ORDER OF OPERATIONS
When doing a calculation it is important to do operations, such as addition and
multiplication, in the correct order.
For example, if you purchased 2 books at $20 each and 3 magazines at $3 each you, would
calculate the total amount spent by, first of all calculating the total cost of the books, then
calculating the total cost of the magazines and finally adding these two totals together.
(2  $20) + (3  $3) = $40 + $9 = $49
Namely you would do the two multiplications first before adding the results. This leads us
to see that you would perform multiplications and divisions before additions and
subtractions.
There is a common pneumonic, which is easy to remember, for the order in which to
perform operations.
B
E
D
M
A
S
BRACKETS
ADDITION
SUBTRACTION
same order of precedence work
from left to right
EXPONENT OR
POWER
DIVISION
MULTIPLICATION
same order of precedence work from left
to right
In any calculations that you perform, you would action operations that lie in brackets first,
then you would calculate an exponent (or power), next you would either multiply or divide
and finally you would perform additions or subtractions.


7  (4 + 1) - 5  3 =
7  5 - 5  3 = 35 - 15 = 20
(4 – 1)2  8 - 2 = 32  8 - 2 = 9  8 - 2 = 72 - 2 = 70
1
Updated March 2013
Order of operations exercises
A Calculate
1.
6 + 2  9
2.
15 - 3  2
3.
13 - 6  2
4.
42  2 + 7
5.
17 - 3  5
6.
(7 - 3)  5
7.
5  3 - 4  2
8.
8 + 2  9 + 4
9.
(11 - 9)  10 + 7  3
10.
24 + (3  4)  6
11.
18  (21 - 9  2)
12.
3 + 42 - 7
13.
5  (3 + 2) - 4  5
14.
(31 + 7  3)  4
15.
[12 - (7 - 2)]  (6 + 3)
16.
3  (9 - 4) - 2  (1 + 4)
17.
(6 – 2)  20 + 7  3
18.
22 + [(4 + 5)  3]
19.
3  (6 + 1) - 14  2
20.
50 - 18  (13 – 11)  4
21.
32  8  12  3
22.
25  (7 – 2) + 5  3
23.
4  12 - 32 + 5 - (3 + 5)  (8 – 2)
B
Put in brackets where necessary to make each of the following statements true.
1.
4 + 5 - 2 = 7
2.
16 - 9  2 = 14
3.
7 + 4  9 - 3 = 66
4.
7 + 4  9 - 3 = 40
5.
5 + 1  0 = 0
6.
5 + 1  0 = 5
7.
72  8 - 3 + 1 = 7
8.
72  8 - 3 + 1 = 5
9.
21  5 - 3 - 5 + 6 = 31
10.
24  4  3 + 2 = 30
11. 16 - 7 + 4 - 1 = 4
12.
200  20 + 20 = 5
13. 12 + 8 - 5 - 1 = 16
14.
12 + 8 - 5 - 1 = 14
2
Updated March 2013
Order of operations exercises solutions
A
1.
24
3.
10
2.
9
4.
28
5.
2
6.
20
7.
7
8.
30
9.
41
10.
26
11.
6
12.
12
13.
5
14.
13
15.
63
16.
5
17.
101
18.
49
19.
14
20.
41
21.
16
22.
20
23.
-27
B
1.
4 + 5 - 2 = 7
2.
(16 - 9)  2 = 14
3.
(7 + 4)  (9 - 3) = 66
4.
7 + (4  9 - 3) = 40
5.
(5 + 1)  0 = 0
6.
5 + 1  0 = 5
7.
72  8 - 3 + 1 = 7
8.
72  8 - (3 + 1) = 5
9.
21  (5 - 3) - (5 + 6) = 31
10.
24  4  (3 + 2) = 30
11. 16 - (7 + 4) - 1 = 4
12.
200  (20 + 20) = 5
13. 12 + 8 - (5 - 1) = 16
14.
12 + (8 - 5) - 1 = 14
3
Updated March 2013