Maths

Order of operation

Do you remember BIDMAS? It stands for 'brackets', 'indices', 'division', 'multiplication', 'addition' and 'subtraction'.

The order in which we carry out a calculation is important.

What is 2 + 3 x 4?

If we calculate the '2 + 3' part first, we get:

2 + 3 x 4 = 5 x 4

= 20

If we calculate the '3 x 4' part first, we get:

2 + 3 x 4 = 2 + 12

= 14

These are obviously two different answers - but which one is correct?

**BIDMAS** tells us that 'multiplication' comes before 'addition', so the **second** answer is correct:

2 + 3 x 4 = 2 + 12

= 14

**Worked example:**

Calculate: 3 x (7 - 3)

**Solution**

In this question, we have a bracket, a subtraction and a multiplication.

**BIDMAS** tells us that brackets come first, so we calculate:

3 x (7 - 3) = 3 x 4

= 12

- Question
Calculate: 2 + 3 x 5 - 4

- Answer
Did you get 13? Well done.

If not, remember that multiplication comes before addition and subtraction, so we have:

2 + 3 x 5 - 4 = 2 + 15 - 4 = 13

- Question
Paula says that 2 x 3 – 2 x 5 = -4

Steve says the answer is 10. Who is right, and why?

- Answer
Paula is correct.

Multiplication comes before addition and subtraction, so:

2 x 3 – 2 x 5 = 6 - 10 = -4

- Question
a) 10 - 3

^{2}=b) (15 - 3 x 2)

^{2}=c) Put brackets into this equation to make it work 4 x 5 – 3 = 8

d) Put symbols in to make this work: 7 5 3 = 6

- Answer
a) BIDMAS tells us indices come before subtraction. So

10 - 3

^{2}= 10 - 9 = 1b) BIDMAS tells us brackets come before indices. So work out the part inside the bracket first. Inside the bracket use BIDMAS again to see that you do the multiplication before the subtraction. So all together:

(15 - 3 x 2)

^{2}= (15 - 6)^{2}= (9)^{2}= 81c) 4 x (5 – 3) = 8

d) (7 - 5) x 3 = 6

**Now try a **Test Bite