# Using the Order of Operations in Calculations (1)

In this worksheet, students observe the order of priority in carrying out mixed operations.

Key stage:  KS 3

Curriculum topic:   Number

Curriculum subtopic:   Use Conventional Notation for Priority of Operations

Difficulty level:

### QUESTION 1 of 10

When you are working something out that involves more than one operation, the order in which they are carried out matters.

The agreed order is:

Brackets
Powers or indices
Division and Multiplication

This can be remembered using the word:    BIDMAS.

However, remember that multiplication and division are equally important, so in a calculation just involving multiplication and division, you carry this out from left to right.  Similarly with addition and subtraction.

Examples

6 + 9 ÷ 3 = 6 + 3 = 9. divide first

(6 + 9) ÷ 3 = 15 ÷ 3 = 5. brackets first

15 - 4 × 2 = 15 - 8 = 7. multiply first

(15 - 4) × 2 = 11 × 2 = 22. brackets first

4 × 32 = 4 × 9 = 36. power first

(4 × 3)2 = 122 = 144. brackets first

14 - 4 + 5 = 15.  equally important, so left to right.

Work out

11 × 6 + 6 =

Work out

11 × (6 + 6) =

Calculate

11 + 6 × 6 =

What is ?...

(11 + 6) × 6 =

Work out

11 × 62 =

Work out

(11 × 6)2 =

Work out

12 - 8 + 2 =

Work out

12 × (8 + 2) =

Calculate

12 + 8 × 2 =

Calculate

(12 + 8) × 2 =
• Question 1

Work out

11 × 6 + 6 =
72
EDDIE SAYS
Remember the rules of BIDMAS. We must multiply first: 11 x 6 = 66 Then we complete the addition: 66 + 6 = 72 How did you do? Did you remember the order?
• Question 2

Work out

11 × (6 + 6) =
132
EDDIE SAYS
Can you remember what the first letter B in the word BIDMAS stands for? It stands for Brackets, so this is what we must begin with here. 6 + 6 = 12 (Brackets completed) 11 x 12 = 132 Solved!
• Question 3

Calculate

11 + 6 × 6 =
47
EDDIE SAYS
Think carefully about the BIDMAS order here. Which comes first multiplication or addition? It's the multiplication phase, so we begin with: 6 x 6 = 36 Then we complete the addition: 36 + 11 = 47 Is this becoming easier?
• Question 4

What is ?...

(11 + 6) × 6 =
102
EDDIE SAYS
How did you do with this one? Remember the question we did before using brackets? Using BIDMAS the sum in a bracket must always be done first: 11 + 6 = 17 Now, we can complete the sum by doing a multiplication: 17 x 6 = 102
• Question 5

Work out

11 × 62 =
396
EDDIE SAYS
Always begin with remembering the order. In BIDMAS, the indices are second in the order of completion. So, let's begin here: 6 ² is the same as 6 x 6 = 36 Now, we complete the final step which is the multiplication: 11 x 36 = 396 Let's keep going!
• Question 6

Work out

(11 × 6)2 =
4356
EDDIE SAYS
This sum uses the first two orders in BIDMAS, but it's still important we do them in the correct order. This means we start with the brackets and then apply the indices. 11 x 6 = 66 66 ² is 66 x 66 = 4356 Quite a big number there!
• Question 7

Work out

12 - 8 + 2 =
2
EDDIE SAYS
In this question, it may not be immediately obvious what to do but just look back at the word BIDMAS. We know that we need to complete the addition before the subtraction here. 8 + 2 = 10 (addition) Then we complete the subtraction: 12 - 10 = 2 Did you get this one right? If you completed the sum without this applying BIDMAS you would have got 7, which is incorrect.
• Question 8

Work out

12 × (8 + 2) =
120
EDDIE SAYS
You know what to do here! Let's start with the brackets as that is our first order of operation. 8 + 2 = 10 Now, we apply the next order which is the multiplication: 12 x 10 = 120 Excellent work!
• Question 9

Calculate

12 + 8 × 2 =
28
EDDIE SAYS
For this sum, we must begin with the multiplication first: 8 x 2 = 16 Now, we can apply the addition as this is next in the order. 12 + 16 = 28 Last question coming up!
• Question 10

Calculate

(12 + 8) × 2 =
40
EDDIE SAYS
OK, you know what to do here. Let's finish on a good one. First up we tackle those brackets, as this is what the order of operation using BIDMAS tells us! 12 + 8 = 20 Now, we tackle that multiplication: 20 x 2 = 40 Great work, that's another activity completed! Ready to try another?
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