Striving To Improve Series: Fractions, for ages 11-15 years

e v o r p m I o T g Strivin

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

Fractions will help students consolidate written and mental methods of calculation. Equivalent fractions, simplifying fractions, improper fractions, mixed numerals, the addition and subtraction of fractions with and without common denominators, as well as the division and multiplication of fractions are all examined in this book.

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STRIVING TO IMPROVE

Fractions ISBN 978 186 397 851 4

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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 © 2013 Ready-Ed Publications Printed in Australia Edited by: Mirella Trimboli

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

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2.

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3.

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4.

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ISBN: 978 186 397 851 4 2

Contents

This is a Ready-Ed Publications' book preview.

Teachers’ Notes Curriculum Links

4 5

Understanding Fractions Teachers’ Notes Shading Fractions 1 Shading Fractions 2 Shading Fractions 3 Equivalent Fractions 1 Equivalent Fractions 2 Equivalent Fractions 3 Equivalent Fractions 4 Equivalent Fractions 5 Simplifying Fractions 1 Simplifying Fractions 2 Simplifying Fractions 3 Comparing Fractions 1 Comparing Fractions 2 Comparing Fractions 3 Comparing Fractions 4 Improper Fractions 1 Improper Fractions 2 Mixed Numerals 1 Mixed Numerals 2 Fraction Skills Review 1 Fraction Skills Review 2 Fraction Skills Review 3 Fraction Skills Review 4 Fraction Skills Review 5

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Calculating With Fractions Teachers’ Notes Addition With The Same Denominator Addition And Subtraction With The Same Denominator 1 Addition And Subtraction With The Same Denominator 2 Addition With Different Denominators Subtraction With Different Denominators Subtraction With Mixed Numerals 1 Subtraction With Mixed Numerals 2 Mixed Addition And Subtraction Of Fractions Multiplying Fractions Division Of Fractions Multiplying And Dividing Fractions Expressing As A Fraction 1 Expressing As A Fraction 2 Fractions Of An Amount 1 Fractions Of An Amount 2 Fractions Of An Amount 3 Real Life Fractions

31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

Go to www.readyed.net Answers

49-52

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 Understanding Fractions enables students to reencounter ideas of equivalent fractions, simplifying fractions, improper fraction, mixed numerals and comparing fractions. 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 Calculating With Fractions walks students through the four core calculations. 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 addition and subtraction of fractions with and without common denominators. Similarly, students explore how to multiply and divide fractions before applying them to a variety of applications. Students also begin to see the common uses for fractions by finding fractions of a quantity and be expressing various quantities as fractions.

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 4 through to Year 7 and are appropriate for students requiring extra support in Years 7, 8 and 9.

It is hoped that Fractions 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.

Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole (ACMNA058) Investigate equivalent fractions used in contexts (ACMNA077)

Count by quarters halves and thirds, including with mixed numerals.

Locate and represent these fractions on a number line (ACMNA078)

Compare and order common unit fractions and locate and represent them on a number line (ACMNA102) 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) 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)

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Teachers’ Notes

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

The activities in this section provide students with the opportunity to explore the concept of a fraction and the many different ways to represent fractions.

The concepts include: Equivalent Fractions Students explore a few different methods for recognising and utilising fractions that hold equivalent values.

Simplifying Fractions Students explore the common methods used to simplify fractions so that they are easier to use in calculations.

Comparing Fractions Students explore methods to compare the size of fractions using their skills of simplifying and establishing equivalence.

Mixed Numerals Students learn to convert improper fractions to mixed numbers.

Improper Fractions Students learn to convert mixed numerals to improper fractions.

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Shading Fractions 1 * A fraction is a part of a whole. It is used to describe how

This is a Ready-Ed Publications' book preview. much of something is left. Look at the first circle right.

We can say that 6⁄6 are equal to a whole. The number on top is known as the numerator and tells us how many parts we have. The bottom number is known as the denominator and tells us exactly how many parts the whole has been divided into. The second circle has four pieces left. How can we represent this as a fraction?

* Task a

Circle the denominator in each of these fractions.

* Task B

What fraction is shaded in each of these pictures?

3 4

6 7

a)..................

* Task C 1 4

*

Task D 2 4

= =

7 8

b)..................

4 8

6 6

=

=

9 10

4 4

1 6

c). ................

d). ................

Shade the fraction for each of these.

3 6

4 8

2 7

6 6

2 3

Complete the number sentences below by shading in the correct amount.

The first one has been done for you.

4 2 1 3 = 4 8 5 = 10 3 = 6 6 =

=

Go to www.readyed.net =

challenge * taskWhate: should I order if I’m really hungry: a pizza cut into ten pieces or twelve pieces?

7

* Task a

* Shading Fractions 2

Shade each of the following fractions on the diagrams.

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

3 8

b)

2 5

c)

1 6

d)

3 4

e)

4 9

f)

6 10

* Task b

Look at each shaded diagram and write down the fraction that is shaded.

a)

b)

c)

d)

e)

f)

Task c:Go Challenge to Your Partner www.readyed.net * Create four of your own shaded grids (you may like to use grid paper) similar to those in Task B above.

See if your partner can give you the correct fraction for each of your grids.

8

* Task a

* Shading Fractions 3 Slice up each of these shapes into the correct number of equal parts and shade the amount to be shared.

This is a Ready-Ed Publications' book preview. a) 2

b) 1

5

c) 2

2

3

•

d) 3

e) 11

4

25

f)

1 8

•

* Task b a) 5

8

•

Slice up each of these shapes into the correct number of equal parts and shade the amount to be shared. b) 2

3

c) 3

4

Task c: Personal Challenge * When you get home, look in your fridge and estimate each of these fractions.

Go to www.readyed.net • Estimate the fraction of milk left in the carton.

• Estimate the fraction of soft drink left in the bottle.

• Estimate the fraction of jam left in the jar.

9

* Equivalent Fractions 1

Equivalent fractions have the same value. Look at the pizza below.

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

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

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

In the first picture, half of the pizza has been eaten. We can say that two quarters of the second pizza has been eaten. In the third picture we can see that three pieces or 3⁄6 of the pizza has been eaten.

Each picture shows that half the pizza has been eaten. The only difference is that each pizza has a different number of pieces left. Write the number of pieces left as a fraction under each pizza.

We can say that these three fractions are equivalent as they represent the same value.

* Task1 a

Shade these equivalent fractions in the shapes below.

3 4 2 6 8 4

* Task B

Circle the fractions that represent the amount shaded in the picture.

There may be more than one answer.

2

a. 1 4

2 8

1 3

b. 2 4

1 2

1 3

c. 1 5

5 10

2 5

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c: Challenge * taskAnthony has ⁄ of his chocolate bar left and Mel has a quarter. Who has the most chocolate left?

1

10

3

4 10

* Equivalent Fractions 2 Task A * This is a)

1 3

a Ready-Ed Publications' book preview.

Shade each of these fractions and decide if they are the same fraction. and

2 6

b)

1 2

and

3 4

c)

1 2

and

4 8

and

2 8

f)

1 3

and

3 9

1 = 3 2 = 6

1 = 3 2 = 6

The same!

Draw the fractions in yourself before shading. d)

4 5

* Task b

and

1 4

e)

1 4

Circle which pair of fractions are the same.

a)

1 5

and

2 10

b)

1 2

and

2 4

c)

1 3

and

1 4

d)

1 2

and

5 10

e)

2 7

and

3 14

f)

8 10

and

16 20

g)

2 6

and

5 12

h)

25 50

and 50

100

* Task c: Research Challenge

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In small groups of 3 or 4 students, research “Equivalent Fractions”. Write a half page report on what Equivalent Fractions are and use pictures and diagrams to help explain what you mean. Make sure you give some examples of pairs of equivalent fractions. Present your report to the class.

11

* Equivalent Fractions 3

*

Task a

Look at the fraction in the column and circle the equivalent fractions.

The first one has been done for you.

This is a Ready-Ed Publications' book preview.

2 a. 3

3 6

5 8

6 8

8 12

6 9

1 b. 2

2 4

5 10

4 9

6 12

7 12

1 c. 3

3 6

4 12

3 9

2 8

4 6

1 d. 4

2 8

3 6

2 5

3 7

3 12

2 10

1 4

3 15

4 20

3 6

1 e. 5

* Task b 1 4

3 5

Shade in the correct amount to match each fraction with its diagram.

2 3

5 6

3 6

4 4

1 3

3 4

Order the above fractions starting with the smallest. ________________________________

Challenge * taskMareec:Go tomade eachwww.readyed.net and Paul’s mum of them a blueberry pie. Maree cut her pie into eight pieces and Paul cut his pie into ten pieces. Both of the children then ate half of their pies.

How many pieces would each child have left?

12

Equivalent Fractions 4 * We know that there are many ways of writing a half. For example, if a cake has been cut into four even pieces then two pieces will be equal to a half. We would write this as 2⁄4 and say that 2⁄4 = 1⁄2. We now know that there are two 1⁄4 in a 1⁄2.

This is a Ready-Ed Publications' book preview.

Fraction Chart

1 10 1 9

1 10 1 9

1 8

1 10

1 10

1 9

1 9

1 8

1 7 1 6

1 10

1 8 1 7

1 4

1 8 1 7

1 7 1 6

1 5

1 5

1 4

1 3

1 8

1 6

1 5 1 4

1 10 1 9

1 8

1 7 1 6

1 5

1 10 1 9

1 9

1 8

1 6

1 10

1 9

1 7

1 6 1 5

1 10

1 9

1 8 1 7

1 10

1 4

1 3

1 3

1 2

1 2 1 1

Task A Look at the fraction chart and the way that it has been divided up.

*

Use the chart above to answer these. How many …

a) 1

‘s in 6

b) 1

‘s in 1

c) 1

‘s in 1

d) 1

‘s in 2

e) 1

‘s in 5

f) 1

‘s in 1

g) 1

‘s in

h) 1

‘s in 4

4

6

8

3

10

4

5

10

9

8

3

4

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2

3

3

6

* taskIs b:⁄ Challenge greater than or less than ⁄ 3

50

3

?

500

13

* Equivalent Fractions 5 Task a Simplify each fraction to make it into a smaller, equivalent fraction. * This is a Ready-Ed Publications' a.

b.

45 ÷ 5 60 ÷ 5

=

9 ÷ 3 12 ÷ 3

=

c.

book preview.

3 4

d.

8 24

16 36

e.

21 28

f.

55 75

g.

110 250

h.

36 48

54 90

*

Task b

a.

4 5

i.

=

16

20

32 46

For every fraction you can think of, there are many equivalent fractions that you can make. Fill in the spaces to make the equivalent fractions.

40

=

50

=

80

b.

100

d.

c. =

3

10

=

6 9

=

60

e.

50

=

4 20

=

7

=

g.

=

24

=

3

=

15 40

h.

1

=

60

=

2 12

=

=

4

=

25 = 75 100

f.

6

15

2

70

35

=

21 30

=

=

200

i.

5 11

=

33

=

10 55

=

22

15

=

12

=

40

=

to www.readyed.net Partner Challenge * Task c:Go

16 60

Create a task of ten questions, similar to those in Task B, for your partner to answer. Make sure you work out the answers before giving the worksheet to your partner!

14

Simplifying Fractions 1 * The fractions below can all be expressed as 1 because they represent all parts of a whole.

This is a Ready-Ed Publications' book preview.

3 3

9 9

* Task A

7 7

50 50

6 6

20 20

Write four fractions below that are equivalent to a whole.

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

* Task b

Shade the shapes below according to the fraction.

2 2

4 4

12 12

20 20

* Task c2

Use the pictures and circle the amounts shown below.

4 3 4 8 6

12 12

All of the amounts you have shown above are equal to _________________

*

Task d

4 8

4 12

Use a red pen to circle the fractions below that represent a third.

Use a blue pen to circle the fractions equivalent to a half.

3 9

20 40

5 10

50 100

2 6

5 15

6 12

100 200

e: Challenge Go to www.readyed.net * task Kathy was checking her netball goal scoring for the last three games. In the first game she scored 15 of the 28 goals for the game. In the second game a total of 36 goals were scored by her team of which Kathy scored 18 and in the third game she scored 12 out of 26 goals. In which game did Kathy score exactly half the goals?

15

Simplifying Fractions 2 * We can simplify fractions in another way. By looking at the

This is a Ready-Ed Publications' book preview. * Task A fraction chart on page 13 we can see that 6⁄8 is equivalent to 3⁄4.

If we look at the fraction itself we can see that for 6⁄8 to become 3 ⁄4 we divide both the numerator and the denominator by 2.

6 ÷ 2 = 3 8 ÷ 2 = 4

Simplify these fractions by dividing by two.

8 = 12

4 = 10

* Task b 9 ÷ 3 = 3 12 ÷ 3 = 4

2 = 6

2 = 4

4 = 12

We can divide by other numbers to simplify fractions.

Write simplified fractions for these: 5 = 20

80 = 100

3 = 18

4 = 12

Sometimes it is possible to divide the numerator into the denominator to simplify a fraction. For example, with 3⁄9 we have 3 as the numerator and 9 as the denominator.

We know that 3 goes into 9 exactly three times and we can simplify the fraction to 1⁄3 because 3 goes into 3 once and into 9 three times.

* Task c

Use this method to simplify the fractions below.

*4 Task d

Express these fractions in the simplest form.

e * Task 3

Match a fraction on the top line with a fraction on the bottom line.

4 3 10 4 12 = .............. 15 = .............. 20 = . ............. 8 = ..............

20 2 40 50 200= .............. 10 = .............. 80 = . ............. 100= .............

6 9 3 20 = .............. 30 = .............. 18 = . ............. 27 = ..............

2 8 10 15 80 = .............. 100= .............. 12 = . ............. 20 = .............

*

4 16 = .............

6 18 = .............

5 20 = ..............

7 14 = ..............

5 30 = .............

3 12 = .............

4 10 = ..............

8 10 = ..............

4

7 8

9 20

200 1000

3 50

6 200

14 16

6 8

3 100

4 20

6 100

18 40

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task f: Challenge In his last maths test Aaron scored 75 out of a possible 100. What is the simplest way of expressing the fraction of the sums that Aaron correctly answered?

16

* Simplifying Fractions 3

Task A * 1000

Simplify these by dividing by ten or a hundred.

Task b * 35

Simplify these fractions.

This is a Ready-Ed Publications' book preview.

50 1000 = ............ 60 = .............

200 800 800 = ............ 500 = .............

40 25 75

700 900 = . .............

800 1000 = ............

60 20 100 = . ............. 50 = ............

80 20 = .............

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

10 50 100 = ............. 200 = . ........

54 25 85 25 30 = ............ 60 = ............. 30 = . ............. 90 = ............ 40 = ............. 90 = . .........

40 75 120 480 48 = ............ 80 = ............. 100 = . ............. 200 = ............ 2000= ............. 50 = . .........

* Task c

Word Problems: Where possible express your answers in the simplest form.

1. Mark has sixteen apples and Tony has eight. Mark has eaten eight of his apples and Tony has eaten three. What fraction does Mark have left? _________ What fraction does Tony have left? _________ 2. Sandra has twelve socks in her draw. One third of the socks are red and the rest are blue. How many blue socks does Sandra have? _________ 3. Donelle is sharing her birthday cake with four friends. She has cut the cake into ten pieces. What fraction will each person receive? _________ 4. Tarlie has counted twenty students in her class and has noticed that five of the students wear glasses. What fraction of the students do not wear glasses? _________ 5. Fiona and Peter played twelve games of chess. If Fiona won nine games, what fraction did Peter win? _________ 6. Steve sells hotdogs at the football. He had enough supplies for 100 hotdogs. At the end of the day he had twenty hot dogs left over. What fraction did Steve sell? _________ 7. In Jamie’s maths exam there were 30 questions of which he answered twenty five

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correctly. What fraction did Jamie answer incorrectly? _________

8. Jason is captain of his cricket team and there are twelve boys in the team. Four boys were injured in the last game. What fraction of the team were injured? _________ 17

* Comparing Fractions 1 * Task A

Shade in the boxes to show which is larger.

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

3

2

4

Which is larger?

4

________

/8

/8

4

2

Which is larger? ________

Rule: If the denominator is the same, then the one with the HIGHER numerator is larger.

* Task b

Put these fractions in order.

/4, 2/4, 1/4, 3/4 =

______________________________________

/8, 4/8, 1/8, 5/8, 3/8, 2/8, 8/8, 6/8, =

______________________________________

4

7

* Task c

< 2/3 /3 _____

1

Using the symbols > and <, show which fraction is larger.

6

/7 _____ 3/7 > more than

/10 _____ 8/10

5

3

/6 _____ 1/6

< less than

Go to www.readyed.net /8 _____ 2/8

4

18

5

/9 _____ 9/9

3

/6 _____ 2/6

7

/9 _____ 3/9

* Comparing Fractions 2 * Task A

Shade in the boxes to show which is larger.

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

2

2

4

Which is larger?

5

________

/8

/6

1

1

Which is larger? ________

Rule: If the numerator is the same, then the one with the smaller denominator is larger.

*

Task b

If you like pizza, would you rather have 1/4 of a pizza or 1/2?

/4 is smaller

1

The denominator is larger.

* Task c

/4 _____ 1/3

1

/2 is larger

1

The denominator is smaller.

Using the symbols > (more than) and < (less than), show which fraction is larger.

2

/7 _____ 2/4

/10 _____ 5/6

5

/5 _____ 3/6

3

Go to www.readyed.net /5 _____ 4/8

4

5

/9 _____ 5/7

3

/6 _____ 3/9

/8 _____ 7/10

7

19

* Comparing Fractions 3

*

Task A

Look at the pairs of fractions below. Which is larger? Circle the correct answer.

You may like to draw your own rectangles to help work this out. Look at the first example.

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

1 = 3 1 = 4

d)

1 3

b)

1 5

or

1 4

c)

1 5

or

1 3

1 10

e)

1 7

or

1 2

f)

1 6

or

1 9

1 is larger!

3

1 20

Task B * a 3 4

d

1 4

or

1 3

or

Circle which of each pair of fractions is the largest.

1 4

or

or

4 6

b

3 12

or

7 12

c

2 5

or

5 5

e

5 8

or

1 2

f

2 9

or

2 6

Challenge * Task C: class Think of a fraction, any fraction, with a denominator of either 2, 4, 8, 16, 32 or 64.

Go to www.readyed.net Write your fraction nice and large on a piece of A4 paper.

Everyone in the class has to line up in order from the smallest fraction to the largest fraction.

Be sure to help your classmates get the order right!

20

* Comparing Fractions 4

Task a * Divide this line into 8 equal sections. Place each of these fractions on the right spot on the line.

This is a Ready-Ed Publications' book preview.

3

A: 8

7

B: 8

1

C: 2

1

D: 4

7 8

B

Divide this line into 10 equal sections. Place each of these fractions on the right spot on the line.

4

A: 10

*

Task b 1

A: 6

9

B: 10

1

C: 5

3

D: 5

1

E: 10

Draw a line and divide it into 9 equal sections so that you can place each of these fractions on the right spot on the line.

2

B: 3

3

C: 9

5

D: 9

Draw a line and divide it into 12 equal sections so that you can place each of these fractions on the right spot on the line.

5

A: 12

1

B: 3

1

C: 12

3

D: 4

11

E: 12

c: Small group challenge *In Task a group of 3 or 4 students you will make a pack of cards to use to play “Snap”.

Go to www.readyed.net snap!

Make up 20 cards, and on each card write a fraction that has a denominator of 2, 3, 4, 6, or 12. The numerator can be any number smaller than the denominator.

It will be played like the normal game of “Snap”, but instead of having matching cards, you need matching fractions (fractions that are equivalent).

21

Improper Fractions 1 * Look at the three pies below. Each has been cut into quarters.

This is a Ready-Ed Publications' book preview.

How many quarters are there altogether?__________ We can express this as

* Task A

12 . This is known as an improper fraction.

4

Use the shapes below to complete the following. The first one has been done for you. b)

a)

+

+

3+3 6 2 =1 = 4 4 4

2 4 = + 5 5

=

d)

c)

+ 5 3 = + 6 6

+ 4 8 = + 10 10

=

=

f)

e)

+ 7 5 = + 9 9

+ 4 4 = + 5 5

=

=

h)

g)

+

+

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4 6 = + 7 7

=

7 5 = + 8 8

=

b: Challenge * task Joe had six apples which he cut into quarters. Express the number of quarters Joe has as an improper fraction.

22

* Improper Fractions 2 Follow this example: 3 2 3+2 5 1 + = = = 1 4 4 4 4 4 5 ⁄4 is known as an improper fraction because the numerator is greater than the denominator. This means that there is more than 1 whole. We know that 4⁄4 is equal to one whole so 5⁄4 must be equal to 1 whole and 1⁄4 or 11⁄4 .

This is a Ready-Ed Publications' book preview.

A. Express the answers to these sums as improper fractions.

6 5 = .............. + 9 9

2 5 + = ..............

6 6

8 4 + = ..............

10 10

3 6 + = ..............

7 7

4 3 = .............. + 5 5

4 7 + = ..............

8 8

10 10 + = ..............

15 15

12 15 + = ..............

20 20

B. Simplify these fractions. The first one has been done for you.

1

2 8

= 1

1 4

2

6 9

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

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

2

6 8

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

5 108 = .....................

3 126 = .....................

3

4 6

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

2

1

3 6

4 8

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

C. 4⁄4 = 1 so 14⁄4 is equal to 2. Complete the following by adding the fractions.

2 2 2 3 4 2 5 4 + + + = .............. = .............. = .............. 1 4 + 1 4 = ..............

5 5 6 6 9 9

2

2 9

+ 1

7 9

9 1 2 = .............. 7 10 + 1 10 = ..............

3

+ 1

1 3

= .............. 4

5 6

+ 2

1 6

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

D. Jessica had four whole oranges and half of an orange and Ben had one orange and a half. If they put them together how many oranges would there be?

E. Hamish divided six bananas into thirds. How many thirds did he now have?

Express your answer as an improper fraction.............................................................................

F. Suzanne had four sets of pencils each with eight colours

and half a set with four colours. Drew gave her three

pencil sets and four extra pencils. Write a number

sentence to show how many pencils Suzanne has.

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

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Mixed Numerals 1 * When there is more than one whole the fraction is expressed as a mixed numeral.

This is a Ready-Ed Publications' book preview.

For example, the shaded area in the circles below represents 41⁄3.

1

+

* Task A 2

1 5

4

2 3

3

1 8

1

3 6

1

+

1

+

1

1 3

+

Shade in the correct amount below.

We can also express the above mixed numerals as improper fractions.

For example, 2

* Task b

1 5

is equal to

5 5

+

5 5

+

1 5

= 11 5

Express these mixed numerals as improper fractions.

4 6

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

3

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

2

5 6

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

6

1 2

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

4

3 4

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

2 109 = .....................

3

5 6

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

2

4 7

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

5

2 3

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

8

1

*

2 4

4 5

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

45 3 100 = .....................

55 1 200 = .....................

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task c: Challenge At a party Mark cut 5 cheesecakes into 10 pieces each. At the end of the party the following amounts were left on each plate; 3 pieces, 2 pieces, 6 pieces, 1 piece and 4 pieces. Express the amount left over as a mixed numeral.

24

* Mixed Numerals 2 To convert improper fractions into a mixed numeral divide the denominator into the numerator. For example, 3⁄2 = 11⁄2. There are three halves and we know that two halves make a whole. One half is left over so the answer is 11⁄2.

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

Change these improper fractions into mixed numerals.

5 7 8 2 = .............. 3 = . ............. 2 = ..............

15 9 8 2 = .............. 3 = . ............. 5 = .............

85 32 25 16 10 = .............. 5 = .............. 6 = . ............. 3 = ..............

4 3 = ..............

12 6 = ..............

* Task b

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

20 6 = .............

10 6 = ..............

20 9 = ..............

39 100 7 = ............. 20 = ..............

Change these mixed numerals into improper fractions.

3

1 4

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

5

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

6

2 6

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

2

3 7

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

9

1 2

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

7 101 = .....................

8

4 8

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

7

4 6

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

9

8 9

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

5

*1 Task c 8

2 3

4 5

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

4 203 = .....................

60 3 100 = .....................

Place these fractions in order starting with the smallest.

3

20 8

1 8

6 8

8 8

4

2 8

2

13 8

5 8

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

* Task d

Use <, > or = to make these true.

11 6

1

1 6

2 3

3 2

5 7

75

9 5

1

21 3

3

12 2

4

4 5

4 3

4 5

5 2

2

13 6

1

3 6

5 10

10 5

3

18 6

24 6

16 4

1 5

task e: Challenge Go to www.readyed.net *Nicole cut some oranges into quarters for her netball team to eat at half time. At the end of the game there were 17 quarters left on the tray. Express the fraction of oranges on the tray as a mixed numeral.

25

* Fraction Skills Review 1

* Task A

Write an equivalent fraction for each of these:

* Task b

Place = or ≠ in the box.

This is a Ready-Ed Publications' book preview.

2 = ................... 6 = ...................

4 8 2 1 = ................... = ...................

6 4 1 2 3 = ................... 3 = ...................

3 = ................... 2 = . .................. 3 = ....................

9 10 5 4 6 4 = ................... = . .................. = ....................

4 9 8 4 8 4 = ...................

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

6 10 5 = ....................

1 4

2 3

3 4

6 8

2 5

3 6

2 3

3 4

4 6

2 3

4 8

1 2

1 3

1 2

2 4

2 5

3 3

6 6

4 5

5 6

7 8

7 9

2 2

9 9

* Task c

Use <, >, or = to make these correct.

1 3

1 2

3 4

4 4

5 6

7 9

2 5

2 6

3 8

3 6

3 6

4 8

2 5

4 10

2 7

7 8

1 5

1 4

2 3

3 4

7 7

3 4

1 1

4 9

* Task d

3 7

Shade the correct number of pieces for each picture.

2 4

5 8

6 9

9 10

4 6

Now write the fractions above in order starting with the smallest.

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

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

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

*

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task e: Challenge Michelle and Andy collect stamps. Michelle’s album is 3⁄4 full while Andy’s is 3⁄8 full.

Who has collected the most stamps?

26

* Task A

* Fraction Skills Review 2

Fill in the missing numerators for these equivalent fractions.

This is a Ready-Ed Publications' book preview.

1 = 4 8

1 = 3 9

1 = 10 20

1 = 2 10

1 = 3 12

3 = 4 12

4 = 5 10

3 = 5 15

2 = 6 3

1 = 5 10

3 = 9 12

2 = 4 8

* Task b

Write the missing denominators into the boxes.

1 2 = 5

2 4 = 3

3 6 = 10

2

4 8

3 6 = 5

4 8 = 6

4 2 = 10

2

5 1 = 10

3 1 = 9

4 1 = 12

9 3 = 12

* Task c

=

1 3

=

Write these fractions in the simplest form. The first one has been done for you.

3 8 = .............. 4 = . ............. 6 = .............. 20 = .............

9 = 12 4 10 8 12 40 50 = .............. 5 = .............. 15 = . ............. 30 = .............. 4 = .............

100 15 30 60 10 100 5 14 18 160 = .............. = .............. = . ............. = .............. = .............

200 10 20 20 200

3 = ..............

6 6 = ..............

8 40 = ..............

40

d: word problems * 1. taskJessica has three bread rolls and has cut them into quarters.

How many quarters does she have altogether?................................

2. Simon has four red marbles and six blue marbles. He gave two of the red marbles to Fiona and three of the blue marbles to John.

What fraction of each colour did Simon give away?........................

3. Natalie has six pieces of fruit and two pieces are bananas.

A third of the pieces are apricots and the rest are pears.

How many of each fruit does she have?...............................................

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4. There are ten students in the art class. One fifth of the class are painting and two tenths of the class are drawing. Six tenths are making pottery.

How many students are doing each activity?

Painting:................................ Drawing:............................... Pottery:....................................

27

* Fraction Skills Review 3 * Task A

What fractions of the shapes below are shaded? Simplify your answer.

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

* Task b

Shade these amounts below.

1 3

2 6

* Task c

Complete the following using = or ≠. You might like to refer back to the fraction chart on page 15.

1 4

2 8

1 3

2 6

2 8

4 16

3 12

2 16

1 3

2 9

2 6

2 3

2 8

3 12

1 4

1 3

* Task d

*

3 9

Use =, < or > to make these true.

1 4

1 3

1 6

1 8

2 4

2 3

5 6

7 8

4 9

2 7

3 8

3 7

9 10

9 9

4 4

3 3

2 5

2 6

1

2 3

5 5

2 2

1 6

1 9

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task e: Challenge Emily and Sarah are painting the fence in the backyard. Sarah has painted 1⁄3 of the fence posts and Emily has painted 3⁄8 of the fence posts. Who has painted the most posts?

28

* Task A

* Fraction Skills Review 4

Circle the greater fraction in each pair. The first one has been done for you.

This is a Ready-Ed Publications' book preview.

1 5

3 10

2 6

3 6

1 2

2 5

4 9

1 2

1 3

6 7

4 6

4 5

5 10

5 8

4 8

3 9

2 6

2 5

7 8

8 9

1 2

1 10

5 5

3 4

b * Task 3 6

2 3

1 3

3 9

2 4

5 10

3 6

1 2

4 10

14 20

6 9

4 6

8 10

4 5

9 9

7 7

c * Task 3 6

<

8 < 12

* Task d

Place = or ≠ in the boxes below.

Complete the following by adding a fraction of your own.

2 > 3

4 6 < > 5 12 6 > 4 < 3 < 9 > 8 6 7 10 How much of each pie is shaded? Express your answer in the simplest fraction.

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

Task e * a. 2

9 > 9

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

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

Match the fractions on the left with a fraction on the right.

b. 4 c. 3 50 60 4 3 100 6 90 9 16 4 8 7 8 2 2 9 18 8 12 8 5 75 3 40 3 4 2 100 8 60 4 10 6 5 6 2 14 8 4 10 16 3 16 12 6 task f: Challenge Murray and Sue each receive the same amount of pocket money each week. Murray has spent 3⁄7 of his pocket money and Susie has spent 4⁄5. Which child has spent the most money?

*

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29

* Fraction Skills Review 5

* Task1 A

Order these fractions from smallest to largest.

4 1 1 6 5 2

This is a Ready-Ed Publications' book preview.

Task b 3

2 5

3 3

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

*

Place these fractions in order from largest to smallest.

1 6

10 10

3 9

1 4

1 7

2 5

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

* Task c 5 6

1

Use < or > in the boxes below to make the number sentences true.

2 12

1

3 6

4

* Task d

2 6

5 5

1

7 7 6 7

4

* Task e

5 8

7 8

1

2 3

3 7 9

7 5 10

5 7 10 2

2 3

4 1 2

2

5 6

1 3

4

3 4

2 4

5

1 5

5

4 12

1 3

5 9

9

2

3 4

6

1 2

5 6

3

2 3

11 3

7 10

7 7 10

1

1 7

2

1 7

15 5

9 3

8 3 12

3

2 3

15 15

6 6

Colour the amounts shown and complete the number sentence using =, < or >.

3 6

5 6

7 8

3 4

7 8

task f:Go Challenge to www.readyed.net *Joanne gets 80¢ a page for typing. If she types ⁄ of a page how much money will she receive?

3

30

1 3

Use <, > or = to complete these.

3 3

4

1

1 9

4

Teachersâ&#x20AC;&#x2122; Notes

This is a Ready-Ed Publications' Calculating With Fractions book preview.

This section equips students with the skills necessary to calculate with fractions.

Students explore addition and subtraction of fractions both with and without common denominators, and are always encouraged to give answers in their most simplified form.

Students also learn the mental strategies involved to multiply and divide fractions.

These calculation skills are then applied to common calculations such as finding the fraction of an amount and expressing an amount as a fraction of another amount. It is important here that students have a good grasp of units and their conversion.

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* Task A

Addition With The Same Denominator * Add these fractions and express the answer as a mixed numeral.

This is a Ready-Ed Publications' book preview.

For example:

4 107 + 6 109 = 7 = 4 + 6 + 10 + = 10 +

9 10

16 10

= 10 + 1 +

6 10

6

= 11 10 = 11 2

+ 4

5

4 5

3

=

3

3 5 5 6

+

4 6

=

1 3

+ 2

2 3

6

=

* Task b

2

7 9

2 9

+ 4

=

3 7

=

+

5 7

3

5

3 8

+ 6

7 8

3 8

+

5 8

=

5 8

5 8

+ 4

=

3

=

Add the amounts shown in the shapes below.

+

+

+

task c:Go Challenge to www.readyed.net *Jerry had three bread rolls and ⁄ of a roll and Kelly had five rolls and ⁄ of a roll. What fraction of bread rolls did ...................................................... . ...................................................

2

they have together?

32

5

4

5

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

* Addition And Subtraction With The Same Denominator 1

This is a Ready-Ed Publications' book preview.

You can only add or subtract fractions easily if the denominator is the same.

Add whole numbers and fractions separately.

Rule: whole number × denominator + numerator = new numerator.

e.g. 11/2 + 51/2 = 6 + 2/2 = 6 + 1 = 7

You + or – fractions by + or – the numerator. Do not change the denominator.

Sum

+ or – whole numbers and fractions separately

Change any improper fractions

+ or – all parts

Add these:

3

2 + 3

2

1 3

5 and

2 3

4

5 + 8

1

7 8

5 and 128

2

5 + 6

5

2 6

4

3 + 7

2

5 7

2

4 + 5

4

3 5

3

3 + 4

5

3 4

None

5 +1

4 8

5

2 3

6

4 or 8

2

1 6

6

1 2

Subtract these:

3

3 – 6

1

2 6

3

8 – 9

2

2 9

2 and

1 6

None

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4 108 3 107

33

* Addition And Subtraction With The Same Denominator 2

* Task a

Add the following fractions.

This is a Ready-Ed Publications' book preview.

1

3

1 3

+

1

4

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

2 3

1

+

2 3

3 7

2

+ 2

5 7

1 4

2

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

1

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

+

2 4

+ 2

1 4

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

2

8

+

7 8

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

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

Task b *

–

4

2 3

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

2 5

– 1

1 5

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

1

–

+

2 3

1

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

3

2 5

+ 4

4 5

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

5

+ 4

3 4

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

1 5

+ 2

2 5

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

3

8

9 10 + 3 10

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

2

4 5

+ 2

4 5

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

Subtract the fractions below.

1 3

2

1 3

5 6

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

3

–

1 4

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

3

1 3

–

2 3

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

10

–

3 5

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

6

9

–

2 9

1

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

4

2 5

– 2

3 5

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

2

– 1

2 3

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

2 3

–

2 3

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

6

3 9

– 4

4 9

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

6

– 3

4 5

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

c: word problems *1. taskSarah had nine chocolate biscuits and five of them were iced. She cut each

biscuit in half. Express the total number of iced biscuits as a fraction. _____________

2. Lucy had 4 pears which she cut into quarters. She ate two pears and a quarter.

How much does she have left? _____________ 3.

Amanda has made some soup and is serving dinner for the family.

She has given half of the soup to her Dad, a quarter to her Mum, an eighth to her younger sister and an eighth to herself.

What fraction of the soup remains? _____________

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4. Julian makes model aeroplanes and buys each piece separately.

Each aeroplane had 10 pieces. He has seven completed aeroplanes and 2⁄5 of another one. How many pieces does he have in his collection?_____________ 5. Brad is 14⁄10 of a metre tall. How many centimetres tall is Brad? _____________ 34

* Addition With Different Denominators So far we have added thirds to thirds and quarters to quarters and so on. We can say that these fractions have like denominators. Sometimes we need to add fractions with unlike denominators. Look at the diagrams below and write the fraction of the remaining portions of pie underneath.

This is a Ready-Ed Publications' book preview.

If we combine the leftovers, what fraction will we have? To find the answer we need to express the fractions so that the denominator is the same. This is known as finding the lowest common denominator.

Example 1: To add

1 4

we convert

1 4

so sum is

=

3 8

+

* Task b

2+5 8

2 3

Example 2:

2 8

=

6+1 9

7 8

=

7 9

1 9

+

Complete these sums by using equivalent fractions to find the lowest common denominator.

* Task a 3 4

5 8

+

1 3

5 6

+

2 3

2 9

+

1 5

1 10

+

Add these fractions and simplify the answer.

2 6

+

1 3

2 4

+

4 8

4 10

+

2 5

1 9

+

2 3

3 4

+

5 8

2 6

+

2 3

3 6

+

1 2

1 2

+

6 10

c: Challenge Go to www.readyed.net * task Darren played in three quarters of his basketball match this Saturday. Last Saturday he played half a game, and the Saturday before that he was on for only half of the first quarter. What fraction of games has Darren played in the last three weeks?

35

Subtraction With Different Denominators * When we want to add fractions with different denominators, we must first convert each fraction so that they share the same denominator, or the lowest common denominator.

To subtract fractions with different denominators we follow the same process.

This is a Ready-Ed Publications' book preview.

4

1

Example: To calculate 5 − 4 The lowest common denominator of 5 and 4 is 20, so we want to convert both fractions so that they have a denominator of 20.

4

16

We convert 5 to 20 by multiplying the top and bottom by 4.

1 5 We convert 4 to 20 by multiplying the top and bottom by 5.

16

5

16-5

11

Our calculation becomes 20 − 20 = 20 = 20 In this case, this is our final answer since we cannot simplify this fraction further.

* Task a

Calculate each of the following by first filling in the boxes.

a. 9 2 – 10 5

–

=

c. 4 1 – 5 3

b. 7 1 – 8 3

=

–

=

=

=

=

=

=

=

d. 4 1 – 5 6

e. 2 1 – 3 2

–

=

=

f. 4 1 = 6 4

–

=

=

=

=

=

=

=

Task b * a. 1 1

–

–

Calculate each of the following by showing all working. Be sure to simplify the answers.

– 2 3

b. 5 1 – 6 3

c. 18 2 – 20 5

d. 7 2 – 8 5

e. 6 1 – 7 4

f. 4 1 – 5 10

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36

* Subtraction With Mixed Numerals 1

To subtract mixed numerals, first convert the fractions to improper fractions.

For example: 2 15 – 1 35 3 18 – 2 38

This is a Ready-Ed Publications' book preview.

11– 8 5 3 = 5

25 – 19 8 6 = 8 3 = 4

=

* Task a 2

1 6

–

=

Convert these fractions to improper fractions to find the answer.

4 6

3

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

* Task b

4 9

–

7 9

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

6

3 7

4 7

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

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

– 5

Express these whole numbers as improper fractions. The first one has been done for you.

2 =

18 9

3 =

6

4 =

5

6 =

2

4 =

1

5 =

2

6 =

3

7 =

3

* Task c

Subtract the fractions from the whole numbers by changing to improper fractions.

Write your answer as a mixed numeral.

3 4

8 –

7 –

3 10

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

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

10 3 – 2 20

4 –

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

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

* Task d 3

4 8 2 10 – 1 10

4 5

10

–

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

7 30

6 –

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

2 –

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

2 6

1 9

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

Subtract these fractions.

– 2

1 5

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

9 –

75 100

2 3

4 –

6 7

10 –

2 3

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

4 –

7 20

5

2 6

–

3 6

3

2 5

– 2

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

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

9 11 3 50 – 2 50

8 – 3

4 5

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

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

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

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

e: Challenge * task During the term Steve had to read 5 books. So far he has read 2 books and ⁄ of a book. What fraction of the 4

books does he still have to read?

6

37

* Subtraction With Mixed Numerals 2

Look at these examples.

This is a Ready-Ed Publications' book preview.

5 8 – 37 – 31 = 8 6 = 8 3 = 4

4

* Task a 5

2 6

1 6

4

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

– 3

2 5

– 3

4 8

9

* Task b 7

6

3 5

2

5

25 – 13 7 12 = 7 5 = 7

1

2 9

– 3

5 9

6

3 5

– 2

4 5

1

3 9

–

4 7

– 4

5 7

3

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

4 5

2

–

4

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

–

– 1

7 8

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

7 10

3

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

7 9

2 8

4 6

– 1

5 6

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

8 20

5

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

2 7

– 3

6 7

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

Fill in the square to make each number sentence true.

1 7

–

1 5

– 5 6

2 3

= 2 2 5

–

–

6 7

– 1

=

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

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

2

4 7

3

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

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

6

7 8

Complete the following and simplify answers where possible.

– 3

10

3

= 3

= 2 = 7

2 5

1 5

–

1 3

= 5

25 5 4 100 – 2 100 = 2

10 –

9

= 9

3 9

1 3

4

4 5

– 3

5

= 1

2 5

4

3 8

– 2

8

= 1

7 8

5 –

2 6

= 4

6

1 6

c: Challenge * task Jason has five bags of marbles and each bag contains eight marbles. He gave two bags

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and three quarters of the marbles in another bag away to David.

What fraction does Jason still have?..........................................................................

How many marbles did David receive from Jason?................................................................................

38

* Task a

* Mixed Addition And Subtraction Of Fractions Perform each calculation and be sure to show all your working.

Leave your answers as mixed numbers in the most simplified form.

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

b.

c.

d.

e.

f.

g.

h.

i.

j.

1 4

k.

1 = 3

l.

4 1 − = 5 2

3 8

m.

5 = 6

+

n.

7 1 − = 10 4

1 12 + 2 13 3 45 2 15

=

1 13 =

−

+

o.

3 = 30

15 1 − = 20 5

3 2 12

+

1 13 =

p.

q.

r.

s.

4 7

4 = 5

7 1 − = 8 7

1 35 + 3 47

=

2 89 + 3 45

=

1 13 −

4 = 5

2 12 −

7 = 8

3 15 + 2 34 1 4 12 −

=

5 = 6

5 14 − 2 23

=

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4 20 30

−

1 16 =

t.

10 25 − 4 79

=

39

* Multiplying Fractions Multiplying fractions is a breeze! Simply multiply the numerators, then multiply the denominators, and simplify your final answer.

This is a Ready-Ed Publications' book preview.

Example: If we wish to multiply 2/3 and 1/4 we multiply the numerators and the denominators (2×1)/(3×4) we then have 2/12 which simplifies to 1/6

Task a * a.

2 1 × 5 3

=

Calculate each of the following by filling in the boxes provided. b. 3 3 × 4 5

=

c. 4 1 × 20 2

= =

d. 5 2 × 6 8

e. 2 4 × 3 6

f. 3 2 × 15 3

=

=

=

=

=

=

* Task b

Calculate each of the following by showing all working. Be sure to simplify your answers.

a. 2 1 × 3 4

b. 7 2 × 20 10

c. 3 2 × 5 12

d. 11 3 × 15 4

e. 7 3 ×4 8

f. 7 4 × 12 6

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Division Of Fractions * Here is a handy little poem to help you remember how to divide two fractions.

This is a Ready-Ed Publications' book preview.

“Dividing fractions is easy as pie! Simply flip the second and then multiply!”

4

1

Let’s see how that works. Example: If we want to calculate 5 ÷ 3 4 3 Then we change our calculation to 5 × 1 where we change the × to a ÷ and then flip the second fraction.

4×3 12 We now have 5 × 1 which gives us 5 . We now change our answer to a mixed 2 numeral which gives us 2 5 .

Task a * a.

Calculate each of the following by filling in the boxes provided. b. 4 3 ÷ 10 4

7 2 ÷ 8 3

×

=

=

c. 5 3 ÷ 6 11

×

=

=

=

=

=

=

=

d. 5 1 ÷ 6 4

e. 3 4 ÷ 12 5

×

=

=

f. 2 2 ÷ 9 5

×

=

=

=

=

=

=

=

Task b * a.

×

×

Calculate each of the following by showing all working. Be sure to simplify your answers.

5 1 ÷ 6 3

b. 3 4 ÷ 10 5

c. 11 1 ÷ 20 2

d. 5 1 ÷ 8 3

e. 3 1 ÷ 5 4

f. 5 2 ÷ 7 3

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* Multiplying And Dividing Fractions

Multiplying two fractions together is easier than adding two fractions together!

All you need to do is multiply the numerators together and multiply the denominators together.

Then just simplify your answer.

2 ×3 6 2 = = For example, if we want to multiply 2 and 3 we can work out the answer like this:

This is a Ready-Ed Publications' book preview. * Task a 3

3 ×5

5

15

Calculate each of the following.

c.

b.

a.

1 4

2 = 5

×

5 8

×

2 = 6

3 4

6 8

2 = 9

×

3 11

×

4 = 6

5 10

1 1 45 × 1 23

2 12 × 3 57

=

×

5 = 6

i.

h.

g.

4 = 7

f.

e.

d.

×

4 16 × 2 34

=

=

Dividing two fractions is easy! We simply flip the second and multiply. For example, if we want to 4 1 4 × 1 = 4 ×2 = 8 = 13 divide by we can work out the answer like this: 5

2

Task b * a.

4 5

÷

5

2

2 = 3

3 4

1 = 3

7 8

÷

1 = 6

÷

1 = 4

÷

2 = 7

10 12

÷

2 = 5

i.

2 58 ÷ 1 12

=

5 9 f.

h.

g.

1 13 ÷ 14

5

c.

b.

e.

÷

5

Calculate each of the following.

d.

5 11

5 ×1

10 35 ÷ 2 15

=

=

ask c: Personal Challenge * TUse Go to www.readyed.net your skills learned on this page to calculate, without a calculator, this sum: 2 5 42

×

5 3

×

4 10

÷

1 10

×

3 4

4 ÷ × 10

4 6

×

2 6

5

Expressing As A Fraction 1 * In everyday life there are many quantities that are expressed as fractions. Every time

you get an assessment back from your teacher you often see what mark you scored out of the total. This is a fraction you see quite often.

When we see quantities expressed as fractions we often want to simplify them so that they are easier to use in future calculations.

For example, if we say there is 200 mL left in a 1L carton of milk, we can first express this as this fraction: 200 since we know that 1L is 1000mL. It’s very 1000 important that the numerator and denominator are of the same units.

To simplify this fraction we then divide the numerator and denominator by the largest number that goes into each. In this case the highest common factor is 200.

So 200 becomes 1 .

This is a Ready-Ed Publications' book preview.

1000

* Task a a.

c.

e.

g.

5

Express each of the following quantities as fractions and then simplify your fraction.

500 g out of 2000g

b.

50c out of 300c

=

=

=

=

25 children out of 75 people

d.

120 mL out of 360 mL

=

=

=

=

5 m out of 1 km

f.

25c out of $2

=

=

=

=

300 g out of 2 kg

h.

150 mL out of 2L

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=

=

=

=

43

* â&#x20AC;&#x2030; Expressing As A Fraction 2

Express each of the following quantities as a fraction. Remember to simplify your answers and to make sure all quantities are in the same units before you begin.

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

c.

e.

g.

i.

k.

m.

44

24 marks out of 48 marks

3 kg out of 21 kg

350g out of 3kg

12mm out of 3cm

45c out of $5

620 mg out of 4g

b.

d.

f.

h.

j.

l.

n.

$15 out of $150

18mL out of 36mL

$1.00 out of $8

450kg out of 2 tonnes

350 m out of 2 km

15 mins out of 2 hours

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3 hours out of 1 day

30 seconds out of 1 hour

Fractions Of An Amount 1 * Often we want to calculate a fraction of a given amount.

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For example, if we want to calculate 3 of 60, this means 1 x 60.

5 3 The word “of” means “multiply”.

To do this easily without a calculator, we first think of how many times 3 can be divided into 60.

3 goes into sixty 20 times.

So 60 broken into thirds looks like 20 20 20.

The numerator tells us that we want just one of these thirds, so just one 20.

So 1 of 60 is 20.

3 Without a calculator, use the above method to calculate each of the following. a.

c.

e.

g.

i.

k.

m.

o.

1 of 24 2

1 of 65 5

1 of 150 10

1 of 64 8

1 of 132 11

1 of 40 20

1 of 63 7

b.

d.

f.

h.

j.

l.

n.

1 of 30 3

1 of 12 4

1 of 20 000 100

1 of 42 6

1 of 108 9

1 of 60 15

1 of 45 000 1000

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1 of 84 12

p.

1 of 350 50

45

* Fractions Of An Amount 2 Let’s say we want to calculate 2 of 40.

5 First of all we want to see how many times 5 can be divided into 40.

5 goes into forty 8 times.

So 40 broken into fifths looks like 8 8 8 8 8.

The numerator tells us that we want 2 of these fifths. So we want 2 lots 8, which is 16.

So 2 of 40 is 16.

This is a Ready-Ed Publications' book preview.

5

* Task a a.

c.

e.

g.

i.

k.

m.

o.

46

3 of 40 4

2 of 60 3

4 of 80 5

5 of 30 6

3 of 50 5

4 of 15 5

3 of 32 8

Without a calculator, use the above method to calculate each of the following. b.

d.

f.

h.

j.

l.

n.

2 of 20 5

2 of 36 6

3 of 35 7

3 of 150 10

5 of 49 7

4 of 36 9

2 of 21 7

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2 of 27 9

p.

3 of 44 11

â&#x20AC;&#x2030; Fractions Of An Amount 3 * Without a calculator, and using the above method, calculate each of the following.

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

c.

e.

g.

i.

k.

m.

o.

q.

s.

1 of 200g 5

2 of 330 m 3

3 of 4900 ml 7

4 of 5000 km 10

5 of $4200 6

5 of 2400L 8

2 of 4400 cm 11

1 of 393c 3

4 of $600 8

b.

d.

f.

h.

j.

l.

n.

p.

r.

1 of $1420 2

3 of 480 mm 4

1 of $320 000 8

3 of $9000 5

1 of 630 people 9

2 of 3500 kg 7

2 of $1200 6

7 of 144 tonnes 12

4 of 900 mL 6

Go to www.readyed.net 3 of 2100g 9

t.

4 of 155 m 10

47

* Real Life Fractions

Answer each of these word problems and be sure to show how you got your answer.

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

b

c

d

e

f

George has 50 bricks and stacks them into groups of 10. Three groups of bricks is what fraction?

Lilly and Billy are sister and brother.

Lilly says to Billy “Mum gave me 14 of the chocolate biscuits!” Billy says 2 to Lilly “Mum gave me 8 of the chocolate biscuits!” Mum says “I gave you both the same amount!”. Is Mum right? Why?

Josie stacked her 40 books into 8 equal piles. How many books does 5 represent?

8

Mrs Clarence has 30 desks in her classroom and she puts 5 desks in each group. Four groups of desks is what fraction?

Billy says to Lilly “I swam in the pool 3 for 4 of an hour and you only swam 4 in the pool for 5 of an hour. I swam longer than you!” Is Billy right? Why?

Timmy’s Mum says he can watch 3 of an hour of TV. How many 5 minutes is Timmy allowed to watch?

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* Answers

Shading Fractions 1 pg 7 Task A: 4, 7, 8, 8, 10, 6 Task b: 2/4, 5/9, 6/8, 2/4 Task c: Check diagrams Task d: 2/4, 4/10, 2/6 Task e challenge: They would both be equal to a whole

Task c challenge: Maree - 4; Paul - 5

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Shading Fractions 2 pg 8 Task A: Check diagrams Task B: a.4/8 b.6/16 c.1/3 d.3/8 e.6/16 f.6/20 Shading Fractions 3 pg 9 Task A: Check diagrams Task B: Check diagrams Equivalent Fractions 1 pg 10 Task A: Check diagrams Task B: a. ¼, 2/8 b. 2/4, ½ c. 2/5, 4/10 Task c challenge: Anthony Equivalent Fractions 2 pg 11 Task A: b. not the same, c. same, d. not the same, e. same, f. same Task B: a. 1/5 and 2/10 b. ½ and 2/4 d. ½ and 5/10 f. 8/10 and 16/20 h. 25/50 and 50/100 Equivalent Fractions 3 pg 12 Task A: a. 8/12, 6/9 b. 2/4, 5/10, 6/12 c. 4/12, 3/9 d. 2/8, 3/12 e. 2/10. 3/15, 4/20 Task B: Check diagrams Order - ¼, 1/3, 3/6, 3/5, 2/3, ¾, 5/6, 4/4

Equivalent Fractions 4 pg 13 Task A: a.3, b.2, c.3, d.4, e.2, f.2, g.6, h.2 Challenge: Greater than

Equivalent Fractions 5 pg 14 Task A: b.1/3, c.4/9, d.¾, e.11/15, f.11/25, g.¾, h.3/5, i.16/23 Task B: b. 2/3 = 10/15 =40/60 c. 2/8 = ¼ = 75/300 d. 10/50 = 7/35 = 3/15 e. 6/16 = 9/24 = 3/8 f. 70/100 = 35/50 = 140/200 g. 1/6 = 10/60 = 5/30 h. 2/11 = 6/33 = 22/121 i. 4/15 = 12/45 = 40/150 Simplifying Fractions 1 pg 15 Task A: Answers will vary Task B: Check Diagrams Task C: Check Diagrams All of the amounts shown are equal to ½ Task d: Red: 4/12. 3/9. 2/6, 5/15, Blue: 4/8, 20/40, 5/10, 50/100, 6/12, 100, 200 Task e challenge: Second game 18/36=1/2 Simplifying Fractions 2 pg 16 Task A: 4/6, 2/5, 1/3, ½, 2/6 Task B: ¼, 4/5, 1/6, 1/3 Task C: 1/3, 1/5, ½, ½, ¼, ¼, 1/5, 1/5, ½, ½, 1/3, ½ Task D: 1/5, 1/5, ½, 1/9, 1/6, 2/5, 1/10, 1/10, 1/6, ¾, ¼, 4/5 Task E: ¾ = 6/8, 7/8 = 14/16, 9/20 = 18/40, 200/1000 = 4/20, 3/50 = 6/100, 6/200 = 3/100 Task f challenge: ¾

Go to www.readyed.net Simplifying Fractions 3 pg 17 Task A: 10/10, 5/6, 7/8, 9/10, 8/10, 2/10, 8/8, 2/5, 6/10, 2/5, 1/10, 5/20

49

Task B: 7/8, 9/10, 5/6, 17/18, 5/8, 1/3, 1/3, ½, ¾, 3/5, 6/25, 24/25 Task C: 1.Mark ½, Tony 5/8, 2.8, 3.1/5, 4.¾, 5.¼, 6.4/5, 7.1/6, 8.1/3

4½+3½=8 Mixed Numerals 1 pg 24 Task A: Check diagrams Task B: 10/6, 14/4, 17/6, 13/2, 19/4, 29/10, 23/6, 18/7, 17/3, 44/5, 345/100, 255/200 Task c challenge: 1 3/5

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Comparing Fractions 1 pg 18 Task A: ¾ is larger, 4/8 is larger Task B: ¼, 2/4, ¾, 4/4 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8, 8/8 Task C: >, <, >, >, <, >, > Comparing Fractions 2 pg 19 Task A: 2/4 is larger, 1/6 is larger Task c: <,<,<,>, >,<,>,> Comparing Fractions 3 pg 20 Task A:: a.1/3, b.¼, c.1/3, d.1/10, e.½, f.1/6 Task B: a.¾, b.7/12, c.5/5, d.4/6, e.5/8, f.2/6 Comparing Fractions 4 pg 21 Task A: Check diagrams Task B: Check diagrams Improper Fractions 1 pg 22 Task A: b.1 1/5, c.2 2/6, d.1 2/10, e.1 3/9, f.1 3/5, g.1 3/7, h.1 4/8 Challenge: 24/4 Improper Fractions 2 pg 23 Task A: 11/9, 7/6, 12/10, 9/7, 7/5, 11/8, 20/15, 27/20 Task B: 1 ½, 2 ¾, 5 4/5, 2 2/3, 3 ½, 3 2/3, 2 ½ Task C: 1, 1, 1, 3, 4, 9, 2, 7 Task D: 6 Task E: 18/3 Task F:

Mixed Numerals 2 pg 25 Task A: 1 1/3, 2 ½, 2 1/3, 4, 1 2/7, 1 4/6, 2, 4 ½, 2 2/3, 3, 3 2/6, 2 2/9, 8 5/10, 6 2/5, 4 1/6, 5 1/3, 5 4/7, 5 Task B: 13/4, 17/3, 38/6, 17/7, 19/2, 71/10, 68/8, 46/6, 89/9, 29/5, 83/20, 360/100 Task C: 1/8, 6/8, 8/8, 13/8, 20/8, 2 5/8, 3 1/8, 4 2/8 Task D: >, <, >, >, <, =, >, <, >, >, =, = Task e challenge: 4 ¼ Fraction Skills Review 1 pg 26 Task A: Answers will vary Task B: ≠,=,≠,≠,=,=, ≠,≠,=,≠,≠,= Task C: <, <, >, >, <, =, =, <, <, <, >, > Task D: Check diagrams Task E: 3/7, 2/4, 5/8, 6/9, 4/6, 9/10 Task f challenge: Michelle Fraction Skills Review 2 pg 27 Task A: 2, 3, 2, 5, 4, 9, 8, 9, 1, 2, 4, 4 Task B: 10, 6, 20, 4, 10, 12, 5, 6, 2, 3, 3, 4 Task C: 4/5, ½, ½, ½, ½, ½, 1/3, ½, ½, 2/5, ¾, ½, ½, 7/10, 9/10, 4/5, 1 task d word problems: 1.12, 2.red ½ blue ½, 3.2 pieces of bananas, apricots and pears, 4.painting 2 drawing 2 pottery 6

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50

Fraction Skills Review 3 pg 28 Task A: ¾, ¼, 1/3, 3/5 Task B: Check diagrams Task C: =,=,=,≠, ≠,≠,=,≠ Task D: <,>,<,<, >,<,<,=, >,>,=,> Task e challenge: Emily

Addition And Subtraction With The Same Denominator 1 pg 33 2 5/6 + 5 2/6 4 3/7 + 2 5/7 2 4/5 + 4 3/5 3¾+5¾

7 and 7/6 6 and 8/7 6 and 7/5 8 and 6/4

7 + 1 1/6 6+ 1 1/7 6 + 1 2/5 8 + 1 2/4

3 8/9 – 2 2/9

1 and 6/9

None

8 1/6 7 1/7 7 2/5 9 2/4 or 9½ 1 6/9 or 1 2/3 1 1/10

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Fraction Skills Review 4 pg 29 Task A: 3/6, ½, ½, 6/7, 4/5, 5/8, 4/8, 2/5, 8/9, ½, 5/5 Task B: ≠, =,=,=,=, ≠,=,=,= Task C: Answers will vary Task D: ¾, 1/3, 4/5 Task E: 4/9 = 8/18, 3/8 = 6/16, 5/10 = 50/100 4/6 = 8/12, 7/8 = 14/16, ¾ = 75/100, 2/3 = 60/90 3/9 = 2/6, 2/8 = 4/16, 4/10 = 2/5, 8/12 = 4/6 Task f challenge: Susie Fraction Skills Review 5 pg 30 Task A: 1/5, 1/3, 2/5, ½, 4/6, 3/3 Task B: 10/10, 2/5, 3/9, ¼, 1/6, 1/7 Task C: <,>,>,>,>, <,>,<,>,< Task D: =,<,>,<, =,=,<,=, >,<,=,=, Task E: >,<,< Task f challenge: 60 c Addition With The Same Denominator pg 32 Task A: 5 1/5, 4 1/2, 7, 12 1/4, 6, 7 1/7, 8 1/4, 4 Task B: 3 ¼ + 2 2/4 = 5 ¾, 3 2/3 + 1 2/3 = 5 1/3, 1 2/6 +1 3/6 = 2 5/6 Task c challenge: 3 2/5 + 5 4/5 = 9 1/5

4 8/10 – 3 7/10 1 and 1/10

None

Addition And Subtraction With The Same Denominator 2 pg 34 Task A: 2/3, 2/4, 2, 3 3/5, 2 1/3, 3 ¾, 8 1/5, 13 1/10, 5 1/7, 1 1/8, 9 ¾, 5 3/5 Task B: 1/3, 2/4, 4/9, 1, 1 1/5, 2 2/3, 1 4/5, 1 8/9, 1/6, 9 2/5, 1/3, 2 1/5 task c Word Problems: 5/9, 1 ¾, none, 74, 140 cm Addition With Different Denominators pg 35 Diagram: ¼, 5/8 Task a: 1 1/8, 1 1/6, 8/9, 3/10 Task b: 2/3, 1, 4/5, 7/9, 1 3/8, 1, 1, 1 1/10 Task c challenge: 1 3/8 of a game Subtraction With Different Denominators pg 36 Task A: 9/10 – 4/10 = ½, 21/24 – 8/24 = 13/24, 12/15 – 5/15 = 7/15, 24/30 – 5/30 = 19/30, 4/6 – 3/6 = 1/6, 8/12 – 3/12 = 5/12 Task B: 1/6, ½, ½, 19/40, 17/28, 7/10 Subtraction With Mixed Numerals 1 pg 37 Task A: 1 ½, 2 2/3, 3/5, 6/7 Task B: 18, 20, 12, 4, 10, 18, 21 Task C: 7 ¼, 6 7/10, 3, 1/3, 9 4/6, 10/20, 3 ¼, 5 23/30, 1 8/9 Task D: 1 3/5, 9 1/3, 4 5/6, 1 2/5, 8 1/7, 3 13/20, 24/25, 4 1/5 Task e challenge: 2 1/3

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51

Subtraction With Mixed Numerals 2 pg 38 Task A: 2 1/6, 2/3, 1 6/7, 1 3/8, 6 ½, 6 4/5, 1 3/10, 1 5/6, 2 3/5, 5/9, 3 3/5, 1 3/7 Task B: 1, 5, 2, 3, 20/100, 4, 3, 6, 4, 8 Task c challenge:: 2 ¼, 22

Fractions Of An Amount 3 pg 47 a) 40g b) $710 c) 220 m d) 360 mm e) 2100mL f ) $40 000 g) 2000 km h) $5400 i) $3500 j) 70 people k) 1500 mL l) 1000 kg m) 800 cm n) $400 o) 131 c p) 84 tonnes q) $300 r) 600 mL s) 700g t) 62m

This is a Ready-Ed Publications' book preview.

Mixed Addition And Subtraction Of Fractions pg 39 7/12 b) 3/10, c) 1 5/24, d), 9/20, e) 3 5/6, f ) 2 7/15, g) 7/30, h) 11/20, i) 3 7/12, j) 3 ½, k) 1 13/35, l) 41/56, m) 5 6/35, n) 6 31/45, o) 8/15, p)1 5/8, q) 5 19/20, r)3 ¼, s) 2 7/12, t) 5 28/45

Fractions In Real Life pg 48 a) 3/5 b) 4/6 c) Yes, ¼ = 2/8, d) No, ¾ < 4/5 e) 25 books f ) 36 mins

Multiplying Fractions pg 40 Task A: a)2/15, b) 9/20, c) 1/10, d) 5/24, e) 4/9, f ) 2/15 Task B: a) 1/6, 7/100, 1/10, 11/20, 21/32, 7/18 Division Of Fractions pg 41 Task A: a)7/8 x 3/2 = 1 5/16, b) 4/10 x 4/3 = 8/15, c) 5/6 x 11/3 = 3 1/18, d) 5/6 x 4/1 = 3 1/3, e) 3/12 x 5/4 = 15/48, f ) 2/9 x 5/2 = 5/9 Task B: a) 2 ½, b) 3/8, c) 1 1/10, d) 1 7/8, e) 2 2/5, f ) 1 1/ 14 Multiplying And Dividing Fractions pg 42 Task A: a) 1/10, b) 5/24, c) 3/7, d) 1/6, e) 2/11, f ) 5/12, g) 1 19/27, h) 9 2/7, i) 11 11/24 Task B: a) 1 1/5, b) 4 ½, c) 1 17/18, d) 1 4/11, e) 3 ½, f ) 2 1/12, g) 5 1/3, h) 1 ¾, i) 4 9/11 Expressing As A Fraction 1 pg 43 a) ¼ b) 1/6 c) 1/3 d) 1/3 e) 5 /1000 = 1/200, f ) 25/200 = 1/8 g) 300/2000 = 3/20 h) 150/2000 = 3/40 Expressing As A Fraction 2 pg 44 a) ½ b) 1/10 c) 1/7 d) ½ e) 7/60 f ) 1/8 g) 2/5 h) 9/40 i) 9/100 j) 7/40 k) 31/200 l) 1/8 m) 1/8 n) 1/120 Fractions Of An Amount 1 pg 45 a)12 b) 10 c) 13 d) 3 e) 15 f ) 200 g) 8 h) 7 i) 12 j) 12 k) 2 l) 4 m) 9 n) 45 o) 7 p ) 7

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Fractions Of An Amount 2 pg 46 a) 30 b) 8 c) 40 d) 12 e ) 64 f ) 15 g) 25 h) 45 i) 30 j) 35 k) 12 l) 16 m) 12 n) 6 o) 6 p) 12 52