# Using BODMAS / BIDMAS

In this worksheet, students will follow the rules of BODMAS / BIDMAS to prioritise the order of operations to successfully reach the correct answer in mental calculations.

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   Pearson Edexcel, OCR, Eduqas, AQA

Curriculum topic:   Number, Number Operations and Integers

Curriculum subtopic:   Structure and Calculation, Combining Arithmetic Operations

Difficulty level:

### QUESTION 1 of 10

BODMAS or BIDMAS is a powerful tool we use in maths to ensure that all the more complex equations we solve will have the correct answer.

Imagine that you had the sum 4 + 2 x 7, before BODMAS was invented, nobody knew if the multiplication or the addition should be tackled first.

Both answers that you could get (56 and 18) may both have been right, but BODMAS changed that.

BODMAS tells you which order you need to perform sums in:

B    Brackets

O    Orders (or Indices)
D    Division
M    Multiplication
S    Subtraction

All this means is that you deal with all your brackets first, then deal with all your orders (powers, etc.), then deal with your divisions and multiplications, before finally dealing with your additions and subtraction.

e.g. Evaluate the expression: 4 - 2 x 3

The first thing we would recommend is write out BODMAS with our sum:

4 - 2 x 3

B           ----

O           ----

D           ----
M           4 - 6
A           ----
S          - 2

From this, you can see that we have ignored brackets, orders and division, before we have worked out the multiplication (2 x 3 = 6) and replaced this value in our original sum.

Then we ignored the addition and finally subtracted 6 from 4 at the end to reach an answer of -2.

e.g. Work out: (3 + 2)2 - (6 ÷ 2)

(3 + 2)2 - (6 ÷ 2)

B           (5)2 - (3)

O           25 - 3

D           ----
M           ----
A           ----
S           22

Once again, we have worked through each step in turn, ignoring the symbols that aren't applicable, working out one calculation at a time.

Now it's your turn to give this a try!

In this activity, you will follow the rules of BODMAS / BIDMAS to prioritise the order of operations so that you successfully reach the correct answer in mental calculations.

Which order should you perform the following operations in?

## Column B

Brackets
5th
Orders
2nd
Division
1st
Multiplication
4th
3rd
Subtraction
6th

Which is the correct answer to the sum below?

3 + 4 x 5

35

23

17

How would you solve the equation below?

6 - 4 ÷ 2

35

23

17

Evaluate:

3 x 7 + 2

Apply the order of operations to find the answer to the expression below.

(4 - 3) x 2

Work out:

5 x 42 + 3

Evaluate:

(3 - 6)2

For each of the calculations in the table, select which operation you would tackle first.

For the calculation:

(3 + 2) x (4 - 2)

Which bracket should be completed first?

(3 + 2)

(4 - 2)

It makes no difference

Evaluate:

(3 + 7)2 - 6 x 4

• Question 1

Which order should you perform the following operations in?

## Column B

Brackets
1st
Orders
2nd
Division
3rd
Multiplication
4th
5th
Subtraction
6th
EDDIE SAYS
This was a nice refresher to start with. Just follow the letters in BODMAS and you won't go wrong! If you prefer the word 'Indices' to 'Orders', you may choose to use the acronym of BIDMAS instead.
• Question 2

Which is the correct answer to the sum below?

3 + 4 x 5

23
EDDIE SAYS
If we start by thinking what operators we have, we can see that we Addition (A) and Multiplication (M) are relevant here. BODMAS tells us that M comes before A, so we need to multiply the 4 and 5 first, then add this to the 3. (4 x 5) + 3 = 23
• Question 3

How would you solve the equation below?

6 - 4 ÷ 2

EDDIE SAYS
Once again, we just need to follow the letters of BODMAS. We have subtraction (S) and division (D) present in this sum. In the order of operations, divide (D) comes before subtraction (S), so this sum could be rewritten as: (4 ⊃ 2) - 6 = -4
• Question 4

Evaluate:

3 x 7 + 2

23
EDDIE SAYS
Evaluation is just a fancy way of saying "work out". Did you follow BODMAS? Remember that multiplication (M) comes before addition (A). So this sum is already in the right order, but we can just add some brackets to make this even clearer: (3 x 7) + 2 = 23
• Question 5

Apply the order of operations to find the answer to the expression below.

(4 - 3) x 2

2
EDDIE SAYS
This question tells you what you should be using! "Apply the order of operations" just means "use BODMAS". Look our for this in exams. It is easy to get a bit lost on this one, because there is a subtraction (S) and a multiplication (M) present. However, the subtraction element is within a set of brackets (B) so this takes priority and comes before the multiplication. So we can simply calculate along the line from left to right: (4 - 3) x 2 = 2 Great focus; you're halfway there!
• Question 6

Work out:

5 x 42 + 3

83
EDDIE SAYS
This time we have three things going on - multiplication (M), addition (A) and a power (O). This doesn't make the slightest difference; it just takes a little longer. We need to deal with the power first, then the multiplication and finally the addition. So we can rewrite our sum as: 42 x 5 + 3 = 83
• Question 7

Evaluate:

(3 - 6)2

9
EDDIE SAYS
It's easy to get this one wrong and write -9. We have a bracket to deal with (3 - 6) which gives us -3. So far, so good. The mistake takes place when you have to think that -32 actually means (-3)2 which is -3 x -3. As two - symbols in a multiplication become a + overall, the correct answer here is 9. Did you spot that?
• Question 8

For each of the calculations in the table, select which operation you would tackle first.

EDDIE SAYS
Does it have brackets? Deal with them first. Does it have powers? Deal with them next. And so on... In the first sum, we have addition (A) and a multiplication (M) present. BODMAS tells us to work out the multiplication first. In the second, we have brackets (B) and addition (A) - brackets come first. In the third, we have subtraction (S) and a power (O/I) - the power comes first. Finally, in the fourth, we have two sets of brackets (B) and two subtractions (S). However, we can ignore the subtractions as they are within the brackets. How did you do there?
• Question 9

For the calculation:

(3 + 2) x (4 - 2)

Which bracket should be completed first?

It makes no difference
EDDIE SAYS
It makes no difference which one you calculate first, so long as you do them both before you multiply them together. If the sum had any other symbol in the centre, rather than a multiplication, then it would matter. For example, 5 - 2 and 2 - 5 do not give the same answers.
• Question 10

Evaluate:

(3 + 7)2 - 6 x 4

76
EDDIE SAYS
This is about a tricky as it'll get in an exam, but you still take it step by step as with easier questions. B (10)2 - 6 x 4 O 100 - 6 x 4 D ---- M 100 - 24 A ---- S 76 How did you do there? Congratulations on completing this activity!
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