Page 84 - Mathematics Coursebook

7.7 Finding remainders

7.7 Finding remainders

When you are working out a division, the number you are dividing by is called the divisor and the
number you are dividing into is called the dividend.

Example: In the division 163 ÷ 12, 12 is the divisor and 163 is the dividend.
When the answer to a division is not an exact whole number, there You can check this answer using
will be a remainder. inverse operations like this:

Example: 163 ÷ 12 = 13 remainder 7 12 × 13 = 156, 156 + 7 = 163

!e remainder can be written as a fraction of the divisor.
Example: 163 ÷ 12 = 13 7 You can think of this as changing
12
When you are solving a problem and you have a remainder, you an improper fraction to a mixed
may need to decide whether to round up or down. Whether you number (see Topic 7.4).
round up or down depends entirely on the question. 163 = 13 7
12 12

Worked example 7.7
a Work out these divisions. Write the remainders as fractions.
i 16 ÷ 3 ii 90 ÷ 8
b Raul shares 50 sweets equally between his 3 children.
How many sweets do they each get?
c 276 children are going on a school trip by bus. Each bus holds 48 children.
How many buses do they need?

1
a i 5 16 ÷ 3 = 5 remainder 1
3
ii 11 2 = 11 1 90 ÷ 8 = 11 remainder 2; 2 cancels to 1
8 4 8 4
b 50 ÷ 3 = 16 remainder 2 Here you have to round down so they have 16 sweets each
16 sweets each There are not enough sweets for them to have 17 each.

c 276 ÷ 48 = 5 remainder 36 In this question you have to round up so they can take everyone on
6 buses are needed. the trip. 5 buses would not be enough for everyone.

) Exercise 7.7

1 Work out these divisions. Write the remainders as fractions.
a 19 ÷ 7 b 35 ÷ 11 c 41 ÷ 6 d 65 ÷ 9
2 Work out these divisions. Write the remainders as fractions in their simplest form.
a 6 ÷ 4 b 20 ÷ 8 c 26 ÷ 6 d 38 ÷ 10
e 50 ÷ 12 f 33 ÷ 9 g 55 ÷ 15 h 52 ÷ 20
3 Angel uses this method to work out some harder Question Work out 257 ÷ 3
divisions. Use Angel’s method, or a similar
method of your own, to work these out. Solution ) 85 remainder 2
2
1
a 225 ÷ 4 b 363 ÷ 5 c 373 ÷ 3 32 57
d 447 ÷ 6 e 758 ÷ 8 f 920 ÷ 12 257 ÷ 3 = 85 2
3

7 Fractions 83