© boardworks ltd 2004 1 of 49 n5 using fractions ks3 mathematics

© Boardworks Ltd 2004 1 of 49

N5 Using Fractions

KS3 Mathematics

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AN5.1 Fractions of shapes

Contents

N5 Using fractions

N5.3 One number as a fraction of another

N5.5 Ordering fractions

N5.4 Fractions and decimals

N5.2 Equivalent fractions

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Quarter or not?

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Quarters

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Dividing shapes into given fractions

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Remember, one quarter is written:

one thing 1divided into

four equal parts 4

Fractions of shapes

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What fraction of this diagram is shaded?

Fractions of shapes

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Two fifths is written as:

two parts 2out of

five parts altogether 5

numerator

denominator

Fractions of shapes

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Fractions of shapes activity

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N5.2 Equivalent fractions

Contents

N5 Using fractions

N5.1 Fractions of shapes

N5.3 One number as a fraction of another

N5.5 Ordering fractions

N5.4 Fractions and decimals

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Equivalent fractions

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What does equivalent

mean?

What does equivalent

mean?

Equivalent fractions

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Look at this diagram:

3

4=

6

8

×2

×2

=18

24

×3

×3

Equivalent fractions

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Look at this diagram:

2

3=

6

9

×3

×3

=24

36

×4

×4

Equivalent fractions

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Look at this diagram:

18

30=

6

10

÷3

÷3

=3

5

÷2

÷2

Equivalent fractions

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Equivalent fractions

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Cancelling fractions to their lowest terms

A fraction is said to be expressed in its lowest terms if the numerator and the denominator have no common factors.

A fraction is said to be expressed in its lowest terms if the numerator and the denominator have no common factors.

Which of these fractions are expressed in their lowest terms?

14

16

20

27

3

13

15

21

14

35

32

15

Fractions which are not shown in their lowest terms can be simplified by cancelling.

7

8

5

7

2

5

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Drag and drop equivalent fractions

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Mixed numbers and improper fractions

When the numerator of a fraction is larger than the denominator it is called an improper fraction.

When the numerator of a fraction is larger than the denominator it is called an improper fraction.

For example,15

4is an improper fraction.

We can write improper fractions as mixed numbers.

15

4can be shown as

15

4= 3

3

4

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Improper fractions to mixed numbers

Convert to a mixed number.378

378

=88

+ + +88

88

88

+58

581 + 1 + 1 += 1 +

= 4 5

8437 ÷ 8 = 4 remainder 5 37

8= 4

5

84This is the number of times 8 divides into 37.

4

This number is the remainder.

5

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Mixed numbers to improper fractions

Convert to a mixed number.273

273 =

271 + 1 + 1 +

=77

+ + +77

77

27

=237

To do this in one step,

=

Multiply these numbers together …

… and add this number …

… to get the numerator.237

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Find the missing number

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N5.3 One number as a fraction of another

Contents

N5 Using fractions

N5.1 Fractions of shapes

N5.2 Equivalent fractions

N5.5 Ordering fractions

N5.4 Fractions and decimals

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Writing one amount as a fraction of another

Sometimes we need to know one amount as a fraction of another.

3

7

three days

out of

seven days altogether

What fraction of one week is three days?

Monday Tuesday Wednesday Thursday Friday Saturday SundayMonday Tuesday Wednesday

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Writing a number as a fraction of another

We can describe one number as a fraction of another.

What fraction of 72 is 45?

We write4572

=

÷9

5

÷9

8

We can say 45 is 5/8 of 72.

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What fraction of 2.5 metres is 75 centimetres?

First, convert 2.5 metres to 250 centimetres.

We write75250

=

÷25

3

÷25

10

We can say 75 centimetres is 3/10 of 2.5 metres.

Writing a number as a fraction of another

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Writing a number as a fraction of another

We can also write a larger number as a fraction of a smaller one.

What fraction of 25 is 35?

We write3525

=

÷5

7

÷5

5

We can say 35 is 7/5 of 25 or 12/5 of 25.

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Writing one amount as a fraction of another

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Fractions of distances

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Fractions on a clock face

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N5.4 Fractions and decimals

Contents

N5 Using fractions

N5.1 Fractions of shapes

N5.3 One number as a fraction of another

N5.2 Equivalent fractions

N5.5 Ordering fractions

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Pelmanism – Fractions and decimals

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Comparing decimals and fractions

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Converting decimals to fractions

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We can convert some fractions to decimals by converting them to an equivalent fraction over 10, 100 or 1000.

Using equivalent fractions over 10, 100, or 1000

For example,

1320

=

× 5

100

× 5

65

10065

= 0.65

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Converting fractions to decimals

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Fractions and division

A fraction can be thought of as the result of dividing one whole number by another.

For example,

30 ÷ 8 =308

=683 =

343

We can also write this answer as a decimal:

343 = 3.75

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Converting fractions to decimals

There are many ways to convert a fraction to a decimal.

The quickest way is to use a calculator.

For example,

516

= 5 ÷ 16 = 0.3125 This is a terminating decimal.

611

= 6 ÷ 11 = 0.545454… This is a recurring decimal.

All recurring and terminating decimals can be written as exact fractions.

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Recurring decimals

13

= 1 ÷ 3 = 0.33333… = 0.3.

16

= 1 ÷ 6 = 0.16666… = 0.16.

211

= 2 ÷ 11 = 0.18181… = 1.18. .

37

= 3 ÷ 7 = 0.42857142857142… = 0.428571. .

We can also write = 0.43 (to 2 decimal places). 37

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We can also convert fractions to decimals using short division.

For example,

57

= 5 ÷ 7

5 . 0 07

05

.71

1

03

4

02

2

06

8

04

5

05

7 . . .

57

= 0.714285. .

Using short division

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N5.5 Ordering fractions

Contents

N5.3 One number as a fraction of another

N5 Using fractions

N5.1 Fractions of shapes

N5.2 Equivalent fractions

N5.4 Fractions and decimals

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Using diagrams to compare fractions

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Using decimals to compare fractions

Which is bigger or ?38

720

We can compare two fractions by converting them to decimals. For example,

38

= 3 ÷ 8 = 0.375

= 7 ÷ 20 = 0.35720

0.375 > 0.35

so 38

>720

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Which is bigger or ?38

512

Another way to compare two fractions is to convert them to equivalent fractions.

First we need to find the lowest common multiple of 8 and 12.

The lowest common multiple of 8 and 12 is 24.

Now, write and as equivalent fractions over 24. 38

512

38

=24

×3

×3

9and

512

=24

×2

×2

10so,

38

512

<

Using equivalent fractions

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Using a graph to compare fractions

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Ordering fractions

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Fractions on a number line

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Mid-points

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Connect three fractions