# Prioritise Operations using BIDMAS

In this worksheet, students will replace letters with numbers and solve problems using BIDMAS. They must give their final answers as letters not numbers.

Key stage:  KS 2

Curriculum topic:   Verbal Reasoning

Curriculum subtopic:   Maths Codes

Difficulty level:

### QUESTION 1 of 10

Make sure that you’ve got your thinking cap on as we are going to be number decoders!

For this activity, we must follow the rules of BIDMAS (or you may know them as BODMAS).

BIDMAS tells us the order in which we should answer long calculations:

 1 B Brackets Anything inside brackets must be calculated first. 2 I Indices (or Orders) Any squared numbers or square roots must be calculated next. 3 D  M Division and  Multiplication Then division and multiplication steps. If you have both of these within one calculation, then complete it from left to right as it has been written. 4 A  S Addition and   Subtraction Then addition and subtraction steps. If you have both of these within one calculation, then complete it from left to right as it has been written.

Let’s crack a code using BIDMAS:

If a = 8, b = 6, c = 3, d = 7 and e = 12, what is b x a ÷ e + c?

First, we must swap the letters back into numbers to help us work it out. This would be written as: 6 x 8 ÷ 12 + 3 = ___.

There are not any brackets or indices so, according to BIDMAS rules, we must calculate the multiplication and division first. This must be done in the order that it is written, so 6 x 8 = 48.

Then we are left with: 48 ÷ 12 + 3.

Following BIDMAS, let’s do the division first, 48 ÷ 12 = 4.

Then we are left with 4 + 3 = 7.

So the answer is 7 but we must convert this back into a letter. The number 7 is represented by the letter d, therefore d is the final answer.

Let’s try one more and write the answer as a letter:

If a = 4, b = 125 , c = 3, d = 11 and e = 7, what is d (c x a) - e?

Where there isn’t a -, +, x or ÷ between the first letter and the bracket, it means we have to multiply the outside number by what is in the brackets.

So the steps we follow are:

c x a = 12

d x 12 = 132

132 - e = 125

We must turn the number 125 back into a letter. This number corresponds to the letter b.

Now it’s your turn to crack the codes. Good luck number detective!

What does the I stand for in BIDMAS?

Inverts

Indices

Index

Inplant

When should you tackle indices according to the rules of BIDMAS

After multiplication

Before brackets

After brackets

According to the rules of BIDMAS, which part of the equation below would you would need to tackle first?

You should highlight the operation (+, -, x, ÷, ², etc.) and the one or two letters it affects to be marked correctly.

B² x A ÷ E - C

According to the rules of BIDMAS, which part of the equation below would you would need to tackle first?

You should highlight the operation (+, -, x, ÷, ², etc.) and the one or two letters it affects to be marked correctly.

b (a + e) - c²

According to the rules of BIDMAS, which part of the equation below would you would need to tackle first?

You should highlight the operation (+, -, x, ÷, ², etc.) and the one or two letters it affects to be marked correctly.

C + D ÷ E

If c = 7, d = 15 and e = 2, what is c² - d?

37

44

34

If C = 7, D = 15 and E = 2, what is (C x D) - E²

101

105

103

If c = 7, d = 15 and e = 2, what is c² + d - e

64

62

20

When you see addition and subtraction in a calculation, what should you do according to the rules of BIDMAS

You must add after you subtract

You must add before you subtract

If both are present, work through left to right

If A = 32, B = 2, C = 7, D = 15 and E = 8, what is B² (A ÷ E) - C?

10

9

11

• Question 1

What does the I stand for in BIDMAS?

Indices
EDDIE SAYS
The letter I in BIDMAS stands for Indices (or Orders) such as squared numbers or square roots.
• Question 2

When should you tackle indices according to the rules of BIDMAS

After brackets
EDDIE SAYS
Indices are the second highest priority in the BIDMAS acronym.
The only thing more important is B which stands for Brackets.
If you read the three statements given, only the last one is true.
• Question 3

According to the rules of BIDMAS, which part of the equation below would you would need to tackle first?

You should highlight the operation (+, -, x, ÷, ², etc.) and the one or two letters it affects to be marked correctly.

x A ÷ E - C
EDDIE SAYS
There are four operations present in this calculation: a power (²), x, ÷ and -.
According to the rules of BIDMAS, the power is the highest priority as it is an example of an indices.
The multiplication (x) and division (÷) have equal weight, so we should work through them in the order they have been written from left to right.
The subtraction (-) is the lowest priority of the four operations.
Using this information, the sum you should tackle first in this example is B².
• Question 4

According to the rules of BIDMAS, which part of the equation below would you would need to tackle first?

You should highlight the operation (+, -, x, ÷, ², etc.) and the one or two letters it affects to be marked correctly.

b (a + e) -
EDDIE SAYS
There are five operations present in this calculation: brackets, a power (²), x, + and -.
According to the rules of BIDMAS, the sum in brackets (which includes the addition) is the highest priority.
The indices (²) is the next priority, followed by the multiplication (x).
The subtraction (-) is the lowest priority of the five operations.
Using this information, the sum you should tackle first in this example is (a + e).
• Question 5

According to the rules of BIDMAS, which part of the equation below would you would need to tackle first?

You should highlight the operation (+, -, x, ÷, ², etc.) and the one or two letters it affects to be marked correctly.

C + D ÷ E
EDDIE SAYS
There are two operations present in this calculation: + and ÷.
According to the rules of BIDMAS, the division is the highest priority.
The addition (+) is the lowest priority.
Using this information, the sum you should tackle first in this example is D ÷ E.
• Question 6

If c = 7, d = 15 and e = 2, what is c² - d?

34
EDDIE SAYS
There are two operations present in this calculation: a power (²) and -.
According to the rules of BIDMAS, the power (²) is the highest priority as it is an example of an indices.
The subtraction (-) is the lowest priority.
Working out the indices first, we find that c² becomes 7² or 7 x 7. The answer to this is 49.
Working on the subtraction second, we need to then take d (which is 15) away from this answer, which gives us an overall answer of 34. Did you get those calculations in the right order maths coder?
• Question 7

If C = 7, D = 15 and E = 2, what is (C x D) - E²

101
EDDIE SAYS
There are four operations present in this calculation: a power (²), brackets, x and -.
According to the rules of BIDMAS, the sum in the brackets (which includes the multiplication) id the highest priority.
Then the power (²) is the next priority as it is an example of an indices.
The subtraction (-) is the lowest priority.
Working out the brackets first, we find that (C x D) becomes (7 x 15). the answer to this is 105.
Concentrating on the indices next, we find that E² becomes 2² or 2 x 2. The answer to this is 4.
Finally we need to subtract 4 from 105 to reach our overall answer, which is 101.
• Question 8

If c = 7, d = 15 and e = 2, what is c² + d - e

62
EDDIE SAYS
There are three operations present in this calculation: a power (²), + and -.
According to the rules of BIDMAS, the power (²) is the highest priority.
In BIDMAS, the addition (+) and subtraction (-) have equal weight, so we should work through them from left to right.
Working out the power first, we find that c² becomes 7² or 7 x 7. The answer to this is 49.
We then need to add d (which is 15) to this, so we reach 64.
Finally we need to subtract e (which is 2) from this total, to arrive at 62 as our final answer.
• Question 9

When you see addition and subtraction in a calculation, what should you do according to the rules of BIDMAS

If both are present, work through left to right
EDDIE SAYS
In BIDMAS, addition and subtraction are given equal weight in terms of priorities.
So if both appear in the same question, then you calculate from the left to right of the equation.
• Question 10

If A = 32, B = 2, C = 7, D = 15 and E = 8, what is B² (A ÷ E) - C?

9
EDDIE SAYS
There are five operations present in this calculation: a power (²), brackets ÷, x and -.
According to the rules of BIDMAS, the sum in the brackets (which includes the division) is the highest priority.
The power (²) is the second priority.
In BIDMAS, the multiplication (x) and the division (÷) have equal weight, so we should work through them from left to right.
Finally, the subtraction (-) is the lowest priority.
Working out the sum in the brackets first, we find that (A ÷ E) becomes (32 ÷ 8). The answer to this is 4.
Then we need to calculate the power to find that B² becomes 2² or 2 x 2. The answer to this is 4.
We then need to multiply these two answers together to arrive at 16.
Finally we need to subtract C (which is 7) from this total, to arrive at 9 as our final answer.
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