© Boardworks 20101 of 15
Unit 1 – Number SystemsMultiplying Fractions
© Boardworks 20102 of 15
Counting with fractions
© Boardworks 20103 of 15
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
© Boardworks 20104 of 15
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
© Boardworks 20105 of 15
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
© Boardworks 20106 of 15
So: 8 × = 214
12 × = 934
9 × = 3.13
and
What do you notice?
Multiplying fractions by integers
© Boardworks 20107 of 15
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
© Boardworks 20108 of 15
Means the same as:
35
20 ×
35
× 2035
of 2015
3 × of 20
20 × 3 ÷ 5 20 ÷ 5 × 3 3 ÷ 5 × 20
Equivalent calculations
© Boardworks 20109 of 15
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
© Boardworks 201010 of 15
57
12 × ?What is
57
12 × = 12 × 5 ÷ 7
= 60 ÷ 7
=607
= 8 47
Multiplying fractions by integers
© Boardworks 201011 of 15
712
What is 16 × ?
We can write 16 × as:712
161
×712
4
3=
283
=139
Using cancellation to simplify calculations
© Boardworks 201012 of 15
825
What is × 40?
We can write × 40 as:825
825
×401
8
5=
645
=4512
Using cancellation to simplify calculations
© Boardworks 201013 of 15
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
© Boardworks 201014 of 15
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
© Boardworks 201015 of 15
Multiplying fractions mentally