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.)

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 = 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 = 70, G = 18, L = 23, P = 35.

Can you match the letters to their correct numbers?

Column B

P
70
L
18
G
23
D
35

If d = 70, g = 18, l = 23 and p = 35, what is d + l + g?

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

70 + 18 - 23

18 + 23 - 70

70 + 23 + 18

35 + 70 + 18

Continuing from the last question:

If d = 70, g = 18, l = 23 and p = 35, what is d + l + g?

Can you type the final answer to this question as a number

You have been given the following information: F = 24, K = 32, E = 16, A = 8.

Can you match the letters to their correct numbers?

Column B

A
16
E
32
F
24
K
8

If A = 8, E = 16, F = 24 and K = 32, what is F + K + E?

24 + 32 + 16

16 + 24 + 32

32 + 16 + 24

8 + 32 + 24

If a = 8, e = 16, f = 24 and k = 32, what is f + k + e?

Can you type the answer to this question as a number?

You have been given the following information: G = 37, B = 18, F = 23, A = 12.

Can you match the letters to their correct numbers?

Column B

A
18
B
12
F
37
G
23

If A = 12, B = 18, F = 23 and G = 37, what is G + B - A?

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

23 + 18 - 12

37 + 12 - 18

37 + 18 - 12

24 + 37 - 12

TRUE or FALSE?

When we are adding and subtracting numbers in the same number sentence, we cannot move the order in which we answer them.

True

False

If A = 12, B = 18, F = 23 and G = 37, what is G + B - A?

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

 Correct answer Incorrect answer 12 + 37 - 18 = 31 37 + 18 - 12 = 43 18 + 37 - 12 = 43 37 + 12 - 18 = 31
• Question 1

You have been given the following information: D = 70, G = 18, L = 23, P = 35.

Can you match the letters to their correct numbers?

Column B

P
35
L
23
G
18
D
70
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 = 35, L = 23, G = 18 and D = 70.
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 = 70, g = 18, l = 23 and p = 35, what is d + l + g?

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

70 + 23 + 18
EDDIE SAYS
The question tells us that d = 70, l = 23 and g = 18.
If we swap the letters for the numbers they represent, we find that d + l + g becomes 70 + 23 + 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 23 + 18 + 70 or 70 + 18 + 23 would also have been correct.
• Question 3

Continuing from the last question:

If d = 70, g = 18, l = 23 and p = 35, what is d + l + g?

Can you type the final answer to this question as a number

111
EDDIE SAYS
The question tells us that d = 70, l = 23 and g = 18.
If we swap these numbers in for the letters, then d + l + g becomes 70 + 23 + 18.
You can choose to add these numbers in any order you choose.
When we add these three numbers, we reach the answer of 111.
• Question 4

You have been given the following information: F = 24, K = 32, E = 16, A = 8.

Can you match the letters to their correct numbers?

Column B

A
8
E
16
F
24
K
32
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 = 8, E = 16, F = 24 and K = 32.
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 = 8, E = 16, F = 24 and K = 32, what is F + K + E?

24 + 32 + 16
16 + 24 + 32
32 + 16 + 24
EDDIE SAYS
The question asks us to find F + K + E.
We know that F = 24, K = 32 and E = 16.
When we swap these numbers in the place of the letters, the sum becomes 24 + 32 + 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 = 8, e = 16, f = 24 and k = 32, what is f + k + e?

Can you type the answer to this question as a number?

72
EDDIE SAYS
The question tells us that f = 24, k = 32 and e = 16.
If we swap these numbers in for the letters, then f + k + e becomes 24 + 32 + 16.
You can choose to add these numbers in any order you choose.
When we add these three numbers, we reach the answer of 72.
How did you answer this question? 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 32.
Number bonds are the numbers that add together to make 10.
• Question 7

You have been given the following information: G = 37, B = 18, F = 23, A = 12.

Can you match the letters to their correct numbers?

Column B

A
12
B
18
F
23
G
37
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 = 12, B = 18, F = 23 and G = 37.
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 = 12, B = 18, F = 23 and G = 37, what is G + B - A?

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

37 + 18 - 12
EDDIE SAYS
The question tells us that G = 37, B = 18 and A = 12.
If we swap the letters for the numbers they represent, we find that G + B - A becomes 37 + 18 - 12.
Remember that as we have both addition (+) and subtraction (-) in this calculation, we must do each step in order.
• Question 9

TRUE or FALSE?

When we are adding and subtracting numbers in the same number sentence, we cannot move the order in which we answer them.

True
EDDIE SAYS
This statement is TRUE.
When adding and subtracting within one calculation, we will reach a different answer if we change the order of the operations from what is written.
• Question 10

If A = 12, B = 18, F = 23 and G = 37, what is G + B - A?

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

 Correct answer Incorrect answer 12 + 37 - 18 = 31 37 + 18 - 12 = 43 18 + 37 - 12 = 43 37 + 12 - 18 = 31
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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