
99
5A Adding Integers
5A Prime Numbers
Add. Use the number lines to help add.
Write the first 20 prime numbers.
Example:
Example:
is a positive whole
2 is a prime number. 2 รท 1 = 2 and 2 รท 2 = 1 .
Number lines make adding integers easier. When you add positive integers, move to the right. When you add negative integers, move to the left.
number that can only be divided evenly by 1 and itself.
Any divisor besides 1 and itself, will result in a fraction or mixed number,
3 + (- 5 ) = (- 2 ) Find 3 on the number line. Move 5 spaces to the left.
(- 2 ) + 4 = 2
A prime number
-5 - 4 - 3 - 2 - 1
0
1
2
3
4
5
-5 - 4 - 3 - 2 - 1
0
1
2
3
4
5
-5 - 4 - 3 - 2 - 1
0
1
2
3
4
5
3 can be divided only by 1 and 3. It is a prime number.
Prime Numbers:
(- 3 ) + (- 1 ) = (- 4 )
10 10
2 + (-3 ) =
-5 - 4 - 3 - 2 - 1 0 1 2 3 4 5
(-2 ) + (-1 ) =
-5 - 4 - 3 - 2 - 1 0 1 2 3 4 5
(-3 ) + 4 =
-5 - 4 - 3 - 2 - 1 0 1 2 3 4 5
(-1 ) +2 =
-5 - 4 - 3 - 2 - 1 0 1 2 3 4 5
4 + (-5 ) =
-5 - 4 - 3 - 2 - 1 0 1 2 3 4 5
0 + (- 5 ) =
-5 - 4 - 3 - 2 - 1 0 1 2 3 4 5
11 11
5A Mean
5A Degrees Celsius
Find the mean for each set of numbers. The average of numbers is the mean. To find the mean, add all the given numbers, then divide by how many numbers there are.
The principle of Barthwood Elementary School counts the number of students for each grade. He wants to find the mean. Grades Number of Students 1 st 2 nd 3 rd 4 th 5 th 6 th
41 47 39 41 44 40
Add the numbers: 4 1 + 4 7 + 39 + 4 1 + 44 + 40 = 252 Divide 252 by 6 because there are 6 numbers in total: 252 ÷ 6 = 4 2 . The mean is 42 students. The mean may or may not be one of the given numbers. 2 , 6 , 10 , 4 , 3 _______________________ 1 4 , 5 , 8 , 1 2 , 3 , 9 , 10 , 1 1 _______________
Write the temperature in degrees Celsius (°C). The Celcius thermometer is used for measuring temperature. A degree is a unit of temperature.
40º
40º
40º
20º
30º
30º
30º
10º
20º
20º
20º
0º
10º
10º
10º
-10º
_____________ 25ºC
_____________
_____________
_____________
20º
50º
40º
10º
40º
50º
30º
0º
30º
40º
20º
-10º
20º
30º
10º
5 , 2 , 1 , 2 , 1 , 1 ______________________ - 2 , - 2 , - 8 , - 16 ________________________
-5 , - 2 , - 5 , - 6 , - 7 ___________________ - 4 , - 2 , - 2 , -4 ________________________
10º
2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 __________________ 4 , 8 , 5 , 2 , 4 , 8 , 1 1 , 4 , 7 , 7 ______________ 9 , 6 , 3 , 3 , 8 , 5 , 0 , 7 , 4 _____________ 1 0 , 8 , 14 , 1 1 , 1 5 , 2 , 1 3 , 7 ________________
12 12
_____________
_____________
_____________
_____________
13 13