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3.1 Multiplying and dividing decimals mentally

3.1 Multiplying and dividing decimals mentally

To multiply or divide a number by a decimal number, you need to be able to work out an equivalent
calculation that you can do ‘in your head’, or mentally.

!is might be easy for a simple question. For a more di$cult question, you can use brief notes to write
down some of the steps in the working. !ese are called jottings. !ey help you remember what you
have worked out so far, and what you still need to do.
Here are two reminders to help you check whether your answer could be right or wrong.
t 8IFO ZPV multiply any number by a decimal number between 0 and 1, your answer will be smaller
than the number you started with.
t 8IFO ZPV divide any number by a decimal number between 0 and 1, your answer will be greater
than the number you started with.

Worked example 3.1
36 × 05
.
Work these out mentally. a 12 × 0.6 b 0.3 × 0.15 c 16 ÷ 0.4 d 8 ÷ 0.02 e 02 . × 45
.
a 12 × 6 = 72 Ignore the decimal point and work out 12 × 6 = 72 in your head.
12 × 0.6 = 7.2 The answer 72 is 10 times bigger than the actual answer, because 6 is
10 times bigger than 0.6. Divide the answer 72 by 10 to get 7.2.
b 3 × 15 = 45 Ignore the decimal points, and work out 3 × 15 = 45 in your head.
0.3 × 0.15 = 0.045 3 × 15 = 45 A 0.3 × 15 = 4.5 A 0.3 × 0.15 = 0.045.
c 16 × 10 In your head, think of the division as a fraction, then multiply the top and the
04 × 10
.
160 bottom of the fraction by 10 to eliminate the decimal from the division.
4 = 40 This makes an equivalent calculation, which is much easier to do.
d 8 × 100 Again, in your head, think of the division as a fraction, then multiply the top
002 × 100 and the bottom of the fraction by 100 to eliminate the decimal.
.
800 = 400 This again makes an equivalent calculation, which is much easier to do.
2
e 36 × 0.5 = 18 Work out the answer to the numerator first. Since 0.5 is the same as one half,
1
work out × 36 = 18. Jot down the answer 18 so you don’t forget it.
2
2 × 4.5 = 9 Work out 2 × 4.5 = 9 in your head.
So 0.2 × 4.5 = 0.9 2 is 10 times bigger than 0.2, so divide the answer 9 by 10 to get 0.9.
36 × 05 . 18
=
02 × 45 09 .
.
.
18 ×
09 × 10 Multiply the top and the bottom of the fraction by 10 to eliminate the decimal.
.
10
180 = 20 This makes an equivalent calculation, which is much easier to do.
9
) Exercise 3.1

1 Work these out mentally.
a 8 × 0.2 b 12 × 0.3 c 8 × 0.7 d 0.6 × 9 e 0.4 × 15
f 6 × 0.05 g 18 × 0.02 h 22 × 0.03 i 0.08 × 30 j 0.04 × 45

24 3 Place value, ordering and rounding