Page 42 - MAT KS3 Y8 Cambridge CheckPoint

3.7 Dividing by decimals

3.7 Dividing by decimals

When you divide a number by a decimal, use the place values of the decimal to work out an equivalent
calculation.
You already know that dividing a number by 0.1 has the same effect as multiplying the number by 10.
When you divide a number by 0.01 it has the same effect as multiplying the number by 100.
Examples: When you divide a number by 0.3, multiply the number by 10 and then divide by 3.
When you divide a number by 0.08, multiply the number by 100 and then divide by 8.

Worked example 3.7

Work these out. a 28 ÷ 0.4 b 92.4 ÷ 0.06

a (28 × 10) ÷ 4 Dividing by 0.4 is the same as multiplying by 10 and then dividing by 4.
28 × 10 = 280 Start by multiplying by 10.
4 ) 2 8 0
7 0 Now divide by 4.

28 ÷ 0.4 = 70 Write down the final answer.
b (92.4 × 100) ÷ 6 Dividing by 0.06 is the same as multiplying by 100 and then dividing by 6.
92.4 × 100 = 9240 Start by multiplying by 100.
1 5 4 0
6 ) 9 3 2 2 4 0 Now divide by 6.

92.4 ÷ 0.06 = 1540 Write down the final answer.

✦ Exercise 3.7

1 Use equivalent calculations to work these out.
a 32 ÷ 0.2 b 75 ÷ 0.5 c 15 ÷ 0.6 d 23.4 ÷ 0.3 e 612 ÷ 0.8
f 35 ÷ 0.07 g 32 ÷ 0.04 h 56 ÷ 0.08 i 21 ÷ 0.03 j 34 ÷ 0.04
k 81 ÷ 0.06 l 8.7 ÷ 0.02 m 34.8 ÷ 0.04 n 2.1 ÷ 0.05 o 156.8 ÷ 0.07

2 This is part of Anders’ homework.
Use Anders’ method to work
these out. Question Work out 28.9 ÷ 0.7.
a 32.5 ÷ 0.3 correct to 1 d.p. Give your answer to 1 d.p.
b 7.8 ÷ 0.9 correct to 1 d.p. Answer 28.9 ÷ 0.7= (28.9 × 10) ÷ 7
c 145 ÷ 0.7 correct to 1 d.p. 28.9 × 10 = 289 41. 2 8
)
6
2
d 6.45 ÷ 0.07 correct to 2 d.p. 289 ÷ 7 = 41.3 (1 d.p.) 7 28 9 . 0 0
e 0.79 ÷ 0.06 correct to 2 d.p.
3 Anders knows that 42 ÷ 7 = 6.
Work out these mentally:
a 4.2 ÷ 7 b 42 ÷ 0.7 c 4.2 ÷ 0.7 d 420 ÷ 0.7

4 Work out (42.7 − 6.93) ÷ (2 × 0.45). Give your answer correct to two decimal places.

40 3 Place value, ordering and rounding