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Unit 1 – Number SystemsMultiplying Fractions

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Counting with fractions

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We can illustrate this calculation on a number line:

0

14

14

12

34 1 1

41 121 3

41 2

14

What is 8 × ?

14

14

14

14

14

14

14

Multiplying fractions by integers

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34

Again, we can illustrate this calculation on a number line:

0

34

34

121 1

42 3 343 1

24 145 6 3

46 127 1

48 9

34

What is 12 × ?

34

34

34

34

34

34

34

34

34

34

Multiplying fractions by integers

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Let’s use a number line to illustrate this sum:

0

13

13

23 1 1

31 231 2 1

32 232 3

13

What is 9 × ?

13

13

13

13

13

13

13

13

Multiplying fractions by integers

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So: 8 × = 214

12 × = 934

9 × = 3.13

and

What do you notice?

Multiplying fractions by integers

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Following the rules of arithmetic, we know that:

8 ×14

=14

× 8

(In math, the word ‘of’ means ‘times.’)

=14

of 8 = 8 ÷ 4

These are equivalent calculations.

Multiplying fractions by integers

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Means the same as:

35

20 ×

35

× 2035

of 2015

3 × of 20

20 × 3 ÷ 5 20 ÷ 5 × 3 3 ÷ 5 × 20

Equivalent calculations

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When we multiply a fraction by an integer we:

multiply by the numerator

and

divide by the denominator

For example:

49

54 × = 54 ÷ 9 × 4

= 6 × 4

= 24

Multiplying fractions by integers

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57

12 × ?What is

57

12 × = 12 × 5 ÷ 7

= 60 ÷ 7

=607

= 8 47

Multiplying fractions by integers

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712

What is 16 × ?

We can write 16 × as:712

161

×712

4

3=

283

=139

Using cancellation to simplify calculations

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825

What is × 40?

We can write × 40 as:825

825

×401

8

5=

645

=4512

Using cancellation to simplify calculations

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To multiply two fractions together, multiply the numerators together and multiply the denominators together:

38

What is × ?25

38

45

× =1240

3

10

=310

Multiplying a fraction by a fraction

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56

What is × ?12255

Start by writing the calculation with any mixed numbers as improper fractions.

To make the calculation easier, remember to simplify wherever possible.

1225

356

× =

7

5

2

1

145

= 2 45

Multiplying a fraction by a fraction

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Multiplying fractions mentally