1. Order of Operations
BGCSE Core

2. 1.3 – Order of Operations (BIDMAS)
This section will show you how to:
Work out the answers to a problem with a number of different mathematical operations.
How quickly can you complete these?
Keywords:
Brackets
Operation
Order
5 + 7
20 – 5
3 x 7
5 + 8
24 ÷ 3
15 – 8
6 + 8
27 ÷ 9
6 x 5
36 ÷ 6
7 x 5
15 ÷ 3
24 – 8
28 ÷ 4
7 + 9
9 + 6
36 – 9
30 ÷ 5
8 + 7
4 x 6
8 x 5
42 ÷ 7
8 + 9
9 x 8
54 - 8 12 15 7 14 35 5 25 40 6 21 13 3 30 16 17 46 8 24 72

3. Order of Operations (BIDMAS)
4 + 5 x 2 = ?

4. Order of Operations (BIDMAS)
Suppose you have to work out the answer to x 2. You may say the answer is 18, but the correct answer is 14.
There is an order of operations which you must follow when working out calculations like this. The x is always done before the +.
In x 2 this gives = 14.

5. Order of Operations (BIDMAS)
Now suppose you have to work out the answer to (3 + 2) x (9 – 5). The correct answer is 20.
You have probably realised that the parts in the brackets have to be done first, giving 5 x 4 = 20.
So, how do you work out a problem such as 9 ÷ x 2?

6. Order of Operations (BIDMAS)
To answer questions like this, you must follow the BIDMAS (or BODMAS) rule. This tells you the order in which you must do the operations. B I D M A S
rackets B O D M A S
rackets
pOwers
ivision
ultiplication
ddition
ubtraction
ndices
ivision
ultiplication
ddition
ubtraction

7. Order of Operations (BIDMAS)
For example, work out 9 ÷ x 2:
First divide: 9 ÷ 3 = 3 giving x 2
Then multiply: 4 x 2 = 8 giving 3 + 8
Then add: = 11

8. Order of Operations (BIDMAS)
For example, work out 60 – 5 x 3² + (4 x 2):
First work out the brackets: (4 x 2) = 8 giving 60 – 5 x 3² + 8
Then the index (power): 3² = 9 giving 60 – 5 x 9 + 8
Then multiply: 5 x 9 = 45 giving 60 –
Then add: = 68 giving 68 – 45
Finally, subtract: – 45 = 23

9. Exercise 1C: G Work out each of these: 2 x 3 + 5 6 ÷ 3 + 4 5 + 7 – 2
12 ÷ 2 + 6
12 ÷ 6 + 2
3 + 5 x 2
12 – 3 x 3 11 6 10 12 11 13 11 12 12 4 13 3 G

10. Work out each of these (Remember to use BIDMAS):
Exercise 1C:
Work out each of these (Remember to use BIDMAS):
2 x (3 + 5)
6 ÷ (2 + 1)
(5 + 7) – 2
5 + (7 – 2)
3 x (4 ÷ 2)
3 x (4 + 2)
2 x (8 – 5)
3 x (4 + 1)
3 x (4 – 1)
3 x (4 ÷ 1)
12 ÷ (2 + 2)
(12 ÷ 2) + 2 16 2 10 10 6 18 6 15 9 12 3 8 G

11. Exercise 1C: G 3 x 3 - 2 7 3 + 2 x 4 9 ÷ 3 – 2 9 – 4 ÷ 2 5 x 2 + 3
Copy each of these and put a ring around the part that you work out first. Then work out the answer. The first one has been done for you:
3 x 3 - 2 7
3 + 2 x 4
9 ÷ 3 – 2
9 – 4 ÷ 2
5 x 2 + 3
5 + 2 x 3
10 ÷ 5 – 2
10 – 4 ÷ 2
4 x 6 – 7
7 + 4 x 6
6 ÷ 3 + 7
7 + 6 ÷ 2 11 1 7 13 8 17 31 9 10 G

12. Exercise 1C: G 3 x 4 + 1 = 15 6 ÷ 2 + 1 = 4 6 ÷ 2 + 1 = 2
Copy each of these and then put in brackets where necessary to make each answer correct.
3 x = 15
6 ÷ = 4
6 ÷ = 2
4 + 4 ÷ 4 = 5
4 + 4 ÷ 4 = 2
16 – 4 ÷ 3 = 4
3 x = 13
16 – 6 ÷ 3 = 14
20 – 10 ÷ 2 = 5
20 – 10 ÷ 2 = 15
3 x = 30
6 x = 36
15 – 5 x 2 = 20
4 x 7 – 2 = 20
12 ÷ = 2
12 ÷ = 7
24 ÷ 8 – 2 = 1
24 ÷ 8 – 2 = 4 G

13. Exercise 1C: G 3 x (4 + 1) = 15 (6 ÷ 2) + 1 = 4 6 ÷ (2 + 1) = 2
Copy each of these and then put in brackets where necessary to make each answer correct.
3 x (4 + 1) = 15
(6 ÷ 2) + 1 = 4
6 ÷ (2 + 1) = 2
4 + (4 ÷ 4) = 5
(4 + 4) ÷ 4 = 2
(16 – 4) ÷ 3 = 4
(3 x 4) + 1 = 13
16 – (6 ÷ 3) = 14
(20 – 10) ÷ 2 = 5
20 – (10 ÷ 2) = 15
3 x (5 + 5) = 30
6 x (4 + 2) = 36
(15 – 5) x 2 = 20
4 x (7 – 2) = 20
12 ÷ (3 + 3) = 2
(12 ÷ 3) + 3 = 7
(24 ÷ 8) – 2 = 1
24 ÷ (8 – 2) = 4 G

14. Exercise 1C: G 3 + 4 + 1 3 + 4 – 1 4 + 3 – 1 4 x 3 + 1 4 x 3 – 1
Three dice are thrown. They give scores of three, one and four.
A class makes the following questions with the numbers. Work them out:
3 + 4 – 1
4 + 3 – 1
4 x 3 + 1
4 x 3 – 1
(4 – 1) x 3
4 x 3 x 1
(3 – 1) x 4
(4 + 1) x 3
4 x (3 + 1)
1 x (4 – 3)
4 + 1 x 3 8 6 6 13 11 9 12 8 15 16 1 7
Jack says that x 7 is equal to 77.
Is he correct? G
Jack is incorrect.

15. Exercise 1C:
This is Micha’s homework. Copy the questions where she has made mistakes and work out the correct answers.
2 + 3 x 4 20
8 – 4 ÷ 4 7
6 + 3 x 2 12
7 – 1 x 5 30
2 x 7 + 2 16
9 – 3 x 3 18
Three different dice give scores of 2, 3 and 5. Add ÷, x, +, - signs and brackets to make each calculation work.
= 11
= 16
= 17
= 4
= 13
= 30 F

16. Exercise 1C:
Which is smaller: x 3 or (4 + 5) x 3? Show your working.
Here is a list of numbers, some signs and one pair of brackets.
x = ( )
Use all of them to make a correct calculation.
÷ = ( ) F

17. Which calculations would give him the correct answer?
A question to end on…
Jeremy has a piece of pipe that is 10m long. He wants to use his calculator to work out how much pipe will be left when he cuts off three pieces, each of length 1.5m
Which calculations would give him the correct answer?
10 – 3 x –
10 – 1.5 – 1.5 – 1.5