© 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


Quarter or not?


Quarters


Dividing shapes into given fractions


Remember, one quarter is written:

one thing 1divided into

four equal parts 4

Fractions of shapes


What fraction of this diagram is shaded?

Fractions of shapes


Two fifths is written as:

two parts 2out of

five parts altogether 5

numerator

denominator

Fractions of shapes


Fractions of shapes activity


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Contents

N5 Using fractions

N5.1 Fractions of shapes





Equivalent fractions


What does equivalent

mean?

What does equivalent

mean?



Look at this diagram:

3

4=

6

8

×2

×2

=18

24

×3

×3




2

3=

6

9

×3

×3

=24

36

×4

×4




18

30=

6

10

÷3

÷3

=3

5

÷2

÷2



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


Drag and drop equivalent fractions


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


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


227733

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


Find the missing number


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Contents

N5 Using fractions






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


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.


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.




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.


Writing one amount as a fraction of another


Fractions of distances


Fractions on a clock face


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Contents

N5 Using fractions






Pelmanism – Fractions and decimals


Comparing decimals and fractions


Converting decimals to fractions


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


Converting fractions to decimals


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


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.


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


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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Contents


N5 Using fractions





Using diagrams to compare fractions


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


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


Using a graph to compare fractions


Ordering fractions


Fractions on a number line


Mid-points


Connect three fractions

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

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