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Substitute Numbers for Letters in Calculations with Three Steps

In this worksheet, students will replace letters with numbers and carry out simple questions using the four number operations. (The student will type the answer as a number and no prioritisation of calculations is required at this stage.)

'Substitute Numbers for Letters in Calculations with Three Steps' worksheet

Key stage:  KS 2

Curriculum topic:   Verbal Reasoning

Curriculum subtopic:   Maths Codes

Difficulty level:  

Worksheet Overview

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 = 1, b = 2, c = 3 and d = 4, what is c x d?

 

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 c x d becomes 3 x 4. We know this is 12.

 

The values of the letters can be different in each question.


 

Let’s try this question next:

If a = 7, b = 4, c = 8 and p = 3, what is a +b + c?

 

Let’s swap the letters back to numbers. This would be written as: 7 + 4 + 8 = 19.

 

Remember, when you are adding lots of numbers, you can choose the order that you add them in.

 

If there is a mixture of addition and subtraction, you must work it out in the order that it is written.


 

Let’s practise this now:

If a = 10, b = 4, c = 3 and d = 9, what is b + d - a + c?

 

Let’s swap the letters back to numbers. This would be written as: 4 + 9 - 10 + 3 =

Remember, we must answer this one in order.

So 4 + 9 = 13…

13 - 10 = 3…

3 + 3 = 6.


 

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

You have been given the following information: D = 7, G = 18, L = 27, P = 31.

 

Can you match the letters to their correct numbers?

Column A

Column B

P
18
L
7
G
27
D
31

If d = 7, g = 18, l = 27, p = 31, what is d + l + g?

 

Can you choose the correct number sentence from the options below? 

 

7 + 18 - 27

18 + 27 - 7

7 + 27 + 18

31 + 7 + 18

If D = 7, G = 18, L = 27, P = 31, what is D + L + G?

 

Can you type the answer to this question as a number

You have been given the following information: A = 3, K = 35, E = 16, F = 24.

 

Can you match the letters to their correct numbers?

 

Column A

Column B

A
16
E
3
F
35
K
24

If A = 3, E = 16, F = 24, K = 35, what is F + K + E?

 

Can you select all the calculations which would help you reach the correct answer?  

 

24 + 35 + 16

16 + 24 + 35

35 + 16 + 24

3 + 35 + 24

If a = 3, e = 16, f = 24, k = 35, what is f + k + e? 

 

Can you choose the correct number sentence from the options below? 

 

You have been given the following information: B = 17, F = 24, G = 36, A = 13.

 

Can you match the letters to their correct numbers?

Column A

Column B

A
24
B
36
F
13
G
17

If a = 13, b = 17, f = 24, g = 36, what is g + b - a?

 

Can you choose the correct number sentence from the options below? 

 

24 + 17 - 13

36 + 13 - 17

36 + 17 - 13

24 + 36 - 13

TRUE or FALSE?

 

When we are adding and subtracting numbers in the same number sentence, we can choose the order that we do them in.

True

False

If A = 13, B = 17, F = 24, G = 36, what is G + B - A?

 

Identify if each number sentence below will get you to the correct answer or not. 

 Correct answerIncorrect answer
13 + 36 - 17 = 32
36 + 17 - 13 = 40
17 + 36 - 13 = 40
36 + 13 - 17 = 32
  • Question 1

You have been given the following information: D = 7, G = 18, L = 27, P = 31.

 

Can you match the letters to their correct numbers?

CORRECT ANSWER

Column A

Column B

P
31
L
27
G
18
D
7
EDDIE SAYS
We need to carefully locate the correct information in the question and match each letter to the number it represents.
If we do this one at a time, we find that: P = 31, L = 27, G = 18 and D = 7.
Be careful to avoid the trap of copying the amounts in the exact order that they appear in the question, as this order has been changed below.
  • Question 2

If d = 7, g = 18, l = 27, p = 31, what is d + l + g?

 

Can you choose the correct number sentence from the options below? 

 

CORRECT ANSWER
7 + 27 + 18
EDDIE SAYS
The question tells us that d = 7, l = 27 and g = 18.
If we swap the letters for the numbers they represent, we find that d + l + g becomes 7 + 27 + 18.
Remember that when we are adding multiple numbers in a sum, we can add them in any order and they will give us the same answer, so 18 + 7 + 27 would also have been correct.
  • Question 3

If D = 7, G = 18, L = 27, P = 31, what is D + L + G?

 

Can you type the answer to this question as a number

CORRECT ANSWER
52
EDDIE SAYS
The question tells us that D = 7, L = 27 and G = 18.
If we swap these numbers in for the letters, then D + L + G becomes 7 + 27 + 18.
You can choose to add these numbers in any order you choose.
When we add these three numbers, we reach the answer of 52.
  • Question 4

You have been given the following information: A = 3, K = 35, E = 16, F = 24.

 

Can you match the letters to their correct numbers?

 

CORRECT ANSWER

Column A

Column B

A
3
E
16
F
24
K
35
EDDIE SAYS
We need to carefully locate the correct information in the question and match each letter to the number it represents.
If we do this one at a time, we find that: A = 3, E = 16, F = 24, K = 35.
Be careful to avoid the trap of copying the amounts in the exact order that they appear in the question, as this order has been changed below.
  • Question 5

If A = 3, E = 16, F = 24, K = 35, what is F + K + E?

 

Can you select all the calculations which would help you reach the correct answer?  

 

CORRECT ANSWER
24 + 35 + 16
16 + 24 + 35
35 + 16 + 24
EDDIE SAYS
The question asks us to find F + K + E.
We know that F = 24, K = 35 and E = 16.
When we swap these numbers in the place of the letters, the sum becomes 24 + 35 + 16.
When we are adding multiple numbers in a sum, we can add them in any order we choose and they will give us the same answer.
So options 1,2 and 3 will work here to give you the same answer.
  • Question 6

If a = 3, e = 16, f = 24, k = 35, what is f + k + e? 

 

Can you choose the correct number sentence from the options below? 

 

CORRECT ANSWER
75
EDDIE SAYS
The question tells us that f = 24, k = 35 and e = 16.
If we swap the letters for the numbers they represent, we find that f + k + e becomes 24 + 35 + 16.
24 + 35 + 16 = 75.
How did you add these numbers? Did you use number bonds? If I wanted to answer this quickly in my head, I would do 24 + 16 first. 24 + 16 = 40 and then add on the 35.
Number bonds are the numbers that add together to make 10.
  • Question 7

You have been given the following information: B = 17, F = 24, G = 36, A = 13.

 

Can you match the letters to their correct numbers?

CORRECT ANSWER

Column A

Column B

A
13
B
17
F
24
G
36
EDDIE SAYS
We need to carefully locate the correct information in the question and match each letter to the number it represents.
If we do this one at a time, we find that: A = 13, B = 17, F = 24 and G = 36.
Be careful to avoid the trap of copying the amounts in the exact order that they appear in the question, as this order has been changed below.
  • Question 8

If a = 13, b = 17, f = 24, g = 36, what is g + b - a?

 

Can you choose the correct number sentence from the options below? 

 

CORRECT ANSWER
36 + 17 - 13
EDDIE SAYS
The question tells us that g = 36, b = 17 and a = 13.
If we swap the letters for the numbers they represent, we find that g + b -a becomes 36 + 17 - 13.
As this question has both an addition (+) and subtraction (-) in it, we must do the calculations in order to reach the correct answer.
  • Question 9

TRUE or FALSE?

 

When we are adding and subtracting numbers in the same number sentence, we can choose the order that we do them in.

CORRECT ANSWER
False
EDDIE SAYS
This is FALSE.
When we are adding and subtracting in the same number sentence, if we change the order of the calculations from what is written, then we will get a different answer.
Be careful not to fall into this sneaky trap!
  • Question 10

If A = 13, B = 17, F = 24, G = 36, what is G + B - A?

 

Identify if each number sentence below will get you to the correct answer or not. 

CORRECT ANSWER
 Correct answerIncorrect answer
13 + 36 - 17 = 32
36 + 17 - 13 = 40
17 + 36 - 13 = 40
36 + 13 - 17 = 32
EDDIE SAYS
This question shows us why we need to keep addition and subtraction in the order that it is written, otherwise we will get different answers!
We can swap the order of the two numbers that are being added together, because they will always make the same total, but the number we are subtracting MUST stay fixed.
Whenever you have mixed addition and subtraction, remember that you should always work in the order in which they are written.
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