# 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, then you must complete the steps from left to right as they have been written. 4 A  S Addition and  Subtraction Then addition and subtraction. If both of these are present within the same calculation, then you must complete the steps from left to right as 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 = 2, e = 32.

Which letter completes the equation: d (b&sup2 ÷ a) = __?

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: √D + E - A = __?

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: c&sup2 - (b - a) = __?

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: B&sup2 ÷ A = __?

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: (d x e) ÷ (b x c - d) = __?

a

b

c

d

e

You have been given the following information: A = 24, B = 9, C = 8, D = 2, E = 1.

Which letter completes the equation: (B x C) ÷ (D + E) = __?

A

B

C

D

E

You have been given the following information: a = 16, b = 7, c = 6, d = 8, e = 12.

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

a

b

c

d

e

You have been given the following information: A = 32, B = 4, C = 8, D = 24, E = 14.

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

A

B

C

D

E

You have been given the following information: A = 81, B = 9, C = 17, D = 4, E = 6.

Which letter completes the equation: √A (D + E) - A = __?

A

B

C

D

E

You have been given the following information: a = 36, b = 6, c = 25, d = 10, e = 110.

Which letter complete the equation: d (√a + √c) = __?

a

b

c

d

e

• Question 1

You have been given the following information: a = 4, b = 8, c = 9, d = 2, e = 32.

Which letter completes the equation: d (b&sup2 ÷ a) = __?

e
EDDIE SAYS
The question tells us that d = 2, b = 8 and a = 4.
If we substitute these numbers for the letters in the equation then d (b² ÷ a) = __ becomes 2 x (8² ÷ 4) = __.
Using the rules of BIDMAS, we must work out the sum in the brackets first, then multiply this answer by 2.
So 2 x (8² ÷ 4) = 2 x 16 = 32.
The letter that corresponds to 32 is e, 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: √D + E - A = __?

E
EDDIE SAYS
The question tells us that D = 9, E = 11 and A = 3.
If we substitute these numbers for the letters in the equation then √D + E - A = __ becomes √9 + 11 - 3 = __.
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 + 11 - 3 = 11.
The letter that corresponds to 11 is E, so this is the correct answer.
Did you spot the sneaky shortcut of ignoring the 3's? You have a + 3 at the beginning of the sum and a - 3 at the end so they just cancel each other out. Well done if you spotted this shortcut!
• Question 3

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

Which letter completes the equation: c&sup2 - (b - a) = __?

e
EDDIE SAYS
The question tells us that c = 4, b = 6 and a = 2.
If we substitute these numbers for the letters in the equation then c² - (b - a) = __ becomes 4² - (6 - 2) = __.
Using the rules of BIDMAS, we need to work out the sum in the brackets first, then the power (²), and then subtract them from each other.
So (6 - 2) = 4 and 4² = 16. 16 - 4 = 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: B&sup2 ÷ A = __?

D
EDDIE SAYS
The question tells us that B = 10 and A = 20.
If we substitute these numbers for the letters in the equation then B² ÷ A = __ becomes 10² ÷ 20 = __.
Using the rules of BIDMAS, we can tackle the steps of the calculation in exactly the order in which they have been written.
So 10² ÷ 20 = 100 ÷ 20 = 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: (d x e) ÷ (b x c - d) = __?

a
EDDIE SAYS
The question tells us that d = 9, e = 11, b = 6 and c = 7.
If we substitute these numbers for the letters in the equation then (d x e) ÷ (b x c - d) = __ becomes (9 x 11) ÷ (6 x 7 - 9) = __.
Using the rules of BIDMAS, we must tackle the two sets of brackets separately first, and then divide the answers we find from each.
So 9 x 11 = 99. And 6 x 7 - 9 = 33.
99 ÷ 33 = 3.
The letter that corresponds to 3 is a, 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 = 24, B = 9, C = 8, D = 2, E = 1.

Which letter completes the equation: (B x C) ÷ (D + E) = __?

A
EDDIE SAYS
The question tells us that B = 9, C = 8, D = 2 and E = 1.
If we substitute these numbers for the letters in the equation then (B x C) ÷ (D + E) = __ becomes (9 x 8) ÷ (2 + 1) = __. Using the rules of BIDMAS, we must tackle the two sets of brackets first, then divide the answer we reach.
So (9 x 8) = 72. And (2 + 1) = 3.
72 ÷ 3 = 24.
The letter that corresponds to 24 is A, so this is the correct answer.
• Question 7

You have been given the following information: a = 16, b = 7, c = 6, d = 8, e = 12.

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

a
EDDIE SAYS
The question tells us that e = 12, d = 8 and c = 6.
If we substitute these numbers for the letters in the equation then e x d ÷ c = __ becomes 12 x 8 ÷ 6 = __.
Using the rules of BIDMAS, we can work through the steps of this calculation in exactly the order in which they have been written.
So 12 x 8 ÷ 6 = 96 ÷ 6 = 16.
The letter that corresponds to 16 is a, so this is the correct answer.
• Question 8

You have been given the following information: A = 32, B = 4, C = 8, D = 24, E = 14.

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

E
EDDIE SAYS
The question tells us that D = 24, A = 32 and B = 4.
If we substitute these numbers for the letters in the equation then (D + A) ÷ B = __ becomes (24 + 32) ÷ 4 = __.
Using the rules of BIDMAS, we can tackle the steps of the calculation in the exact order they have been written.
So (24 + 32) ÷ 4 = 56 ÷ 4 = 14.
The letter that corresponds to 14 is E, 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 = 81, B = 9, C = 17, D = 4, E = 6.

Which letter completes the equation: √A (D + E) - A = __?

B
EDDIE SAYS
The question tells us that A = 81, D = 4 and E = 6.
If we substitute these numbers for the letters in the equation then √A (D + E) - A = __ becomes √81 x (4 + 6) - 81 = __.
Using the rules of BIDMAS, we must work out the sum in the brackets first, then multiply this by the answer from the square root, before subtracting 81 from our total.
So √81 x (4 + 6) - 81 = 9 x 10 - 81 = 9.
The letter that corresponds to 9 is B, 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 = 110.

Which letter complete the equation: d (√a + √c) = __?

e
EDDIE SAYS
The question tells us that d = 10, a = 36 and c = 25.
If we substitute these numbers for the letters in the equation then d (√a + √c) = __ becomes 10 x (√36 + √25) = __.
Using the rules of BIDMAS, must work out the sum in the brackets first then multiply this answer by 10.
So 10 x (6 + 5) = 10 x 11 = 110.
The letter that corresponds to 110 is e, so this is the correct answer.
Well done if you got that one correct - it involved some tricky square roots and BIDMAS prioritisation!
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