# Substitute Numbers for Letters in Calculations With Brackets

In this worksheet, students will replace letters with numbers and carry out questions using the four number operations, with some calculations in sets of brackets. They must give their final answers as numbers not letters.

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!

In this activity, we are going to swap numbers for letters to solve maths problems.

Let’s take a look at this question first:

If a = 4, b = 12, c = 3 and d = 9, what is b ÷ a?

This is called algebra, which is where numbers are replaced with letters. We need to swap the letters back into numbers to solve this problem.

If we put the numbers back in, then b ÷ a becomes 12 ÷ 4. We know this is 3.

If any part of the question is written in brackets, this part has to be calculated first.

Let’s try this question next:

If a = 7, b = 9, c = 6 and d = 4, what is b + (a x d)?

Let’s swap the letters back to numbers. This would be written as: 9 + (7 x 4) = ___.

We must work out 7 x 4 first as it is in brackets. This is 28.

Our number sentence now looks like this: 9 + (28) = ___. The answer is 37.

Let’s try one more together:

If a = 8, b = 10, c = 4 and d = 12, what is b (a + c)?

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 inside the brackets. We must imagine an invisible times sign here.

This can be written as: b x (a + c) = ___.

In numbers this is: 10 x (8 + 4) = ____.

We must solve the brackets first: 8 + 4 = 12.

Our number sentence now becomes: 10 x (12) = 120. So our answer is 120.

Now it’s your turn to crack the codes. Good luck number detective!

If A = 7, B = 10, C = 6 and D = 4, what is B (A x D)?

Which of the calculations below shows the correct way to convert the letters into numbers?

10 + (7 x 4)

10 + (6 x 4)

10 x (7 x 4)

If a = 72, b = 9, c = 6 and d = 8, what is b + (÷ d)?

Remember that when we have brackets in a question we solve the equation inside them first.

Can you find a ÷ d first?

9

8

11

12

And now the final step to solve the problem:

If a = 72, b = 9, c = 6 and d = 8, what is b + (a ÷ d)?

We know from the last question that (a ÷ d) = 72 ÷ 8 = 9.

Now complete the rest of the equation and write your answer as a number.

TRUE or FALSE?

When I see numbers inside a bracket, I should always multiply them.

True

False

If A = 3, B = 27, C = 9 and D = 2, what is A + (B ÷ C)?

Which of the calculations below shows the correct way to convert the letters into numbers?

3 + (27 - 9)

3 + (27 x 9)

3 + (27 ÷ 9)

If A = 3, B = 27, C = 9 and D = 2, what is A + (B ÷ C)?

What part of the equation should be answered first?

3 + 27

27 ÷ 9

3 + 9

Let's put all the steps together now:

If A = 3, B = 27, C = 9 and D = 2, what is A + (B ÷ C)?

Following on from the last question:

If A = 3, B = 27, C = 9 and D = 2, what is A + (B ÷ C)?

Which number are you adding A to?

3

18

4

36

Now you are going to be the examiner!

Three different students have been given the question below:

If a = 10, b = 40, c = 8 and d = 3, what is a + (b ÷ c)?

Which students have answered the question correctly by creating the right calculation from the information given?

Following on from the last question, we will now find the final answer as a number:

If a = 10, b = 40, c = 8 and d = 3, what is a + (b ÷ c)?

• Question 1

If A = 7, B = 10, C = 6 and D = 4, what is B (A x D)?

Which of the calculations below shows the correct way to convert the letters into numbers?

10 x (7 x 4)
EDDIE SAYS
The question tells us that B = 10, A = 7 and D = 4.
If we swap these numbers in for the letters, then B (A x D) becomes 10 (7 x 4).
It may look like a mistake has been made in the question, as there is no symbol between the letter B and the brackets. When this happens it means you should multiply the contents of the bracket by the number that comes before it. Or, in other words, you need to assume that a multiplication has been missed out.
So 10 (7 x 4) is the same as 10 x (7 x 4).
• Question 2

If a = 72, b = 9, c = 6 and d = 8, what is b + (÷ d)?

Remember that when we have brackets in a question we solve the equation inside them first.

Can you find a ÷ d first?

9
EDDIE SAYS
The question tells us that a = 72 and d = 8.
When we divide 72 by 8, we reach the answer of 9.
The first step to solving the problem is now complete! Let's move on to the next step...
• Question 3

And now the final step to solve the problem:

If a = 72, b = 9, c = 6 and d = 8, what is b + (a ÷ d)?

We know from the last question that (a ÷ d) = 72 ÷ 8 = 9.

Now complete the rest of the equation and write your answer as a number.

18
EDDIE SAYS
The question tells us that b = 9.
If we swap this number in for the letter in the rest of the equation, then b + (9) becomes 9 + 9.
When we add 9 and 9, we reach the answer of 18.
Were you able to complete the final step to reach the correct answer? Let's try another for some more practise...
• Question 4

TRUE or FALSE?

When I see numbers inside a bracket, I should always multiply them.

False
EDDIE SAYS
This statement is FALSE.
The brackets show us the part of the sum that needs to be worked out first; this may be a multiplication sum but it could equally be addition, subtraction and/or division.
• Question 5

If A = 3, B = 27, C = 9 and D = 2, what is A + (B ÷ C)?

Which of the calculations below shows the correct way to convert the letters into numbers?

3 + (27 ÷ 9)
EDDIE SAYS
The question tells us that A = 3, B = 27 and C = 9.
If we swap these numbers in for the letters, then A + (B ÷ C) becomes 3 + (27 ÷ 9).
The brackets are very important - can you remember why?
• Question 6

If A = 3, B = 27, C = 9 and D = 2, what is A + (B ÷ C)?

What part of the equation should be answered first?

27 ÷ 9
EDDIE SAYS
The brackets tell us which part of the calculation to work out first.
So we should calculate the sum in brackets first which is B ÷ C.
The question tells us that B = 27 and C = 9.
If we swap these numbers in for the letters, then B ÷ C becomes 27 ÷ 9.
• Question 7

Let's put all the steps together now:

If A = 3, B = 27, C = 9 and D = 2, what is A + (B ÷ C)?

6
EDDIE SAYS
We already know that we must calculate the bracket first, which gives us an answer of 3.
The question tells us that A = 3. If we swap that into the rest of the equation then A + (3) becomes 3 + 3.
When you add 3 and 3, we reach an answer of 6.
Great work putting all those steps together maths coder!
• Question 8

Following on from the last question:

If A = 3, B = 27, C = 9 and D = 2, what is A + (B ÷ C)?

Which number are you adding A to?

3
EDDIE SAYS
In the last question, we worked out that (B ÷ C) needs to be worked out first.
We substituted the letters for numbers to get the sum 27 ÷ 9.
If we divide 27 by 9, we reach the answer of 3.
This needs to be added to A to reach the correct answer.
• Question 9

Now you are going to be the examiner!

Three different students have been given the question below:

If a = 10, b = 40, c = 8 and d = 3, what is a + (b ÷ c)?

Which students have answered the question correctly by creating the right calculation from the information given?

EDDIE SAYS
The question tells us that a = 10, b = 40 and c = 8.
If we swap these numbers in for the letters then a + (b ÷ c) becomes 10 + (40 ÷ 8).
We need to complete the calculation in brackets first, so the order we need to work in is 40 ÷ 8 + 10. So only the second student would reach the right answer! How did you find being the examiner? Was it easy or hard to spot the students' errors?
• Question 10

Following on from the last question, we will now find the final answer as a number:

If a = 10, b = 40, c = 8 and d = 3, what is a + (b ÷ c)?

15
EDDIE SAYS
The question tells us that a = 10, b = 40 and c = 8.
If we swap these numbers in for the letters, then a + (b ÷ c) becomes 10 + (40 ÷ 8).
We must work out the brackets first so 40 divided by 8 is 5.
Then we need to add 10 to this total, so we will reach an answer of 15.
Did you put the steps together in the right order to reach the correct answer?
---- OR ----

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