# Use BIDMAS and Give Answers as Letters

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 within the same calculation, then you should 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 within the same calculation, then you should 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!

If a = 18, b = 3, c = 9 and d = 15, what is b (a - d)?

What is the answer to this problem as a letter?

Remember the letters in your answer have the same value as those in the question.

a

b

c

d

So far you have been giving answers as numbers, now we are going to practice giving the answer as a letter.

If A = 12, B = 2, C = 9 and D = 36, what is C x A?

What is the answer to this problem as a letter?

Remember that the letters in your answer have the same value as those in the question.

A

B

C

D

If A = 16, B = 3, C = 7 and D = 21, which of the equations below is true?

A - B = C

B² + C = A

D ÷ C = A

A + B + C = D

If a = 25, b = 3, c = 7 and d = 15, which of the equations below is true?

(a x b) - (d + b) = d

√a x b = d

c + b + b = a

d ÷ b + c = a

If A = 5, B = 3, C = 7 and D = 22, are the equations below correct or incorrect?

If a = 49, b = 7, c = 8 and d = 14, which of the equations below is true?

√a + b = d

b x c = a

d x c = a

b + c + d = a

If a = 48, b = 6, c = 8 and d = 12, which of the equations below is true?

d - b = c

(a + c) ÷ d = b

b² + d = a

c² - a = d

If A = 32, B = 4, C = 8 and D = 16, are the equations below correct or incorrect?

If a = 72, b = 8, c = 3 and d = 24, which of the equations below is true?

a ÷ b = c

b x c² = a

d (b - c) = a

b x c + d = a

If A = 13, B = 8, C = 3 and D = 24, are the equations below correct or incorrect?

• Question 1

If a = 18, b = 3, c = 9 and d = 15, what is b (a - d)?

What is the answer to this problem as a letter?

Remember the letters in your answer have the same value as those in the question.

c
EDDIE SAYS
The question tells us that b = 3, a = 18 and d = 15.
If we substitute these numbers for the letters in the equation then b (a - d)becomes 3 x (18 - 15).
Using the rules of BIDMAS, we must tackle the brackets first, so the steps we need to take are (18 - 15) x 3.
The answer to 3 x 3 is 9.
The question tells us that the number 9 is represented by the letter c, so this is the correct answer.
• Question 2

So far you have been giving answers as numbers, now we are going to practice giving the answer as a letter.

If A = 12, B = 2, C = 9 and D = 36, what is C x A?

What is the answer to this problem as a letter?

Remember that the letters in your answer have the same value as those in the question.

D
EDDIE SAYS
The question tells us that C = 9 and A = 12.
If we substitute these numbers for the letters in the equation then √C x A becomes √9 x 12.
Using the rules of BIDMAS, we must tackle the square root (√) first as it is an indices.
Have you looked at square roots before? They are the opposite of a square number, so what you reach if you divide a number by itself. For example, 2 x 2 = 4 so the square root of 4 is 2.
So √C becomes √9 which is 3.
Then we need to tackle the multiplication and times this answer by A (which is 12). 3 x 12 = 36.
The letter that corresponds to 36 is D, so this is the correct answer.
• Question 3

If A = 16, B = 3, C = 7 and D = 21, which of the equations below is true?

B² + C = A
EDDIE SAYS
The question tells us that A = 16, B = 3, C = 7 and D = 21.
If we work through each option in order, using BIDMAS to prioritise operations, we find that: Option 1: 16 - 3 = 7. This is not true so cannot be the correct answer. Option 2: 3² + 7 = 16. This is true so is a correct answer! The best detective always double checks their work, so let's calculate the others to be sure we have the only correct answer... Option 3: 21 ÷ 7 = 16. This is also not true. Option 4: 16 + 3 + 7 = 21. This is also not true.
So only option 2 (B² + C = A) is true and must be the only correct answer. Great detective work!
• Question 4

If a = 25, b = 3, c = 7 and d = 15, which of the equations below is true?

√a x b = d
EDDIE SAYS
The question tells us that a = 25, b = 3, c = 7 and d = 15.
If we work through each option in order, using BIDMAS to prioritise operations, we find that: Option 1: (25 x 3) - (15 + 3) = 15. This is not true so cannot be the correct answer. Option 2: √25 x 3 = 15. This is true so is a correct answer! Let's continue detecting just in case... Option 3: 7 + 3 + 3 = 25. This is also not true. Option 4: 15 ÷ 3 + 7 = 25. This is also not true.
So only option 2 (√a x b = d) is true and must be the only correct answer.
• Question 5

If A = 5, B = 3, C = 7 and D = 22, are the equations below correct or incorrect?

EDDIE SAYS
The question tells us that A = 5, B = 3, D = 22 and C = 7.
If we work through each option in order, using BIDMAS to prioritise operations, we find that: Option 1: 5² - 3 = 22. This is correct! Let's check if there are any others... Option 2: 7 x 3 = 22. The answer to this calculation is 21 so this is incorrect. Option 3: 7² - (22 + 5) = 22. This is also correct!
Great work on assessing which calculations were correct and which was a red herring!
• Question 6

If a = 49, b = 7, c = 8 and d = 14, which of the equations below is true?

√a + b = d
EDDIE SAYS
The question tells us that a = 49, b = 7, c = 8 and d = 14.
If we work through each option in order, using BIDMAS to prioritise operations, we find that: Option 1: √49 + 7 = 14. This is true so is a correct answer! Let's check if there are any others... Option 2: 7 x 8 = 49. This is not true so cannot be the correct answer. Option 3: 14 x 8 = 49. This is also not true. Option 4: 7 + 8 + 14 = 49. This is also not true.
So only option 1 (√a + b = d) is true and must be the only correct answer.
• Question 7

If a = 48, b = 6, c = 8 and d = 12, which of the equations below is true?

b² + d = a
EDDIE SAYS
The question tells us that a = 48, b = 6, c = 8 and d = 12.
If we work through each option in order, using BIDMAS to prioritise operations, we find that: Option 1: 12 - 6 = 8. This is not true so cannot be the correct answer. Option 2: (48 + 6) ÷ 12 = 6. This is also not true. Option 3: 6² +12 = 48. This is true so is a correct answer! Let's check the last calculation just in case... Option 4: 8² - 48 = 12. This is also not true.
So only option 3 (b² + d = a) is true and must be the only correct answer.
• Question 8

If A = 32, B = 4, C = 8 and D = 16, are the equations below correct or incorrect?

EDDIE SAYS
The question tells us that A = 32, B = 4, C = 8 and D = 16.
If we work through each option in order, using BIDMAS to prioritise operations, we find that: Option 1: √16 + 4 = 8. The answer to this sum is 8 so the equation is correct! Option 2: 8 x 4 = 32. The answer to this sum is 8 so the equation is correct! Option 3: 4² +16 = 32. The answer to this sum is 32 so the equation is also correct! Option 4: 4 + 8 = 16. The answer to this sum is 12 so this is the only equation which is incorrect.
Just the one red herring here - did you spot it?
• Question 9

If a = 72, b = 8, c = 3 and d = 24, which of the equations below is true?

b x c² = a
EDDIE SAYS
The question tells us that a = 72, b = 8, c = 3 and d = 24.
If we work through each option in order, using BIDMAS to prioritise operations, we find that: Option 1: 72 ÷ 8 = 3. This is not true so cannot be the correct answer. Option 2: 8 x 9 = 72. This is true so is a correct answer! Let's check the other calculations just in case... Option 3: 24 x 5 = 72. This is also not true. Option 4: 8 x 3 + 24 = 72. This is also not true.
So only option 2 (b x c² = a) is true and must be the only correct answer.
• Question 10

If A = 13, B = 8, C = 3 and D = 24, are the equations below correct or incorrect?

EDDIE SAYS
The question tells us that A = 13, B = 8, C = 3 and D = 24.
If we work through each option in order, using BIDMAS to prioritise operations, we find that: Option 1: 24 ÷ 3 = 8 . The answer to this sum is 8 so the equation is correct! Option 2: 8 x 3 = 24. The answer to this sum is 24 so the equation is also correct! Option 3: 32 ÷ 8 = 3. The answer to this sum is 4 so the equation is incorrect. Option 4: 24 - 9 = 13. The answer to this sum is 15 so this is also incorrect.
Did you spy the two red herrings in these equations? Well done if so, super spier!
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