Decimal Calculations 7
BODMAS

It is important that we carry out operations in a calculation in the correct order, which can be summarised by using the acronym 'BODMAS' This stands for:

Brackets first
O
Divide
Multiply
Add
Subtract

Worked Examples

1
Calculate
(a)

16 × 2 + 3

Show me
16 × 2 + 3 = 32 + 3     (M before A)
= 35
(b)

16 × (2 + 3)

Show me
16 × (2 + 3) = 16 × 5     (B before M)
= 80
2
Calculate:
(a)

(3 + 2) × 6 − 8

Show me
(3 + 2) × 6 − 8     (brackets first)
  = 5 × 6 − 8     (multiplication second)
  = 30 − 8     (subtraction last)
  = 22
(b)

4 × 6 + 18 ÷ 2

Show me
4 × 6 + 18 ÷ 2
  = 24 + 9
  = 33
(c)

(17 − 2) ÷ 5 + 6

Show me
(17 − 2) ÷ 5 + 6     (brackets first)
  = 15 ÷ 5 + 6     (division second)
  = 3 + 6     (addition last)
  = 9
3
State whether each one of the statements below is true or false:
(a)

3 + 6 × 2 = 15

Show me
3 + 6 × 2 = 3+12
= 15

Therefore the statement is true.
(b)

30 − 7 × 4 = 92

Show me
30 − 7 × 4 = 30−28
= 2

Therefore the statement is false.
(c)

8 + 20 ÷ 2 = 14

Show me
8 + 20 ÷ 2 = 8+10
= 18

Therefore the statement is false.

Exercises

Find:

(a)
16 ÷ 4
(b)
12 ÷ 6
(c)
15 ÷ 5
(d)
20 ÷ 4
(e)
18 ÷ 9
(f)
40 ÷ 8
(g)
36 ÷ 9
(h)
15 ÷ 3
(i)
64 ÷ 8
(j)
42 ÷ 7
(k)
24 ÷ 6
(l)
32 ÷ 8
(m)
49 ÷ 7
(n)
56 ÷ 8
(o)
45 ÷ 5

Is each of these statements true or false?

(a)
10 ÷ 2 = 2 ÷ 10
(b)
12 + 8 ÷ 2 = 10
(c)
3 + 12 ÷ 4 = 6
(d)
6 ÷ 2 + 3 = 6

Find:

(a)
3 + 4 × 8
(b)
8 + 3 × 6
(c)
8 × 6 − 4
(d)
12 ÷ 2 + 5
(e)
5 − 12 ÷ 3
(f)
14 ÷ 2 + 8
(g)
3 × 2 + 8 ÷ 4
(h)
3 × 6 − 15 ÷ 3
(i)
42 ÷ 7 + 3
(j)
16 ÷ 4 + 24 ÷ 6
(k)
8 × 2 + 5 × 3
(l)
8 × 6 − 45 ÷ 5

A student works out 200 ÷ 4 by this method:

200 ÷ 2 = 100
100 ÷ 2 = 50

Use similar methods to find:

(a)
500 ÷ 4
(b)
52 ÷ 4
(c)
68 ÷ 4
(d)
128 ÷ 4
(e)
224 ÷ 4
(f)
104 ÷ 8
(g)
80 ÷ 16
(h)
112 ÷ 16
(i)
128 ÷ 8

Calculate:

(a)
6 + 7 × 2
(b)
8 − 3 × 2
(c)
19 − 4 × 3
(d)
3 × 6 − 9
(e)
15 − 4 + 7 × 2
(f)
11 × 3 + 2
(g)
16 × 4 − 3
(h)
6 + 7 × 2 − 20 ÷ 4
(i)
18 × 2 − ( 4 + 7)
(j)
16 − 5 × 2 + 3

Fill in the missing numbers:

(a)
3 × + 2 = 17
(b)
× 5 − 8 = 22
(c)
(4 + ) × 2 = 20
(d)
6 − × 2 = 0
(e)
(7 − ) × 4 = 20
(f)
÷ 3 + 4 = 8

Jane writes down:

4 × 7 + 2 × 3 = 90

By using brackets Jane can make her calculation correct. Show how this can be done.

= 90

State whether each one of the statements below is true or false:

(a)
(3 × 6) × 2 = 3 × (6 × 2)
(b)
(4 + 2) + 7 = 4 + (2 + 7)
(c)
(8 − 2) − 1 = 8 − (2 − 1)
(d)
(8 ÷ 2) ÷ 2 = 8 ÷ (2 ÷ 2)