# Substitute Numbers for Letters in Complex Calculations (All Four Operations)

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!

What is A (B + C)?

In this algebraic equation, which symbol is missing between the letter A and the bracket?

x

+

_

÷

If A = 8, B = 10, C = 4 and D = 12, what is A (B + C)?

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

8 x (10 + 4)

8 + (10 + 4)

10 - (8 + 4)

4 ÷ (10 + 8)

And now the final step to solve the problem:

If A = 8, B = 10, C = 4 and D = 12, what is A (B + C)?

We know from the last question that A (B + C) converts to become 8 x (10 + 4).

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

110

84

112

42

If a = 3, b = 12, c = 6 and d = 8, what is a (b + c)?

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

3 x (12 + 8)

3 + (12 + 6)

3 x (12 + 6)

3 ÷ (12 + 8)

Let's move on to the final step now:

If a = 3, b = 12, c = 6 and d = 8, what is a (b + c)?

42

54

56

48

If A = 9, B = 15, C = 8 and D = 4, what is A (B - C)?

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

9 x (15 + 8)

9 + (15 - 8)

9 x (15 - 8)

9 ÷ (15 - 8)

Following on from the last question:

If A = 9, B = 15, C = 8 and D = 4, what is A (B - C)?

207

72

54

63

If a = 8, b = 14, c = 7 and d = 3, what is a (b - c)?

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

8 x (14 - 7)

8 + (14 - 7)

8 x (14 + 7)

8 ÷ (14 - 7)

Following on from the last question:

If a = 8, b = 14, c = 7 and d = 3, what is a (b - c)?

56

72

54

48

Insert brackets into the equation below to make it true.

• Question 1

What is A (B + C)?

In this algebraic equation, which symbol is missing between the letter A and the bracket?

x
EDDIE SAYS
Where there isn’t a -, +, x or ÷ between a letter and a bracket, we need to assume that a x is missing.
This means that we have to multiply the outside number by what is inside the brackets.
• Question 2

If A = 8, B = 10, C = 4 and D = 12, what is A (B + C)?

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

8 x (10 + 4)
EDDIE SAYS
The question tells us that A = 8, B = 10 and C = 4.
If we swap these numbers in for the letters, then A (B + C) becomes 8 (10 + 4).
When there is no symbol between a letter and the brackets, 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.
• Question 3

And now the final step to solve the problem:

If A = 8, B = 10, C = 4 and D = 12, what is A (B + C)?

We know from the last question that A (B + C) converts to become 8 x (10 + 4).

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

112
EDDIE SAYS
The question tells us that A = 8.
If we swap this number in for the letter in the rest of the equation, then 8 x (10 + 4) becomes 9 x 14.
When we multiply 9 by 14, we reach the answer of 112.
Were you able to complete the final step to reach the correct answer? Let's try another for some more practise...
• Question 4

If a = 3, b = 12, c = 6 and d = 8, what is a (b + c)?

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

3 x (12 + 6)
EDDIE SAYS
The question tells us that a = 3, b = 12 and c = 6.
If we swap these numbers in for the letters, then a (b + c) becomes 3 (12 + 6).
We know that when we see a number or letter next to a bracket with no +, -, x or ÷ symbol, we need to assume that it is a multiplication sum.
So the correct answer is 3 x (12 + 6).
• Question 5

Let's move on to the final step now:

If a = 3, b = 12, c = 6 and d = 8, what is a (b + c)?

54
EDDIE SAYS
We already know that we must calculate the bracket first, which gives us an answer of 18.
The question tells us that a = 3. If we swap that into the rest of the equation then a (18) becomes 3 x 18.
When you multiply 3 by 18, we reach an answer of 54.
Great work putting those steps together maths coder!
• Question 6

If A = 9, B = 15, C = 8 and D = 4, what is A (B - C)?

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

9 x (15 - 8)
EDDIE SAYS
The question tells us that A = 9, B = 15 and C = 8.
If we swap these numbers in for the letters, then A (B - C) becomes 9 (15 + 8).
If there is no symbol between a letter or number and a bracket, we need to assume that a x has been missed out.
So the correct answer is 9 x (15 - 8).
• Question 7

Following on from the last question:

If A = 9, B = 15, C = 8 and D = 4, what is A (B - C)?

63
EDDIE SAYS
We already know that we must calculate the bracket first, which gives us an answer of 7.
The question tells us that A = 9. If we swap that into the rest of the equation then A (7) becomes 9 x 7.
. When you multiply 9 by 7, we reach an answer of 63.
• Question 8

If a = 8, b = 14, c = 7 and d = 3, what is a (b - c)?

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

8 x (14 - 7)
EDDIE SAYS
The question tells us that a = 8, b = 14 and c = 7.
If we swap these numbers in for the letters, then a (b - c) becomes 8 (14 - 7).
We know that if we see a letter and a bracket next to each other without a symbol of operation (+, -, x, ÷), then we must assume that it is a multiplication.
Therefore, the correct answer is 8 x (14 - 7).
• Question 9

Following on from the last question:

If a = 8, b = 14, c = 7 and d = 3, what is a (b - c)?

56
EDDIE SAYS
We already know that we must calculate the bracket first, which gives us an answer of 7.
The question tells us that a = 8. If we swap that into the rest of the equation then A (7) becomes 8 x 7.
When you multiply 8 by 7, we reach an answer of 56.
Did you get that one correct maths coder?
• Question 10

Insert brackets into the equation below to make it true.

8 x (15 - 6) = 72
EDDIE SAYS
The brackets would need to go around 15 - 6 to make the question true as this needs to be calculated first.
If this is done, then the sum becomes 8 x (9) which gives an answer of 72.
This equation can be further simplified by removing the multiplication sign to become 8 (15 - 6) = 72.
---- OR ----

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