year 8 maths

218 Chapter 4 Fractions, decimals, percentages and financial mathematics
Key ideas
■ Multiplying decimals
• Initially ignore the decimal points and carry out routine multiplication.
• The decimal place is correctly positioned in the answer according to the following rule:
‘The number of decimal places in the answer must equal the total number of decimal places
in the question.’
5.73 × 8.6
573
5.73 × 8.6 = 49.278
× 86
49278 (3 decimal places in question, 3 decimal places in answer)
■ Dividing decimals
The decimal point in the quotient goes directly above the decimal point in the dividend .
56.34 ÷ 3
Divisor
18.78
3⟌56.34
Quotient (answer)
Dividend
We avoid dividing decimals by other decimals. Instead we change the divisor into a whole
number. Of course, whatever change we make to the divisor we must also make to the dividend,
so it is equivalent to multiplying by 1 and the value of the question is not changed.
We avoid
27.354 ÷ 0.02
Preferring to do 2735.4 ÷ 2 27.354 ÷ 0.02
Example 10 Adding and subtracting decimals
Calculate:
a 23.07 + 103.659 + 9.9
b 9.7 − 2.86
SOLUTION
a
b
23.070
103.659
+ 9.900
136.629
8 16
9. 7 1 0
− 2. 8 6
6. 8 4
EXPLANATION
Make sure all decimal points and places are
correctly aligned directly under one another. Fill in
missing decimal places with zeros.
Carry out the addition of each column, working
from right to left.
Align decimal points directly under one another
and fill in missing decimal places with zeros.
Carry out subtraction following the same
procedure as for subtraction of whole numbers.
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
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