# Use BIDMAS and Give Answers as Letters in Complex Calculations

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 square numbers or square roots must be calculated next. 3 D  M Division and  Multiplication Then division and multiplication. If both of these are present within the same calculation, you should work through the steps from left to right in the order they have been written. 4 A  S Addition and  Subtraction Then addition and subtraction. If both of these are present within the same calculation, you should work through the steps from left to right in they order they have 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!

You have been given the following information: a = 4, b = 8, c = 9, d = 12, e = 18.

Which letter completes the equation: (c x b) ÷ e = __?

a

b

c

d

e

You have been given the following information: A = 3, B = 5, C = 6, D = 9, E = 11.

Which letter completes the equation: E + A - B = __?

A

B

C

D

E

You have been given the following information: a = 2, b = 6, c = 4, d = 8, e = 12.

Which letter completes the equation: a x e - d - c = __?

a

b

c

d

e

You have been given the following information: A = 20, B = 10, C = 4, D = 5, E = 2.

Which letter completes the equation: E x B ÷ C = __?

A

B

C

D

E

You have been given the following information: a = 3, b = 6, c = 7, d = 9, e = 11.

Which letter completes the equation: a x b - e = __?

a

b

c

d

e

You have been given the following information: A = 0, B = 9 C = 8, D = 2, E = 1.

Which letter completes the equation: A (B + C) + E = __?

A

B

C

D

E

You have been given the following information: a = 14, b = 7, c = 6, d = 8, e = 12.

Which letter completes the equation: (b x c + a) ÷ d = __?

a

b

c

d

e

You have been given the following information: A = 32, B = 4, C = 8, D = 24, E = 12.

Which letter completes the equation: E x C ÷ B = __?

A

B

C

D

E

You have been given the following information: A = 8, B = 15, C = 17, D = 4, E = 6.

Which letter completes the equation: (B + C) ÷ A = __?

A

B

C

D

E

You have been given the following information: a = 36, b = 6, c = 25, d = 10, e = 90.

Which letter completes the equation: a x c ÷ d = __?

a

b

c

d

e

• Question 1

You have been given the following information: a = 4, b = 8, c = 9, d = 12, e = 18.

Which letter completes the equation: (c x b) ÷ e = __?

a
EDDIE SAYS
The question tells us that c = 9, b = 8 and e = 18.
If we substitute these numbers for the letters in the equation then (c x b) ÷ e = __ becomes (9 x 8) ÷ 18 = __.
Using the rules of BIDMAS, we can tackle the steps of this calculation in the exact order they have been written.
So (9 x 8) ÷ 18 = 72 ÷ 18 = 4.
The letter that corresponds to 4 is a, so this is the correct answer.
• Question 2

You have been given the following information: A = 3, B = 5, C = 6, D = 9, E = 11.

Which letter completes the equation: E + A - B = __?

D
EDDIE SAYS
The question tells us that E = 11, A = 3 and B = 5.
If we substitute these numbers for the letters in the equation then E + A - B = __ becomes 11 + 3 - 5 = __.
Using the rules of BIDMAS, we can tackle the steps of the calculation in exactly the order in which they have been written.
So 11 + 3 - 5 = 9.
The letter that corresponds to 9 is D, so this is the correct answer.
• Question 3

You have been given the following information: a = 2, b = 6, c = 4, d = 8, e = 12.

Which letter completes the equation: a x e - d - c = __?

e
EDDIE SAYS
The question tells us that a = 2, e = 12, d = 8 and c = 4.
If we substitute these numbers for the letters in the equation then a x e - d - c = __ becomes 2 x 12 - 8 - 4 = __.
Using the rules of BIDMAS, we can tackle the steps of the calculation in exactly the order in which they have been written.
So 2 x 12 - 8 - 4 = 24 - 12 = 12.
The letter that corresponds to 12 is e, so this is the correct answer.
• Question 4

You have been given the following information: A = 20, B = 10, C = 4, D = 5, E = 2.

Which letter completes the equation: E x B ÷ C = __?

D
EDDIE SAYS
The question tells us that E = 2, B = 10 and C = 4.
If we substitute these numbers for the letters in the equation then E x B ÷ C = __ becomes 2 x 10 ÷ 4 = __.
Using the rules of BIDMAS, we can tackle the steps of the calculation in exactly the order in which they have been written.
So 2 x 10 ÷ 4 = 20 ÷ 4 = 5.
The letter that corresponds to 5 is D, so this is the correct answer.
• Question 5

You have been given the following information: a = 3, b = 6, c = 7, d = 9, e = 11.

Which letter completes the equation: a x b - e = __?

c
EDDIE SAYS
The question tells us that a = 3, b = 6 and e = 11.
If we substitute these numbers for the letters in the equation then a x b - e = __ becomes 3 x 6 - 11 = __.
Using the rules of BIDMAS, we can tackle the steps of the calculation in exactly the order in which they have been written.
So 3 x 6 - 11 = 18 - 11 = 7.
The letter that corresponds to 7 is c, so this is the correct answer. Well done super detective - you are on a roll! Keep up the great work with the next question...
• Question 6

You have been given the following information: A = 0, B = 9 C = 8, D = 2, E = 1.

Which letter completes the equation: A (B + C) + E = __?

E
EDDIE SAYS
The question tells us that A = 0, B = 9, C = 8 and E = 1.
If we substitute these numbers for the letters in the equation then A (B + C) + E = __ becomes 0 x (9 + 8) + 1 = __.
Using the rules of BIDMAS, we must tackle the brackets first, then the multiplication, followed by the addition.
So 0 x (9 + 8) + 1 = __ becomes 9 + 8 x 0 + 1 = __ when the operations have been prioritised.
The answer to this sum is 1, and the letter that corresponds to 1 is E, so this is the correct answer.
Did you spot the shortcut to the answer? Anything multiplied by 0 gives 0, so you can ignore the first part of the equation altogether. Well done if you spotted this!
• Question 7

You have been given the following information: a = 14, b = 7, c = 6, d = 8, e = 12.

Which letter completes the equation: (b x c + a) ÷ d = __?

b
EDDIE SAYS
The question tells us that b = 7, c = 6, a = 14 and d = 8.
If we substitute these numbers for the letters in the equation then (b x c + a) ÷ d = __ becomes (7 x 6 + 14) ÷ 8 = __.
Using the rules of BIDMAS, we must tackle the brackets first, then the division.
So (7 x 6 + 14) ÷ 8 = 56 ÷ 8 = 7.
The letter that corresponds to 7 is b, so this is the correct answer.
• Question 8

You have been given the following information: A = 32, B = 4, C = 8, D = 24, E = 12.

Which letter completes the equation: E x C ÷ B = __?

D
EDDIE SAYS
The question tells us that E = 12, C = 8 and B = 4.
If we substitute these numbers for the letters in the equation then E x C ÷ B = __ becomes 12 x 8 ÷ 4 = __.
Using the rules of BIDMAS, we can tackle the steps of the calculation in the exact order they have been written.
So 12 x 8 ÷ 4 = 96 ÷ 4 = 24.
The letter that corresponds to 24 is D, so this is the correct answer.
You're on a roll top detective...nearly there!
• Question 9

You have been given the following information: A = 8, B = 15, C = 17, D = 4, E = 6.

Which letter completes the equation: (B + C) ÷ A = __?

D
EDDIE SAYS
The question tells us that B = 15, C = 17 and A = 8.
If we substitute these numbers for the letters in the equation then (B + C) ÷ A = __ becomes (15 + 17) ÷ 8 = __.
Using the rules of BIDMAS, we can tackle the steps of this calculation in the exact order they have been written.
So (15 + 17) ÷ 8 = 32 ÷ 8 = 4.
The letter that corresponds to 4 is D, so this is the correct answer.
Just one question left top detective!
• Question 10

You have been given the following information: a = 36, b = 6, c = 25, d = 10, e = 90.

Which letter completes the equation: a x c ÷ d = __?

e
EDDIE SAYS
The question tells us that a = 36, c = 25 and d = 10.
If we substitute these numbers for the letters in the equation then a x c ÷ d = __ becomes 36 x 25 ÷ 10 = __.
Using the rules of BIDMAS, we can tackle the steps of this calculation in the exact order they have been written.
So 36 x 25 ÷ 10 = 900 ÷ 10 = 90.
The letter that corresponds to 90 is e, so this is the correct answer.
Well done if you got that one correct - it involved some large calculations!
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