# 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 S stand for in BIDMAS?

Subtraction

Substitute

Substance

Surprise

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.

A + D - C - E

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 x A + E - C²

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

113

128

44

If C = 7, D = 15 and E = 2, what is C² - D + E?

37

44

36

If c = 7, d = 15, e = 2 and f = 4, what is (c x d) - e² x f?

89

404

103

If C = 7, D = 15, E = 2 and F = 4, what is C x D + E² x F?

Insert brackets into the equation so that you would reach an answer of 217

(In other words, you need to order the operations in the equation so that an answer of 217 is reached.)

If C = 7, D = 15,  E = 2 and F = 4, what is C x D - E² x F?

Insert brackets into the equation so that you would reach an answer of 404

(In other words, you need to order the operations in the equation so that an answer of 404 is reached.)

You have been given the following information: a = 32, b = 2, c = 7, d = 15, e = 8.

Select the equation from the options below that will give you an answer of 9

b² x a ÷ e - c

b² - a ÷ e + c

b² x a ÷ (e - c)

• Question 1

What does the S stand for in BIDMAS?

Subtraction
EDDIE SAYS
The letter S in BIDMAS stands for Subtraction.
• Question 2

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.

A + D - C - E
EDDIE SAYS
There are three separate operations present in this calculation: +, - and -.
According to the rules of BIDMAS, the addition (+) and subtraction (-) have equal weight, so we should work through them in the order they have been written from left to right.
Using this information, the sum you should tackle first in this example is A + D.
• 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.

(B² x A) ÷ E - C
EDDIE SAYS
Wow, this is a tricky one! Well done if you got it all correct!
There are a whopping five operations present in this calculation: a power (²), brackets, x, ÷ and -.
According to the rules of BIDMAS, the sum within the brackets is the highest priority. Don't let the power here confuse you - EVERYTHING within the brackets needs to be multiplied first.
The division (÷) should then be tackled after this, and the subtraction (-) is the lowest priority of the five operations.
Using this information, the sum you should tackle first in this example is (B² x A).
• 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 x A + E -
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. Don't let its position at the end of the sum fool you!
The multiplication (x) should be tackled next.
The addition (+) and subtraction (-) have equal weight, so we should work through them in the order they have been written from left to right.
Using this information, the sum you should tackle first in this example is C².
• Question 5

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

113
EDDIE SAYS
There are three operations present in this calculation: a power (²), + and x.
According to the rules of BIDMAS, the power (²) is the highest priority as it is an example of an indices.
The multiplication (x) should be tackled next, and the addition (+) 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 multiplication second, we need to then multiply this answer by e (which is 2), giving us 98.
Finally, we need to add d (which is 15) to this answer, which gives us an overall answer of 113.
Did you get those calculations in the right order maths coder?
• Question 6

If C = 7, D = 15 and E = 2, what is C² - D + E?

36
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 subtract D (which is 15) from this, so we reach 34.
Finally we need to add E (which is 2) to this total, to arrive at 36 as our final answer.
• Question 7

If c = 7, d = 15, e = 2 and f = 4, what is (c x d) - e² x f?

89
EDDIE SAYS
There are five operations present in this calculation: a power (²), brackets, two x's and -.
According to the rules of BIDMAS, the sum in brackets (which contains one of the multiplications) is the highest priority.
The power (²) is the next priority, followed by the multiplication (x) then the subtraction(-).
Working out the brackets first, we find that (c x d) becomes (7 x 15) which is 105.
Then we need to work out the power next. We find that e² becomes 2² or 2 x 2. The answer to this is 4.
We then need to multiply 4 by f (which is 4) to reach 16.
Finally we need to subtract 16 from our total from the brackets (105) to reach a final answer of 89.
• Question 8

If C = 7, D = 15, E = 2 and F = 4, what is C x D + E² x F?

Insert brackets into the equation so that you would reach an answer of 217

(In other words, you need to order the operations in the equation so that an answer of 217 is reached.)

C x (D + E² x F)
EDDIE SAYS
We need to work out the value of each part of the equation and its position in BIDMAS.
If we change all the letters to the numbers they represent, the equation becomes 7 x 15 + 2² x 4.
2² is 4, so this equation can be simplified to 7 x 15 + 16.
This time we are aiming for an answer of 217 and we can see that (15 + 16) will give us a total of 31, which when multiplied by 7, will get us to our 217 total.
This means that we need (D + E² x F) to be in brackets, as we need to do this first before multiplying by 7.
• Question 9

If C = 7, D = 15,  E = 2 and F = 4, what is C x D - E² x F?

Insert brackets into the equation so that you would reach an answer of 404

(In other words, you need to order the operations in the equation so that an answer of 404 is reached.)

(C x D - E²) x F
EDDIE SAYS
We need to work out the value of each part of the equation and its position in BIDMAS.
If we change all the letters to the numbers they represent, the equation becomes 7 x 15 - 2² x 4.
7 x 15 is 105 and 2² is 4, so this equation can be simplified to 105 - 4 x 4.
We are aiming for an answer of 404 and we can see that (105 - 4) will give us a total of 101, which when multiplied by 4, will get us to our 404 total.
This means that we need (C x D - E²) to be in brackets, so we do this first before multiplying by 4.
• Question 10

You have been given the following information: a = 32, b = 2, c = 7, d = 15, e = 8.

Select the equation from the options below that will give you an answer of 9

b² x a ÷ e - c
EDDIE SAYS
We know that b = 2, a = 32, e = 8 and c = 7, so we can substitute these numbers into each option then prioritise the operations in each.
Option 1: 2² x 32 ÷ 8 - 7 remains in the same order when we apply the rules of BIDMAS, which gives us an answer of 9. This is the correct answer!
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