 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 you have both of these present within the same calculation, you must complete each step from left to right as it has been written. 4 A  S Addition and  Subtraction Then addition and subtraction. If you have both of these present within the same calculation, you must complete each step 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!

You have been given the following information: a = 4, b = 3, c = 9, d = 2, e = 29.

Which letter completes the equation: c&sup2; ÷ b + d = __?

a

b

c

d

e

You have been given the following information: A = 3, B = 17, C = 6, D = 9, E = 11.

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

A

B

C

D

E

You have been given the following information: a = 9, b = 6, c = 4, d = 15, e = 12.

Which letter completes the equation: d² ÷ (d + b + c) = __?

a

b

c

d

e

You have been given the following information: A = 20, B = 10, C = 4, D = 5, E = 18.

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

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 c) ÷ (b + a) = __?

a

b

c

d

e

You have been given the following information: A = 32, B = 9, C = 8, D = 7, E = 1.

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

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: e² ÷ c - d = __?

a

b

c

d

e

You have been given the following information: A = 32, B = 4, C = 30, D = 24, E = 14.

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

A

B

C

D

E

You have been given the following information: A = 144, B = 18, C = 17, D = 4, E = 6.

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

A

B

C

D

E

You have been given the following information: a = 17, b = 5, c = 25, d = 10, e = 110.

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

a

b

c

d

e

• Question 1

You have been given the following information: a = 4, b = 3, c = 9, d = 2, e = 29.

Which letter completes the equation: c&sup2; ÷ b + d = __?

e
EDDIE SAYS
The question tells us that c = 9, b = 3 and d = 2.
If we substitute these numbers for the letters in the equation then c² ÷ b + d = __ becomes 9² ÷ 3 + 2 = __.
Using the rules of BIDMAS, we can work through the calculation in the exact order it has been written.
So 9² ÷ 3 + 2 = 81 ÷ 3 + 2 = 27 + 2 = 29.
The letter that corresponds to 29 is e, so this is the correct answer. Well done super detective - you are on a roll!
• Question 2

You have been given the following information: A = 3, B = 17, C = 6, D = 9, E = 11.

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

B
EDDIE SAYS
The question tells us that E = 11, D = 9, A = 3 and C = 6.
If we substitute these numbers for the letters in the equation then (E x D + A) ÷ C = __ becomes (11 x 9 + 3) ÷ 6 = __.
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 x 9 + 3) ÷ 6 = 102 ÷ 6 = 17.
The letter that corresponds to 17 is B, so this is the correct answer.
• Question 3

You have been given the following information: a = 9, b = 6, c = 4, d = 15, e = 12.

Which letter completes the equation: d² ÷ (d + b + c) = __?

a
EDDIE SAYS
The question tells us that d = 15, b = 6 and c = 4.
If we substitute these numbers for the letters in the equation then d² ÷ (d + b + c) = __ becomes 15² ÷ (15 + 6 + 4) = __.
Using the rules of BIDMAS, we need to work out the sum in the brackets first, then the power (²), and then divide them by each other.
So (15 + 6 + 4) = 25. And 15² = 225.
225 ÷ 25 = 9.
The letter that corresponds to 9 is a, so this is the correct answer.
• Question 4

You have been given the following information: A = 20, B = 10, C = 4, D = 5, E = 18.

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

E
EDDIE SAYS
The question tells us that A = 20, C = 4, D = 5 and B = 10.
If we substitute these numbers for the letters in the equation then A (C + D) ÷ B = __ becomes 20 x (4 + 5) ÷ 10 = __.
Using the rules of BIDMAS, we can tackle the brackets first, then multiply this answer to 20, and finally divide by 10.
So 20 x (4 + 5) ÷ 10 = 20 x 9 ÷ 10 = 180 ÷ 10 = 18.
The letter that corresponds to 18 is E, 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 c) ÷ (b + a) = __?

c
EDDIE SAYS
The question tells us that d = 9, c = 7, b = 6 and a = 3.
If we substitute these numbers for the letters in the equation then (d x c) ÷ (b + a) = __ becomes (9 x 7) ÷ (6 + 3) = __.
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 7 = 63. And 6 + 3 = 9.
63 ÷ 9 = 7.
The letter that corresponds to 7 is 2, 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 = 32, B = 9, C = 8, D = 7, E = 1.

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

D
EDDIE SAYS
The question tells us that A = 32, B = 9 and C = 8.
If we substitute these numbers for the letters in the equation then √(A + B + C) = __ becomes √(32 + 9 + 8) = __.
Using the rules of BIDMAS, we must tackle the brackets first, then find the square root of our answer.
So √(32 + 9 + 8) = √49 = 7.
The letter that corresponds to 7 is D, 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: e² ÷ c - d = __?

a
EDDIE SAYS
The question tells us that e = 12, c = 6 and d = 8.
If we substitute these numbers for the letters in the equation then e² ÷ c - d = __ becomes 12² ÷ 6 - 8 = __.
Using the rules of BIDMAS, we need to work out the power (²) first, then divide this answer by 6, and finally subtract 8.
So 12² ÷ 6 - 8 = 144 ÷ 6 - 8 = 24 - 8 = 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 = 30, D = 24, E = 14.

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

C
EDDIE SAYS
The question tells us that D = 24, E = 14, A = 32 and B = 4.
If we substitute these numbers for the letters in the equation then D + E - A ÷ B = __ becomes 24 + 14 - 32 ÷ 4 = __.
Using the rules of BIDMAS, we must tackle the division first. So 32 ÷ 4 = 8.
We can then work through the remainder of the sum as it has been written, replacing the division with the number 8. So 24 + 14 - 8 = 30.
The letter that corresponds to 30 is C, so this is the correct answer.
• Question 9

You have been given the following information: A = 144, B = 18, C = 17, D = 4, E = 6.

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

B
EDDIE SAYS
The question tells us that A = 144, D = 4, E = 6, C = 17.
If we substitute these numbers for the letters in the equation then √A (D + E) - (E x C) = __ becomes √144 (4 + 6) - (6 x 17) = __.
Using the rules of BIDMAS, we must tackle the two sets of brackets first, then multiply the first bracket by the square root and subtract the answer to the second bracket.
So (4 + 6) = 10. And (6 x 17) = 102.
If we substitute these numbers into the rest of the calculation, we reach √144 x 10 - 102 = __.
If we calculate the square root, we get 12. If we substitute that in the sum becomes 12 x 10 - 102 = 120 - 102 = 18.
The letter that corresponds to 18 is B, so this is the correct answer.
• Question 10

You have been given the following information: a = 17, b = 5, c = 25, d = 10, e = 110.

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

a
EDDIE SAYS
The question tells us that e = 110, c = 25, b = 5 and d = 10.
If we substitute these numbers for the letters in the equation then (e + c) ÷ b - d = __ becomes (110 + 25) ÷ 5 - 10 = __.
Using the rules of BIDMAS, must work out the sum in the brackets first then divide this answer by 5 and finally subtract 10.
So (110 + 25) ÷ 5 - 10 = 135 ÷ 5 - 10 = 27 - 10 = 17.
The letter that corresponds to 17 is a, so this is the correct answer. These questions involved lots of tricky BIDMAS prioritisation and mental maths so well done top detective!
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