# 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 = 15, B = 4 and C = 8, what is A (B + C)?

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

15 x (4 +8)

15 + (4 + 8)

15 - (4 + 8)

15 ÷ (4 + 8)

If a = 7, b = 10, c = 3 and d = 13, what is a (d - c)?

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

7 x (13 + 3)

7 + (13 + 3)

7 x (13 - 3)

7 ÷ (13 - 3)

If a = 7, b = 10, c = 3 and d = 13, what is a (d - c)?

We know from the last question that a (d - c) converts to become 7 x (13 - 3).

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

77

70

63

72

If A = 9, B = 24, 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?

9 x (24 - 8)

9 + (24 + 8)

9 x (24 + 8)

9 ÷ (24 + 8)

And now let's solve the whole problem:

If A = 9, B = 24, C = 6 and D = 8, what is A (B - D)?

We know from the last question that A (B - D) converts to become 9 x (24 - 8).

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

132

144

147

150

If a = 8, b = 31, 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?

8 x (31 + 4)

8 + (31 - 4)

8 x (31 - 4)

8 ÷ (31 - 4)

Following on from the last question:

If a = 8, b = 31, c = 8 and d = 4, what is a (b - d)?

216

221

248

212

If A = 13, B = 5, 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?

13 x (5 - 3)

13 + (5 - 3)

13 x (5 + 3)

13 ÷ (5 - 3)

Following on from the last question:

If A = 13, B = 5, C = 7 and D = 3, what is A (B + D)?

108

104

105

106

Insert brackets into the equation below to make it true.

• Question 1

If A = 15, B = 4 and C = 8, what is A (B + C)?

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

15 x (4 +8)
EDDIE SAYS
The question tells us that A = 15, B = 4 and C = 8.
If we swap these numbers in for the letters, then A (B + C) becomes 15 (4 + 8).
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.
• Question 2

If a = 7, b = 10, c = 3 and d = 13, what is a (d - c)?

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

7 x (13 - 3)
EDDIE SAYS
The question tells us that a = 7, d = 13 and c = 3.
If we swap these numbers in for the letters, then a (d - c) becomes 7 (13 - 3).
Don't forget to add the missing multiplication symbol in to reach the correct answer of 7 x (13 - 3).
• Question 3

If a = 7, b = 10, c = 3 and d = 13, what is a (d - c)?

We know from the last question that a (d - c) converts to become 7 x (13 - 3).

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

70
EDDIE SAYS
We know that we need to calculate the answer to 7 x (13 - 3).
Let's do the bracket first, 13 minus 3 leaves us with 10.
When we multiply 7 by 10, we reach the final answer of 10.
Were you able to complete all the steps in the correct order to reach the answer? Let's try another for some more practise...
• Question 4

If A = 9, B = 24, 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?

9 x (24 - 8)
EDDIE SAYS
The question tells us that A = 9, B = 24 and D = 8.
If we swap these numbers in for the letters, then A (B - D) becomes 9 (24 - 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 9 x (24 - 8).
• Question 5

And now let's solve the whole problem:

If A = 9, B = 24, C = 6 and D = 8, what is A (B - D)?

We know from the last question that A (B - D) converts to become 9 x (24 - 8).

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

144
EDDIE SAYS
We know that we must calculate the bracket first, which gives us an answer of 16.
When you multiply 9 by 16, we reach an answer of 144.
Some of the numbers we are multiplying are getting larger now so be sure to take your time and calculate the products carefully.
• Question 6

If a = 8, b = 31, 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?

8 x (31 - 4)
EDDIE SAYS
The question tells us that a = 8, b = 31 and d = 4.
If we swap these numbers in for the letters, then a (b - d) becomes 8 (31 - 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 8 x (31 - 4).
• Question 7

Following on from the last question:

If a = 8, b = 31, c = 8 and d = 4, what is a (b - d)?

216
EDDIE SAYS
We know that we must calculate the bracket first, which gives us an answer of 27.
When you multiply 8 by 27, we reach an answer of 216.
How did you calculate 8 x 27? Did you do it in your head or use a written method? Be sure that you have not made any slips in either method.
• Question 8

If A = 13, B = 5, 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?

13 x (5 + 3)
EDDIE SAYS
The question tells us that A = 13, B = 5 and D = 3.
If we swap these numbers in for the letters, then A (B + D) becomes 13 (5 + 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.
So the correct answer is 13 x (5 + 3).
• Question 9

Following on from the last question:

If A = 13, B = 5, C = 7 and D = 3, what is A (B + D)?

104
EDDIE SAYS
We know that we must calculate the bracket first, which gives us an answer of 8.
When you multiply 13 by 8, we reach an answer of 104.
A quick way to multiply these numbers is to do (10 x 8) + (3 x 8).
Did you get to the correct answer as quickly as possible?
• Question 10

Insert brackets into the equation below to make it true.

(1 + 8) x 16 - 2 = 142
EDDIE SAYS
The brackets would need to go around 1 + 8 to make the question true as this needs to be calculated first.
If this is done, then the sum becomes (9) x 16 - 2 which gives an answer of 142.
This equation can be further simplified by removing the multiplication sign to become (1 + 8)16 - 2 = 142.
Great work maths coder!
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