 # 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 both of these are present within the same calculation, complete the steps from left to right as it has been written. 4 A  S Addition and  Subtraction Then addition and subtraction. If both of these are present within the same calculation, complete the steps 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 = 20, b = 6, c = 9 and d = 4, what is b&sup2 ÷ c?

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 practise giving the answer as a letter.

If A = 8, B = 20, C = 16 and D = 12, what is &radic;C x A - B?

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 = 26, which of the equations below is true?

A - B = C

B² + C = D

D ÷ C = A

A + B + C = D

If a = 12, b = 3, c = 7 and d = 15, which of the equations below is true?

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

a x b - c = d

c + b x d = a

d ÷ b + c = a

If A = 10, B = 2, C = 7, D = 22 and E = 17, are the equations below correct or incorrect?

If A = 64, B = 7, C = 8 and D = 15, which of the equations below is true?

√A + B = D

B x C = A

D x C = A

A ÷ C = B

If a = 39, b = 6, c = 4 and d = 12, which of the equations below is true?

d - b = c

(a + c) ÷ d = b

b² + d ÷ c = a

c² - a = d

If A = 25, B = 4, C = 8, D = 100 and E = 22, 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 ÷ d = c

b x c² - d = a

d (b - c) = a

b x c + d = a

If A = 16, B = 8, C = 4 and D = 24, are the equations below correct or incorrect?

• Question 1

If a = 20, b = 6, c = 9 and d = 4, what is b&sup2 ÷ c?

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.

d
EDDIE SAYS
The question tells us that b = 6 and c = 9.
If we substitute these numbers for the letters in the equation then b² ÷ c becomes 6² ÷ 9.
Using the rules of BIDMAS, we must tackle the power (²) first as it is an example of indices. So b² becomes 6² which is 36.
Then we need to divide this number by c (which is 9). So 36 ÷ 9 = 4.
The letter that corresponds to 4 is d, so this is the correct answer.
• Question 2

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

If A = 8, B = 20, C = 16 and D = 12, what is &radic;C x A - B?

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 = 16, A = 8 and B = 20.
If we substitute these numbers for the letters in the equation then √C x A - B becomes √16 x 8 - 20.
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 √16 which is 4.
Then we need to tackle the multiplication and times this answer by A (which is 8) then subtract B (which is 20). So 4 x 8 - 20 = 12.
The letter that corresponds to 12 is D, so this is the correct answer.
• Question 3

If A = 16, B = 3, C = 7 and D = 26, which of the equations below is true?

A + B + C = D
EDDIE SAYS
The question tells us that A = 16, B = 3, C = 7 and D = 26.
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 = 26. This is also not true. Option 3: 26 ÷ 7 = 16. This is also not true. Option 4: 16 + 3 + 7 = 21. This is true so is a correct answer! Well done for persevering with all these clues top detective. The best clues are always in the last place you look!
So only option 4 (A + B + C = D) is true and must be the only correct answer. Great work!
• Question 4

If a = 12, b = 3, c = 7 and d = 15, which of the equations below is true?

d ÷ b + c = a
EDDIE SAYS
The question tells us that a = 12, 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: (12 x 3) - (15 + 3) = 15. This is not true so cannot be the correct answer. Option 2: 12 x 3 - 7 = 15. This is also not true. Option 3: 3 x 15 + 7 = 12. This is also not true. Option 4: 15 ÷ 3 + 7 = 12. This is true so is a correct answer!
So only option 4 (d ÷ b + c = a) is true and must be the only correct answer.
• Question 5

If A = 10, B = 2, C = 7, D = 22 and E = 17, are the equations below correct or incorrect?

EDDIE SAYS
The question tells us that A = 10, B = 2, D = 22, E = 17 and C = 7.
If we work through each option in order, using BIDMAS to prioritise operations, we find that: Option 1: 10² ÷ 2 = 22. The answer to this calculation is 50 so this is incorrect. This is correct! Let's check if there are any others... Option 2: (2 x 10) - (22 - 17) = 7. The answer to this calculation is 5 so this is incorrect. Option 3: 7² - (22 + 10) = 17. This is correct!
Great work on assessing which calculations were red herrings and finding the only correct answer!
• Question 6

If A = 64, B = 7, C = 8 and D = 15, which of the equations below is true?

√A + B = D
EDDIE SAYS
The question tells us that A = 64, B = 7, C = 8 and D = 15.
If we work through each option in order, using BIDMAS to prioritise operations, we find that: Option 1: √64 + 7 = 15. This is true so is a correct answer! Let's check if there are any others... Option 2: 7 x 8 = 64. This is not true so cannot be the correct answer. Option 3: 15 x 8 = 64. This is also not true. Option 4: 64 ÷ 8 = 7. 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 = 39, b = 6, c = 4 and d = 12, which of the equations below is true?

b² + d ÷ c = a
EDDIE SAYS
The question tells us that a = 39, b = 6, c = 4 and d = 12.
If we work through each option in order, using BIDMAS to prioritise operations, we find that: Option 1: 12 - 6 = 4. This is not true so cannot be the correct answer. Option 2: (39 + 12) ÷ 4 = 39. This is also not true. Option 3: 6² + (12 ÷ 4) = 39. This is true so is a correct answer! Let's check the last calculation just in case... Option 4: 4² - 39 = 12. This is also not true.
So only option 3 (b² + d ÷ c = a) is true and must be the only correct answer.
• Question 8

If A = 25, B = 4, C = 8, D = 100 and E = 22, are the equations below correct or incorrect?

EDDIE SAYS
The question tells us that A = 25, B = 4, C = 8, D = 100 and E = 22.
If we work through each option in order, using BIDMAS to prioritise operations, we find that: Option 1: √100 + 8 + 4 = 22. The answer to this sum is 22 so the equation is correct! Option 2: 100 ÷ 4 = 25. The answer to this sum is 25 so the equation is correct! Option 3: 8 x 4 = 25. The answer to this sum is 32 so this equation is incorrect. Option 4: 4² + 8 = 22. The answer to this sum is 25 so this is also incorrect.
Two red herrings here - did you spot them both?
• Question 9

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

a ÷ d = c
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 ÷ 24 = 3. This is true so is a correct answer! Let's check the other calculations just in case... Option 2: 8 x 9 - 24 = 72. This is not true so cannot be the correct answer. 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 - d = a) is true and must be the only correct answer.
• Question 10

If A = 16, B = 8, C = 4 and D = 24, are the equations below correct or incorrect?

EDDIE SAYS
The question tells us that A = 16, B = 8, C = 4 and D = 24.
If we work through each option in order, using BIDMAS to prioritise operations, we find that: Option 1: 64 ÷ 4 = 16 . The answer to this sum is 16 so the equation is correct! Option 2: 8 x 4 - 16 = 16. The answer to this sum is 16 so the equation is also correct! Option 3: 32 ÷ 8 = 4. The answer to this sum is 4 so the equation is correct too! Option 4: 24 - 16 = 16. The answer to this sum is 8 so this is incorrect.
Did you spot the only red herring in this question, ace detective?
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