Page 80 - MAT KS3 Y8 Cambridge CheckPoint

7.6 Multiplying an integer by a fraction

7.6 Multiplying an integer by a fraction

You have learned how to find a fraction of a quantity, with The word ‘of’ means ‘multiply’, so
whole-number or mixed-number answers. When you multiply 2 of 2 ×
3 15 means the same as 3 15.
an integer by a fraction, you use exactly the same methods
as you used previously.

Worked example 7.6

Work these out. a 2 × 15 b 26 × 3
3 8

a 15 ÷ 3 = 5 You can work this out mentally as 3 will divide exactly into 15 to give you 5.
5 × 2 = 10 Now multiply the 5 by 2 to give an answer of 10.
b 26 × 3 = 78 8 does not divide exactly into 26, so multiply 26 by 3 instead.
6
78 ÷ 8 = 9 Now divide 78 by 8. This gives 9 with a remainder of 6, so the answer is 9 6 .
8
8
9 6 = 9 3 Cancel 6 to 3 , giving 9 3 as the final answer in its lowest terms.
8 4 8 4 4
Notice that the fraction at the end of the solution to part b
Look again at the solution
can be cancelled. It is often easier and quicker to cancel,
to part b. Here is a quicker way
when possible, before doing any of the calculations. to work out the answer.
13
3
Looking again at 26 × , start by dividing 26 and 8 by 2: 26 × 3
8 4 8
3
This has simplified the numbers, so now you have to work out 13 × .
4
You cannot cancel any further, so carry on as normal: 13 × 3 = 39, 39 ÷ 4 = 9 3
4
✦ Exercise 7.6

1 Work these out mentally.
3
2
7
a 3 × 20 b 4 × 30 c 72 × d 27 × e 81 × f 5 × 60
4 5 8 3 9 12
2 Work out the following.
Give each answer as a mixed number in its lowest terms.
a 3 × 33 b 2 × 20 c 41 × 3
8 9 5 In parts d, e and f cancel before you do
d 14 × 5 e 21 × 7 f 3 × 50 any calculations.
6 12 20

3 This is part of Dakarai’s homework.
Has he worked out the answer correctly? Question Work out 4 × 78.
Explain your answer. 15
26
4
Answer
A × 78, 4 × 26 = 104
3 15
104 ÷3 = 34 2
3

78 7 Fractions