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e v o r p m I o T g Strivin

Fractions, Decimals And Percentages Fractions, Decimals And Percentages is one of eight books in the Striving To Improve series. This series is targeted at students aged between 11 and 15 years of age who, for whatever reason, are struggling to keep up with their peers. The activities in this book are designed to prevent students from regressing any further at school. Each worksheet is based on a modi�ied curriculum, and tasks have been designed so that students can work at their own pace and without constant supervision from the teacher.

e v o r p m I o T g n i v i r St

Fractions, Decimals And Percentages For students aged 11 - 15 years who are underachieving at their year level.

Fractions, Decimals And Percentages will help students consolidate written and mental methods of calculation. Decimal place value, calculations with decimals, comparing decimal quantities, rounding decimal amounts and conversions between fractions, decimals and percentages are all explored in this book.

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STRIVING TO IMPROVE

Fractions, Decimals And Percentages ISBN 978 186 397 852 1

   www.istock.com/sjlocke

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Ready-Ed Publications

Edited by Mirella Trimboli


This is a Ready-Ed Publications' book preview.

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This is a Ready-Ed Publications' book preview. Series: Striving to Improve Title: Fractions, Decimals And Percentages © 2013 Ready-Ed Publications Printed in Australia Edited by Mirella Trimboli

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.

Copyright Notice The purchasing educational institution and its staff have the right to make copies of the whole or part of this book, beyond their rights under the Australian Copyright Act 1968 (the Act), provided that: 1.

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2.

Copies are made only by reprographic means (photocopying), not by electronic/digital means, and not stored or transmitted;

3.

Copies are not sold or lent;

4.

Every copy made clearly shows the footnote, ‘Ready-Ed Publications’.

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. The Act allows a maximum of one chapter or 10% of the pages of this book, whichever is the greater, to be reproduced and/or communicated by any educational institution for its educational purposes provided that

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ISBN: 978 186 397 852 1 2


Contents

This is a Ready-Ed Publications' book preview. Teachers’ Notes Curriculum Links

4 5

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

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

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

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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51-55

3


Teachers’ Notes

This is a Ready-Ed Publications' book preview. 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.

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

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. The activities can be used for individual students needing further consolidation in a mainstream classroom or as instructional worksheets for a whole class of 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

This is a Ready-Ed Publications' book preview. Compare, order and represent decimals (ACMNA105)

Investigate strategies to solve problems involving addition and subtraction of fractions with the same denominator (ACMNA103)

Solve problems involving addition and subtraction of fractions with the same or related denominators (ACMNA126) Find a simple fraction of a quantity where the result is a whole number, with and without digital technologies (ACMNA127) 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) Make connections between equivalent fractions, decimals and percentages (ACMNA131) Multiply and divide fractions and decimals using efficient written strategies and digital technologies (ACMNA154) 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) Connect fractions, decimals and percentages and carry out simple conversions (ACMNA157) Find percentages of quantities and express one quantity as a percentage of another, with and without digital technologies. (ACMNA158)

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Teachers’ Notes

With Decimals This is aSkills Ready-Ed Publications' book preview. 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. The concepts covered include: 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

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.

Estimation

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, Multiplication And Division

These activities are designed to develop the mental and written learning processes 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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*   Decimal Place Value 1 *  Task a

This is a Ready-Ed Publications' book preview. Complete the following.

67.9

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

99.4

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

12.3

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

42.75 = ............................................................................................................................................. 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. Hundreds

Example

Ones

1

2

1

4 2

d.

1

4

1/tenth

3

7

405.307

2

1

1

.

3

5

9

.

6

.

5

3

.

4

2

.

3

2

.

4

1/hundredth 1/thousandth

.

1

e. f.

.

1/hundredth 1/thousandth

Write the numbers represented in the table below. Tens

c.

1/tenth

5

Hundreds

b.

g.

Ones

4

*  Task b a.

Tens

3 2

4

7

7 4

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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.

This is a Ready-Ed Publications' book preview. 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 =.................................................................................................................................................... 29.998 =....................................................................................................................................................

*  Task b

What is the face value of the underlined digits below?

56.758 =

35.424

*  Task c

3.222

132.1

Write these numbers in words.

289.78 = two hundred and eighty-nine point seven eight. 301.203 =................................................................................................................................................. 1345.2 =................................................................................................................................................... 1.298 =......................................................................................................................................................

*  Task d 1.9

Order each set of numbers starting from the least. 1.234

210.103

2.013

21.13

1.23

1234.12

2.13

................................................................................................................................................................... 2345

2.345

234.5

23.45

2.543

2543.1

234.05

234.005

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

*  Task e

1.9

18.2 3001 8

Use < or > to complete these.

1.99

4.23

4.023

5.155

1.5

3.00

13.1

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

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*   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.

5432 = 4 x 100 = 400

62.45 = 4 x 1⁄10 = 4⁄10

This is a Ready-Ed Publications' book preview. *  Task a Example

What value does each underlined number represent below?

9675..................... 29.38 ..................... 1.987...................... 135.3...................... 209.08.................

24.34 .................. 147.2...................... 100.333 . .............. 24.24 . ................... 999.99................. zz Look at the decimal Example number 24.35 in expanded form.

*  Task b

24.35 = 20 + 4 +

3 10

5 + 100

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

1 1 10 ) + (5 x 100 )

Write these decimals in expanded form.

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

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

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

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

c. 35.57 = . ...............................................................................................................................................

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

d. 49.08 = . ...............................................................................................................................................

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

e. 765.297 = . ..........................................................................................................................................

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

*  Task c

Use < or > to make these true.

35.46

3.546

2.002

2.2

980

9.8

*

1.256 860.086 12

125.6

24.78

2.478

860.068

2.3

3.2

0.12

154.3

134.5

1000

1.000

56.65

65.56

264.1

264.9

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  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? 9


*   Greater Than/Less Than > means “greater than”; < means “less than”.

This is a Ready-Ed Publications' book preview. 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

Compare 4.570 and 4.507.

Which number has MORE place values (before the decimal point)? Ones 4

1/tenth .

Same

1/hundredth 1/thousandth

5

7

Same

Larger

0

Ones 4

1/tenth .

Same

1/hundredth 1/thousandth

5

0

Same

Smaller

7

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

1/tenth

1/hundredth

Ones

0

9

0

.

Smaller

Same

1/tenth

1/hundredth

5

5

.

Larger

The first number to have a larger digit is 0.55. This is written as 0.09 < 0.55.

  Task a *

Place the symbols in between these sets of numbers to show which is greater.

4.8 _____ < 5.8

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 ?

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............................................................................................................................................................. Use a separate piece of paper to write your own.

10


*   Rounding Decimals 1

This is a Ready-Ed Publications' *  Task a book preview. 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

Round these decimals to the nearest whole number.

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

3.1 ≈................... 4.7 ≈................. 9.8 ≈................. 6.4 ≈................. 1.7 ≈................ 2.9 ≈.............. Remember if the decimal ends in 5 (such as 2.5), it is rounded to the nearest even whole number. Complete these following the rule. 3.5 ≈................... 1.5 ≈................. 6.5 ≈................. 5.5 ≈................. 7.5 ≈................ 9.5 ≈..............

*  Task b

Complete the following.

Round these decimals to the nearest whole number. 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. 26.78 ≈ 27 36.35 ≈................. 19.18 ≈................ 87.94 ≈................ 84.32 ≈............... 63.11 ≈.................. 28.97 ≈................. 24.65 ≈................ 55.34 ≈................ 72.43 ≈............... Round these decimals to the nearest whole number. 56.789 ≈ 57 13.245 ≈.............. 24.865 ≈.............. 2.367 ≈................ 25.895 ≈............. 4.111 ≈.................. 5.555 ≈................. 53.455 ≈.............. 7.001 ≈................ 2.457 ≈...............

  Task c *

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

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 ≈ __

+ + Go to +www.readyed.net

≈ 17

11


*   Rounding Decimals 2

  Task a Complete the following. * 1. Round these decimals to the nearest decimal place. For example 3.54 ≈ 3.5

This is a Ready-Ed Publications' book preview. 4.78 ≈................ 2.34 ≈.............. 7.23 ≈............... 3.57 ≈.............. 6.89 ≈.............. 4.53 ≈............

4.57 ≈................ 9.51 ≈.............. 5.51 ≈............... 2.42 ≈.............. 7.64 ≈.............. 9.54 ≈............

2. Round these decimals to two decimal places. For example 2.344 ≈ 2.34. 3.423 ≈.............. 2.234 ≈.......... 6.342 ≈............ 5.782 ≈............ 9.878 ≈.......... 6.689 ≈.......... 5.459 ≈.............. 4.253 ≈.......... 3.324 ≈.......... 5.551 ≈......... 9.999 ≈.......... 1.959 ≈..........

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

2. Round these decimals to the nearest whole number and complete the sum. 3.45 + 4.67 + 7.58 + 3.22

≈ 3 + 5 + 8 + 3 = 19

2.34 + 3.456 + 5.645 + 4.37 ≈................................................................................................................ 2.67 + 5.645 + 9.001 + 3.424 ≈................................................................................................................ 7.58 + 0.987 + 2.456 + 1.23 ≈................................................................................................................ 3. Round these amounts to the nearest ten cents. For example $5.76 ≈ $5.80 $3.42 ≈.............. $4.56 ≈............ $7.89 ≈.......... $5.42 ≈......... $0.98 ≈.......... $7.79 ≈..........

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

*  Task c

Round these amounts to the nearest cent.

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$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.

This is a Ready-Ed Publications' book preview. Examples

1

1

1

3. 45 + 5. 22

5. 79 + 4. 15

8. 39 + 1. 78

9. 94

10. 17

Regrouping one column

Regrouping two columns

8. 67

No regrouping

WORK FROM RIGHT TO LEFT

*  Task a

Try these sums with no regrouping.

2. 25 + 5. 32

4. 43 + 3. 14

6. 28 + 1. 60

4. 34 + 3. 31

3. 66 + 5. 22

4. 36 + 3. 51

*  Task b

Try these sums regrouping one column.

5. 27 + 2. 13

3. 58 + 4. 13

6. 47 + 2. 38

5. 37 + 2. 24

4. 59 + 1. 28

4. 27 + 4. 65

*  Task c

Try these sums regrouping two columns.

Go to www.readyed.net $4. 46 + $1. 85

$6. 79 + $2. 55

$4. 48 + $2. 87

13


*   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.

This is a Ready-Ed Publications' book preview. Examples

1

3. 45 + 5. 2

5. 79 + 4. 3

10. 09

8. 65

No regrouping

Regrouping one column WORK FROM RIGHT TO LEFT

*  Task a

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

1. 40 + 4. 12

5. 6 + 4. 14

3. 4 + 1. 59

3. 47 + 5. 8

4. 8 + 5. 95

1. 9 + 5. 89

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!

Example

  Task b *

Wrong: 2.45 3.6 0.78 + 5

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

Try lining the sum up in the space. 5.37 + .4 + 23.55 + 7

.

.

Go to www.readyed.net 14

.

+

.

=

.


*   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.

This is a Ready-Ed Publications' book preview. Examples

6

7 12

1

1

5. 45 – 3. 22

5. 74 – 4. 15

8. 36 – 1. 78

2. 23

No regrouping

1. 59

Regrouping one column

6. 58

Regrouping two columns

WORK FROM RIGHT TO LEFT

*  Task a

Try these sums with no regrouping.

7. 55 – 2. 24

5. 28 – 2. 23

9. 67 – 1. 50

7. 43 – 3. 12

8. 89 – 2. 63

2. 87 – 1. 23

*  Task b

Try these sums regrouping one column.

8. 47 – 2. 19

5. 74 – 2. 26

6. 76 – 1. 39

8. 42 – 3. 17

5. 43 – 2. 28

7. 36 – 3. 28

*  Task c

Try these sums regrouping two columns.

Go to www.readyed.net $7. 52 – $1. 86

$8. 32 – $4. 57

$6. 56 – $2. 79

15


*   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.

This is a Ready-Ed Publications' book preview. Examples

4

5 14

1

1

5. 45 – 3. 2

5. 39 – 4. 7

6. 50 – 3. 73

2. 25

No regrouping

0. 69

Regrouping one column

2. 77

Regrouping two columns WORK FROM RIGHT TO LEFT

*  Task a

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

7. 30 – 5. 12

8. 6 – 3. 13

9. 6 – 1. 28

8. 37 – 5. 8

7. 7 – 3. 25

4. 3 – 1. 79

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! Wrong:

Example

b: Challenge *  7task – 4.59

8.45 5

Right: 8. 45 – 5. 00

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Hint: Make 7 into 7.00.

16


*   Adding And Subtracting Decimals 1   Task a Try these sums. *Add the following decimals.

This is a Ready-Ed Publications' book preview. 23.1 34.3 52.3 45.2 65.2 98.6 + 13.2 + 54.4 + 34.5 + 31.4 + 32.1 + 11.3

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

+ 73.4

+ 83.3

+ 79.5

+ 46.9

50.3

  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

¹ 24.6 37.8 53.7 37.4 63.8 63.4 − 13.7 − 21.9 − 23.8 − 18.6 − 26.9 − 59.9

10.9

*  Task c

Try these sums.

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

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

67.89 − 45.67 =

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65.46 − 23.56 = 98.43 − 25.46 =

17


Adding And Subtracting Decimals 2 * zz So far we have added and subtracted decimals to and from

Example

This is a Ready-Ed Publications' book preview. 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.

  4.567 + 12.3    16.867

  Task a * a.

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

*  Task b

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 Add the following amounts. 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

*a.   Task c

Complete the subtraction problems that are set out correctly.

b. c. d. e. f. 24.564 3.789 4.574 253.5 36.434 3.456 − 2.462 − 23.45 − 3.54 − 2.342 − 23.1 − 2.78 d:Go Challenge to www.readyed.net *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?

18


*  Task a

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

This is a Ready-Ed Publications' book preview. 24.567 + 23.45 + 3.46 =

24.567 4.56 + 46.78 + 356.7 23.45     3.46 +

1.009 + 456.7 + 4.302 =

*  Task b

4578.7 - 32.3

35.687 - 2.54

+

23.01 + 345.6 + 45.643 =

+

2 .456 + 456.7 + 4.302 =

=

+

24. 56 + 35.3 + 245.63 =

+

+

Subtract the following amounts. = 4578.7   32.3 −

24.567 - 12.324

=

97.85 - 3.79

= −

=

567.9 - 29.8

= −

116.34 - 35.76

= −

  task c: Challenge *Emily Go tocrateswww.readyed.net picked three 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?

19


*   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

This is a Ready-Ed Publications' book preview. *  Task a

Complete the following by adding zeros where necessary.

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 necessary. 4.65 - 3.234 = 254.3 - 1.987 = 53.57 - 4.634 =

234.35 - 7.677 =

34.34 - 6.352 =

443.34 - 63.366 =

c: word Problems *1.   task 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?

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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? 20


*   Multiplying Decimals 1 *  Task a

Complete the following sets of multiplication problems.

This is a Ready-Ed Publications' book preview. Set 1

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

$3.00 $8.00 $7.00 $6.00 $2.00 $9.00 x 2 x 5 x 6 x 8 x 4 x 7 $6.00 Set 3

$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

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  3 269.2 m

*  task b: word Problems

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? 2. Jess paid $3.95 for 8 books. How much did she pay altogether? 3. Peter bought 10 computer disks for $9.95 each. How much did he spend altogether? 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?

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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


*  Task a

*   Multiplying Decimals 2

This is a Ready-Ed Publications' book preview. 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

2. Multiply these decimals. 0.3 0.7 1.2 x 2 x 4 x 2 x

3.4 4.5 5.3 6 x 3 x 4

0.6

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

3.8 2.3 4.6 4 x 7 x 8 x

8.9 7.6 3.5 2 x 6 x 3

15.2

4. Complete these. Make sure your answer has the same number of decimal places as the multiplicand (factor). 0.32 0.24 0.19 0.87 0.47 0.84 x 8 x 4 x 6 x 5 x 7 x 6

2.56

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

2.3 5.6 4.5 32 x 43 x 63 x

7.3 3.6 6.8 32 x 98 x 57

46 1

690

73.6

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

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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

This is a Ready-Ed Publications' book preview. *  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

3 ) 9.6

5 ) 7.5

4 ) 7.2

2 ) 9.8

7 ) 5.6

4 ) 9.2

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.

*  Task b

Show how you would estimate the answers to these, then complete the original problem to see how close your estimate was.

set 1

5 ) 45.5 ≈ 5 ) 45

6 ) 36.6 ≈

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 ≈

3 ) 46.8 ≈

set 4

2 ) 24.8 ≈

7 ) 14.7 ≈

5 ) 35.5 ≈

8 ) 72.8 ≈

set 5

4 ) 12.8 ≈

6 ) 66.6 ≈

8 ) 32.8 ≈

4 ) 37.6 ≈

  Task c *

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

) ) ) ) Go) to www.readyed.net

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.

This is a Ready-Ed Publications' book preview. 76 ÷ 5 =      15. 2 5 ) 76.10

Example

35 ÷ 4 =      8. 7 5 ) 4 35. 3020

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.

  Task a *

Use a calculator to find the answers to the division problems. Express your answers as recurring decimals.

3 ) 8.0

3 ) 1.0

6 ) 1.0

9 ) 3.0

9 ) 6.2

9 ) 5.0

9 ) 4.0

3 ) 7.0

  Task b *

Calculate answers to the following. Round your answer to the second decimal place.

 3.142857 7 ) 22.00000 ≈ 7 ) 9.3

3.14

7 ) 83

14 ) 7.8

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24

6 ) 7.9

6 ) 5.0

7 ) 59

13 ) 12


Teachersâ&#x20AC;&#x2122; Notes

This is a Ready-Ed Publications' Fractions, Decimals And Percentages book preview. 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. The concepts covered include: Visual Representation

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.

Mixed Applications

The final activities in this section will be useful in determining the fluency of students with relation to their ability to work easily with fractions, decimals and percentages and with their ability to work with short applications.

Go to www.readyed.net 25


*  Task a

*   Shading Decimal And Fraction Quantities 1 Shade in the correct amounts.

This is a Ready-Ed Publications' book preview.

0.1

0.5

0.7

0.6

0.23

0.26

0.69

0.54

0.24

0.63

0.12

0.89

*  Task b

Write the decimal that shows the shaded area.

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

*  Task c

*

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

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

Write the fraction and the decimal for each of the shaded areas.

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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?

26


*   Shading Decimal And Fraction Quantities 2   Task a *

The grids below have been divided into 100 units. Shade the amount shown underneath.

This is a Ready-Ed Publications' book preview.

0.2

0.45

0.01

0.86

0.96

0.05

0.68

0.8

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

b. .................................. c. ................................... d. ................................

e. . ................................. f. . .................................. g. .................................. h. ................................

*  Task b

Complete these using = or ≠.

3 4

0.75

2 6

0.4

8 10

0.8

2 3

0.3

4 8

0.6

1 3

0.3

4 8

0.6

2 5

0.25

*  Task c

Use =, < or > to complete these.

1

1.75

2

9.8

5 6 100

3 4

9 108

4 8

2.4 6.5

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

27


*   Shading Decimal And Fraction Quantities 3 *  Task a

Shade the amounts shown below.

This is a Ready-Ed Publications' book preview. How many squares are shaded in each box? a.______

a. 0.73

  Task b *

b.

b.______

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

3 4

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

0.47

1

⁄2

0.84

4

0.69

7

⁄10

0.35

1

0.15

3

⁄20

0.4

8

  Task c *

⁄4

⁄20

Complete these number sentences using =, < or >. Use squared paper if needed.

3 10

0.13

6.32

6

5 20

2 5

0.5

7 17 20

3 5

0.35

2

3 5

2 5

0.4

3 16 20

Go to www.readyed.net 7.85

*Which is longer:

2.65

  Challenge

2

28

⁄5

5 6

sticks of liquorice or 2.56 sticks of liquorice?

3.16


*   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.

This is a Ready-Ed Publications' book preview. Example 1

Convert

2 to a decimal. 5

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

We can since 5 divides into 10 without a remainder. So to make the 5 into a 10 we need to multiply by 2. Whatever we do to the bottom we do to the top so the 2 becomes 4. 2/5 = 4/10

Example 2

Convert

3 to a decimal. 4

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

This means we have a 4 in the tenths column. So 2/5 = 0.4

  Task a * a.

Convert each of the following to a decimal. b.

6 10 d.

32 50

c. 1 5

e.

g.

2 9

7 20

Example

3/8 = 3÷8 = 0.375

Convert each of the following to a decimal. b.

1 6 d.

f.

17 25

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.

  Task b * a.

14 20

c. 5 8

e.

2 7

2 3 f.

3 40

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5 15

h.

5 7

i.

11 15

29


*   Expressing Decimals As Fractions

This is a Ready-Ed Publications' book preview. 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.

  Task a * a.

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

0.1

c.

0.9

0.3

d.

e.

f.

0.8

1.5

0.4

  Task b * a.

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

0.25

c.

0.32

0.95

d.

e.

f.

0.53

2.48

1.17 g.

h.

i.

Go to www.readyed.net

0.345

30

0.852

0.655


*   Fractions And Decimal Conversions 1 1

5

2.05 = 2 100 = 2 20

Example

This*  Taskisa a Ready-Ed Publications' book preview. Express these decimals as simplified fractions.

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

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

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

3

*  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

23 100

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

7 10

Example

*  Task c

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

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

70 100

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

700 1000

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

435

100 = 4.35

Change these improper fractions to decimals.

16

39 10

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

143 100

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

198 100

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

11 10

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

32

25 10

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

43 10

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

656 100

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

264 100

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

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

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

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

*  Task d

Write five equivalent fractions for each decimal below.

6.5 =............................................................................................................................ 2.25 =......................................................................................................................... 0.75 =......................................................................................................................... 3.6 =............................................................................................................................

Go to www.readyed.net 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.

31


*   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.

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

This is a Ready-Ed Publications' book preview. *  Task a

Express the decimals below as fractions.

0.2 =

0.5 =

*  Task b

Express the fractions below as decimals.

1 = 10

0.6 =

7 = 10

0.23 =

10 = 100

34 = 100

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

*  Task c

0.98 =

0.47 =

28 = 100

Examples

567 = 1000 3 5

= 10 = 0.6

6

1 2

= 10 = 0.5

5

Express the fractions below as decimals.

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

4 10

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

1 5

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

8 20

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

6 20

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

10 50

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

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

20 50

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

2 5

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

3 4

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

1 4

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

15 20

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

150 200 20 200 = ............... 200 = ............... 40

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

40

300 600 =

*  Task d

Use =, < or > to make the following true.

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

0.5 4 5

*

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

20 2000

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

4 10

6 10

6.0

8 100

0.08

0.45

90 100

0.9

8 1000

0.08

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  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.

32


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

*

This is a Ready-Ed Publications' book preview. The first one has been done for you.

c.

b.

a.

42 21 = 100 50

0.42 =

0.05

f.

e.

d.

0.25

1.1 h.

g.

0.82

*

3 8

i.

c.

b.

0.375 8 3 .306040

1 4

3 10

1 3

4 5 f.

1 7

1 9 i.

h.

g.

0.015

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

e.

d.

0.004

0.09

  Task b

a.

0.6

5 8

c: Investigative Challenge *  Task Converting recurring decimals to fractions is difficult if you don’t

5 6

just know the answer. We can use this formula to help us work it out:

Fraction =

1 1 10 = 1 10 1– 10

First Fraction 1 – Fraction Ratio

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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:

×

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

This is a Ready-Ed Publications' book preview. 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.

Example

36 needs to be divided by 6 so that the denominator is 10. 60

6 36 ÷ 6 = 6 = 0.6 10 60 ÷ 6 = 10

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

*  Task a

Simplify the following fractions so that the denominator is 10.

32 40

= 8 = 0.8

35 70

=

64 80

=

42 60

=

81 90

=

56 70

=

24 30

=

14 20

=

48 80

=

36 40

=

63 90

=

28 70

=

10

  Task b * 2 5

4

3 5

Now try converting these fractions to a decimal. Some of them are quite tricky. 3 4

=

3

=

10 204 =

*  Task c a. 0.7 =

=

5 25

=

3 129 =

3 15

=

4

2 8

4 13 20

=

6 503 =

=

9

2 5

=

3 = 2 100

Change these decimals to fractions by filling in the boxes below. 7

70

700

14

35

10

100

1000

20

50

10

100

1000

5

20

10

100

1000

5

40

10

100

1000

5

9

10

100

1000

2

6

b. 0.2 = c. 0.8 = d. 1.0 = e. 1.5 =

d:Go Challenge to www.readyed.net *  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.

34


*  Task a

*   Fractions Into Decimals: Word Problems

Answer the following quick questions.

This is a Ready-Ed Publications' book preview. 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?..............................................................................

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

3 ?................................................................................................. 4

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

9.

11. True or false: Zero point four five is the same as forty five over a hundred......... 12. What is a quarter of twenty?................................................................................................. 13. Two thirds of nine is equal to................................................................................................ 14. Express two and four fifths as a decimal........................................................................... 3 4

15. True or false: 3 is greater than 3.65.................................................................................. b: word Problems *  1. taskAnne bought fifteen bananas from the shop and gave five to her brother. What fraction does she still have?.......................................................................................... 2. Steve rode 6.75 km on the weekend. 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?.................................................................................................

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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

100

This*  Taskisa a Ready-Ed Publications' book preview. Use the grid and complete the following task.

This grid has 100 squares in it.

Colour in 2 squares red. This is 0.02, or 2 hundredths, or 2100, or 2%. Colour in 20 squares green.This is 0.20 or 20 hundredths, or 20 100 or 20%.

Remember that 0.2 is the same as 0.20.

  Task b *

See if you can fill out this chart to compare fractions, decimals and percentages. Imagine that each fraction is a score in a test, e.g. 4/10 means you got 4 correct out of ten questions.

Fractions

Out of 100

310

30

810

80

100

Decimals

Percentages

0.3

30%

100

710

6.5

9.5

100

10

65

10

95

0.65

100

73

100

0.12

0.85

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36

20%

50%


*   Percentages 2

This  Taskisa a Ready-Ed Publications' * book preview. zz Percent means “out of 100”, so if you get 75100 in a test, you would get 75%.

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

2 = 510 = 0.5

1

4 = 25100 = 0.25

2

5 = 210 = 0.2

2

1 1

4 = 50100 = 0.5

3

4 = 75100 = 0.75

5 = 410 = 0.4

3

5 = 610 = 0.6

5 = 810 = 0.8

4

Remember that 0.2 is the same as 0.20. Fraction

Out of 100

Decimals

Percentages

310

30

0.3

30%

810

80

100 100

710

10

65

0.65

10

95

0.95

6.5

100

9.5

100

95%

34 25 = 10 45 = 10 55

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

  Task b *

Use your calculator to divide the numerator by the denominator. This will give you a decimal with hundredths, which you can then convert to a percentage.

e.g. 1840 on the calculator is 18 ÷ 40 = 0.45 or 45%.  Try these. 25 = 0.64 = ______%

16

Hint: Round the decimal to 2 places.

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70 = ______ = ______%

63

30 = ______ = ______%

18

52 = ______ = ______%

48

37


Percentages 3 * zz So far we know that decimals and fractions can be used to represent the same

This is a Ready-Ed Publications' book preview. 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

Complete the following.

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

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

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

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

3. Convert these fractions to a percentage. The first one has been done for you. 55 10 10

....................... = 100 = 50%

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

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

8 10

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

1 100

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

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

4 10

2 5

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

50

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

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

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

75 3 100 = 4

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:Go Challenge to www.readyed.net *  Melanie scored 98% in a Maths test. If there were fifty questions, how many questions must Melanie have answered correctly?

38


Percentages 4 * zz In order to convert these fractions to percentages, we need to find an equivalent

This*  Taskisa a Ready-Ed Publications' book preview. fraction with a denominator of 10, 100 or 1000.

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

40

200 =

20 100

= 20%

20 200

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

1 4

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

460 2000

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

30 50

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

2 20

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

40 800

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

15 20

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

40 60

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

30 40

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

300 400

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

600 800

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

300 3000

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

25 50

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

5 25

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

9 20

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

  Task b *

Match the percentage on the left with the correct fraction and decimal. There may be more than two answers. 2

25

1

5

55

1

a) 25%

0.25

2.5 5 100 4

b) 55%

5.5

0.55 100 5 10

0.5

c) 32%

3.2 10

32

0.23

0.32

32 100

16 50

d) 80% 5

0.08

8.0

0.45

0.8

8 1000

e) 15%

0.15 5

0.015

5.1

15 100

4

1.5

1

0.14

c: word Problems *1.   task Sophie spent 10% of her pocket money on a new pencil. What percentage of her pocket money does she have left?........................................................................................ 2. Taylor spent 4⁄5 of his spare time reading. What percentage of time is this? ............................................................................................................................................................ 3. Marcelle collected snails in the garden. She found 50% of them near the rose 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?....................................

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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.

This is a Ready-Ed Publications' book preview. a.

b.

0.03 × 100 = 0.03 = 3%

d.

c.

0.45

e.

1.3

f.

2.04

g.

h.

0.105

*  Task b

i.

24% = 24 ÷ 100 = 24 = 0.24

c.

4%

95% e.

f.

0.4%

52%

107% h.

2.1%

0.067

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

d.

0.01

0.002

a.

g.

0.78

i.

0.15%

33.3%

c: Small Group Challenge *  Task When we measure our Body Mass Index or BMI we use percentages. In a small group, each of you

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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.

40


*   Fraction And Percentage Conversions

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

*

This is a Ready-Ed Publications' book preview. your answers. The first one has been done for you.

c.

b.

a.

85% =

85 ÷ 5 100 ÷ 5

=

17 20

20%

f.

e.

d.

64%

42%

130%

96% i.

h.

g.

*  Task b

100%

86%

54%

Convert each fraction to a percentage. The first one has been done for you.

a.

c.

b.

20 2 × 100 = 2 × 20 = 40% 5

1 2 f.

e.

d. 3 4

3 10

4 5 i.

h.

g. 3 50

7 25

1 3

2 3

c: Personal Challenge *  Task To convert fractions whose denominator does not divide evenly into 100 we can use short division.

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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

41


Fractions, Decimals And Percentages 1 * zz Decimals and fractions can also be expressed as percentages. Percentages are

This is a Ready-Ed Publications' *  Task a book preview. 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’. Complete the following.

1. Convert the percentages below to fractions.

35% = 35⁄100 56% =................... 98% =.................. 87% =................... 50% =..................... 100% =................ 105% =................ 765% =................ 0% =...................... 12% =..................... 2. Change these decimals to percentages. 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 =...................

20

⁄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. ⁄10 = 10⁄100 = 10 %

4

⁄20 = 5⁄100 = 5%

5

1 1

⁄50 = 20⁄100 = 20%

10

⁄5 = 20⁄100 = 20%

1

⁄10 =............................... 7⁄10 =...............................

⁄1000 =...........................

500

⁄20 =............................... 1⁄25 =............................... 9⁄20 =................................ ⁄50 =............................... 16⁄50 =..............................

4

35

⁄50 =...............................

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

3

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

Example

⁄4 x 100 =

3

=

300

⁄2 x 100 =

1

=

4

=

4 ) 300

=

75 = 75%

=

100 2 50 = 50%

b Change these fractions into percentages. *  Task Go to www.readyed.net

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

1

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

5

42

⁄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.

This is a Ready-Ed Publications' book preview. ⁄10

a. 4 % =

4

0.04

b. 12% =

1.2

12

c. 45% =

4.5

45

d. 72% =

0.72

72

e. 25% =

1

⁄4

⁄100

⁄100

4

40

⁄100

12

⁄200

0.12

⁄100

0.45

45

⁄100

720

72.0

⁄1000

0.25

0.4

⁄10

⁄10

25

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

16

3

5

15 100 × = 75 = 75% 20 1

*  Task b

1

25

12 100 × = 75 = 75% 16 1 4

Use this method to calculate the following percentages.

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

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

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

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

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

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

c: word Problems *1.   task Emily received 35 out of 50 in a test. What percentage did she score? 2. On Saturday Denis climbed 40 metres up a rock face. The next day he climbed 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?

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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.

This is a Ready-Ed Publications' book preview.

Fraction

14 1

5

Decimal

Percentage

0.25

25%

0.2

2 10

36%

0.42

4 5

64%

3 20

0.95

28 100

73%

4 200 175 1000

4.5

*  Task b

20.5%

Use = or ≠ in the boxes below.

0.75

75%

3 4

34%

1 4

25%

0.25

0.8

80%

4 5

0.8

5 25

25%

7 25

2 4

0.28

50%

5.0

17 20

0.59

task c: Challenge *  Joey Go65% to www.readyed.net scored 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?

44


*   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

This is a Ready-Ed Publications' book preview. *  Task a

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

a. a. 15 out of 25

c. 18 out of 20

e. 8 out of 15

b. 8 out of 10

d. 37 out of 40

f. 49 out of 60

*  Task b

Convert each of these quantities to a percentage.

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

What percentage of the class have red hair?

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

Sugar

c. In a school of 1500 students, the 250 Year 11 students are going on camp. What percentage of students will remain at school?

d. During a T.V. program that runs for an hour, there are 12 minutes of commercials. What percentage of the program is television commercials? c: Personal Challenge Go to www.readyed.net *  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.

45


*   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.

This is a Ready-Ed Publications' *  Task a book preview. Complete the following.

1. Find 10% of the following amounts.

$30................. $60.................. $130................ $290 .............. $400 .............. $2000 ............... $25.................. $48.................. $120 . ............. $293 .............. $498 .............. $450 . ................ 2. Find 50% of the following amounts. 20..................... 30.................... 100.................. 150.................. 200.................. 1000................... 1200................ 64.................... 65..................... 250.................. 16.................... 17........................ 44..................... 28.................... 350.................. 12.6................. 25.8................. 243.2.................. 3. Find 20% of the following amounts. $3.00..................... $2.30.................... $1.20.................... $4.80..................... $9.60........................ $0.50..................... $25.50.................. $16.30.................. $29.80.................. $320.00................... 4. Subtract 20% from each amount below. $9.60..................... $10.80.................. $4.00.................... $2.00..................... $150......................... $1000................... $3.50.................... $6.00.................... $7.20..................... $9.50........................

*  task b: word Problems

1. Rick received a 10% discount on his new basketball. Originally, the basketball cost $50.00. How much did Rick pay for the ball? 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?

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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? 46


*   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:

This is a Ready-Ed Publications' book preview. 20 × 180 = $36 100

Sale Price = 180 - 36 = $144

  Task a * Calculate the discount available on the sale items below. a. 10% off $3000

b. 35% off $250

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

d. 8% off $400

  Task b * Using the same method as the one to calculate a discount, calculate the percentage of each of the following amounts.

a. 5% of 200 grams

b. 10% of 54 km

c. 25% of 800 m

d. 12% of 3L

e. 84% of 5000 cm2

f. 27% of 10 hours

*  Task c: Partner Challenge

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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


* â&#x20AC;&#x2030; Mixed Word Problems 1

1. At the town fair the following crowds were recorded: Saturday 976, Sunday 1089,

This is a Ready-Ed Publications' book preview. 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 Wednesday afternoon and 320 km on Thursday. What was the total distance

covered?................................................................................................................................................... 3. Noel scored the following number of runs in a cricket test series: 121, 29, 98, 57, 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 class made it to school?...................................................................................................................... 7. Three brands of chocolate have different amounts of sugar. Brand 1 contains 56% sugar, Brand 2 is 3â &#x201E;5 sugar and in Brand 3 sugar makes up 0.62 of the chocolate. 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 amount paid by the students?......................................................................................................... 9. A man left $9853 to his four children. If it is divided evenly among them how much will each person receive?................................................................................................................... 10. A washing machine was priced at $315. It was then reduced by 20%. What is the reduced price?........................................................................................................................................ 11. On his 15th birthday Dan weighed 65 kg. On his 16th birthday his weight had

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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%.

This is a Ready-Ed Publications' book preview. 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

percentage of the cake is not flour?............................................................................................... 4. Sam is buying books on sale at the local newsagent. Each book is discounted by 20% of what the marked price states. If he wants to buy a book marked at $20.00, 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. What was the total distance she rode?......................................................................................... 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 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?..................................................................................... 10. In the final exam, 30% of the students failed. If 140 students passed how many students must have failed?............................................................................................................... 11. Karen ran 2.46 km on Wednesday. Express this distance as a fraction............................ 12. The bank is offering interest rates of 5% on savings accounts. How many cents for each dollar will the bank pay?.......................................................................................................... 13. At the local mine 85% of the miners were under 30 years of age. What fraction of

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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

This is a Ready-Ed Publications' book preview. 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?........................................................................................................................

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 percentage............................................................................................................................................. 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 spent on History what is the decimal amount left for other subjects?............................ a. How many minutes are spent on Maths?.............................................................................. b. How many minutes are spent on History?............................................................................ 8. The football team won 80% of its matches during the last season. If twenty 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?

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

10. Bill and Ted are playing chess. Bill has beaten Ted 60% of the time. If they have played fifty games, how many has Bill won?............................................................................. 11. Sam and Tess are playing cards. They have played eighteen games and Tess has won two thirds of the games. How many games has Sam won?....................................... 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?..........................................

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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

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

This is a Ready-Ed Publications' book preview. 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: <,>, >, <, <, <, >, >, <, <, <, <. 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.

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;

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. 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 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

Go to www.readyed.net 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

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.

This is a Ready-Ed Publications' book preview. Decimal Subtraction 2 Page 16 Task a: 2.18, 5.47, 8.32; 2.57, 4.45, 2.51; Challenge: 3.45, 2.41

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. 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. 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. 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.

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.

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. 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. 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.

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52

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.

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

This is a Ready-Ed Publications' book preview. 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.

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 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. 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;

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 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.

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. Percentages 1 Page 36

Fractions

Out of 100

Decimals

Percent

8

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

80

7

70

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

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Percentages 2 Page 37 Fractions

Out of 100

Decimals

Percent

8

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

80

7

70

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

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%

This is a Ready-Ed Publications' book preview. 64%, 0.6 = 60%, 0.9 = 90%, 0.92 = 92% 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

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%.

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 2 Page 43 Task a: a. 0.04, 4/100; b. 12/100, 0.12; c. 45/100, 0.45; d. 0.72, 72/100; e. 1/4, 0.25. 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%

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%

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

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

54

f. g. h. i.

0.004 0.021 0.0015 0.333

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Task b: =, ≠, =, ≠, ≠, =, =, ≠, =, ≠. Task c: challenge - Matt.

This is a Ready-Ed Publications' book preview. 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% 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%. 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 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%. 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. 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.

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Striving To Improve Series: Fractions, Decimals and Percentages