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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.

Order of operation

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

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?

Paula is correct.

Multiplication comes before addition and subtraction, so:

2 x 3 – 2 x 5 = 6 - 10 = -4

Question

a) 10 - 32 =

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

a) BIDMAS tells us indices come before subtraction. So

10 - 32 = 10 - 9 = 1

b) 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 = 81

c) 4 x (5 – 3) = 8

d) (7 - 5) x 3 = 6

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