# 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!

If A = 10, B = 3 and C = 7, what is A (B + C)?

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

10 x (3 +7)

10 + (3 + 7)

10 - (3 + 7)

10 ÷ (3 + 7)

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

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

8 x (12 + 4)

8 + (12 + 4)

8 x (12 - 4)

8 ÷ (12 - 4)

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

We know from the last question that a (d - c) converts to become 8 x (12 - 4).

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

56

64

112

72

If A = 3, B = 12, C = 6 and D = 8, what is A (B - D)?

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

3 x (12 - 8)

3 + (12 + 8)

3 x (12 + 8)

3 ÷ (12 + 8)

And now let's solve the whole problem:

If A = 3, B = 12, C = 6 and D = 8, what is A (B - D)?

We know from the last question that A (B - D) converts to become 3 x (12 - 8).

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

60

12

15

18

If a = 9, b = 15, c = 8 and d = 4, what is a (b - d)?

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

9 x (15 + 4)

9 + (15 - 4)

9 x (15 - 4)

9 ÷ (15 - 4)

Following on from the last question:

If a = 9, b = 15, c = 8 and d = 4, what is a (b - d)?

99

81

72

63

If A = 8, B = 14, C = 7 and D = 3, what is A (B + D)?

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

8 x (14 - 3)

8 + (14 - 3)

8 x (14 + 3)

8 ÷ (14 - 3)

Following on from the last question:

If A = 8, B = 14, C = 7 and D = 3, what is A (B + D)?

128

120

136

135

Insert brackets into the equation below to make it true.

• Question 1

If A = 10, B = 3 and C = 7, what is A (B + C)?

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

10 x (3 +7)
EDDIE SAYS
The question tells us that A = 10, B = 3 and C = 7.
If we swap these numbers in for the letters, then A (B + C) becomes 7 (3 + 7).
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 2

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

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

8 x (12 - 4)
EDDIE SAYS
The question tells us that a = 8, d = 12 and c = 4.
If we swap these numbers in for the letters, then a (d - c) becomes 8 (12 - 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

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

We know from the last question that a (d - c) converts to become 8 x (12 - 4).

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

64
EDDIE SAYS
We know that we need to calculate the answer to 8 x (12 - 4).
Let's do the bracket first, 12 minus 4 gives us 8.
When we multiply 8 by 8, we reach the final answer of 64.
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 - D)?

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

3 x (12 - 8)
EDDIE SAYS
The question tells us that A = 3, B = 12 and D = 8.
If we swap these numbers in for the letters, then A (B - D) becomes 3 (12 - 8).
Remember that a multiplication symbol is missing if there is nothing between a number or letter and a bracket.
So the final answer is 3 x (12 - 8).
• Question 5

And now let's solve the whole problem:

If A = 3, B = 12, C = 6 and D = 8, what is A (B - D)?

We know from the last question that A (B - D) converts to become 3 x (12 - 8).

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

12
EDDIE SAYS
We know that we must calculate the bracket first, which gives us an answer of 4.
When you multiply 3 by 4, we reach an answer of 12.
How are you doing with these tricky maths codes so far? Want some more practise?
• Question 6

If a = 9, b = 15, c = 8 and d = 4, what is a (b - d)?

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

9 x (15 - 4)
EDDIE SAYS
The question tells us that a = 9, b = 15 and d = 4.
If we swap these numbers in for the letters, then a (b - d) becomes 9 (15 - 4).
If there is no symbol between a letter or number and a bracket, we need to assume that a x sign 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 - d)?

99
EDDIE SAYS
We already know that we must calculate the bracket first, which gives us an answer of 11.
When you multiply 9 by 11, we reach an answer of 99.
• Question 8

If A = 8, B = 14, C = 7 and D = 3, what is A (B + D)?

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

8 x (14 + 3)
EDDIE SAYS
The question tells us that A = 8, B = 14 and D = 3.
If we swap these numbers in for the letters, then A (B + D) becomes 8 (14 + 3).
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 + D)?

136
EDDIE SAYS
We already know that we must calculate the bracket first, which gives us an answer of 17.
When you multiply 8 by 17, we reach an answer of 136.
We are really cracking those codes now! Just one question left...
• Question 10

Insert brackets into the equation below to make it true.

8 x (21 - 6) = 120
EDDIE SAYS
The brackets would need to go around 21 - 6 to make the question true as this needs to be calculated first.
If this is done, then the sum becomes 8 x (15) which gives an answer of 120.
This equation can be further simplified by removing the multiplication sign to become 8 (21 - 6) = 120.
Great work maths coder!
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