# Substitute Numbers for Letters in Simple Sums

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!

Let's continue practicing converting between letters and numbers.

If A = 1, B = 2, C = 3 and D = 4, what is C x D + A?

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

1 x 2 + 4

3 x 4 + 1

3 + 4 + 1

4 x 1 + 2

What is 3 x 4 + 1?

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

If a = 3, b = 4, c = 5 and d = 6, what is d x b + c?

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

6 - 4 + 5

6 + 4 + 5

6 x 4 + 5

5 x 4 + 6

What is 6 x 4 + 5?

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

If a = 7, b = 5, c = 3 and d = 2, which letters have been used in the sum 7 x 3 + 2?

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

b x c + d

a x c + d

b x a + d

a + c + d

If A = 7, B = 5, C = 3 and D = 2, what is the answer to A x C + D?

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

If A = 10, B = 12, C = 7 and D = 8, which letters have been used in the sum 10 x 12 + 7?

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

B - A + C

B x C + A

A x B + C

B + A + C

If a = 10, b = 12, c = 7 and d = 8, what is a x b + c?

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

If A = 3, B = 17, C = 15 and D = 9, which three letters have been used to reach an answer of 29?

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

C + D + A

D x A

B + D

A + B + D

If a = 3, b = 7, c = 15 and d = 9, which three letters have been used to reach an answer of 13?

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

a x d - b

c + d - b

a x b - d

b + d - a

• Question 1

Let's continue practicing converting between letters and numbers.

If A = 1, B = 2, C = 3 and D = 4, what is C x D + A?

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

3 x 4 + 1
EDDIE SAYS
The question tells us that C = 3, D = 4 and A = 1.
If we swap the letters for the numbers they represent, we find that C x D + A becomes 3 x 3 + 1.
As we have multiplication (x), addition (+) and subtraction (-) in this calculation, we must do each step in order to reach the correct answer.
• Question 2

What is 3 x 4 + 1?

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

13
EDDIE SAYS
Following on from the previous question, we know that when we swap the correct numbers in for the letters, then C x D + A becomes 3 x 4 + 1.
As we have both multiplication and addition in this question, we must complete each step in the correct order to reach the right answer.
When we complete this calculation in the correct order, we reach the answer of 13.
• Question 3

If a = 3, b = 4, c = 5 and d = 6, what is d x b + c?

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

6 x 4 + 5
EDDIE SAYS
The question tells us that d = 6, b = 4 and c = 5.
If we swap the letters for the numbers they represent, we find that d x b + c becomes 6 x 4 + 5.
As we have both multiplication (x) and addition (+) in this calculation, we must complete the steps in the correct order to reach the right answer.
• Question 4

What is 6 x 4 + 5?

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

29
EDDIE SAYS
Following on from the previous question, we know that when we swap the correct numbers in for the letters, then D x B + A becomes 6 x 4 + 5.
As we have both multiplication and addition in this question, we must complete each step in the correct order to reach the right answer.
When we complete this calculation in the correct order, we reach the answer of 29.
• Question 5

If a = 7, b = 5, c = 3 and d = 2, which letters have been used in the sum 7 x 3 + 2?

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

a x c + d
EDDIE SAYS
The question tells us that a = 7, c = 3 and d = 2.
If we swap the numbers for the letters they represent, we find that 7 x 3 + 2 becomes a x c + d.
This is the reverse of what we have been doing before, but works in just the same way. You just need to switch your brain from swapping letters to numbers to the other way around!
• Question 6

If A = 7, B = 5, C = 3 and D = 2, what is the answer to A x C + D?

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

23
EDDIE SAYS
The question tells us that A = 7, C = 3 and D = 2.
If we swap these numbers in for the letters, then A x C + D becomes 7 x 3 + 2.
You can must complete these calculations in the order they have been written to reach the correct answer.
When we complete these steps in the correct order, we reach the answer of 23.
• Question 7

If A = 10, B = 12, C = 7 and D = 8, which letters have been used in the sum 10 x 12 + 7?

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

A x B + C
EDDIE SAYS
The question tells us that A = 10, B = 12 and C = 7.
If we swap the numbers for the letters they represent, we find that 10 x 12 + 7 becomes A x B + C.
Hopefully you have kept your brain in number-to-letter switching mode!
• Question 8

If a = 10, b = 12, c = 7 and d = 8, what is a x b + c?

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

127
EDDIE SAYS
The question tells us that a = 10, b = 12 and c = 7.
If we swap these numbers in for the letters, then a x b + c becomes 10 x 12 + 7.
You must solve these calculations in the order they have been written to reach the correct answer.
When we solve these steps in order, we reach the answer of 127.
• Question 9

If A = 3, B = 17, C = 15 and D = 9, which three letters have been used to reach an answer of 29?

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

A + B + D
EDDIE SAYS
We need to work out how we can use three of these numbers to reach the target of 29. You can try adding, subtracting, multiplying or dividing.
If we look at the options provided, only option 1 and 4 include three numbers so one of these must be the correct answer.
If we swap the letters for the numbers they represent, then option 1 becomes 15 + 9 + 3 and option 4 becomes 3 + 17 + 9.
When we add these groups of three numbers, only A + B + D or 3 + 17 + 9 gets us to the target of 29, so this is the correct answer.
• Question 10

If a = 3, b = 7, c = 15 and d = 9, which three letters have been used to reach an answer of 13?

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

b + d - a
EDDIE SAYS
We need to work out how we can use three of these numbers to reach the target of 13.
This time all the options have three letters, so we need to work through each one-by-one.
If we swap the letters for the numbers they represent, then: Option 1 becomes 3 x 9 - 7 = 20. Option 2 becomes 15 + 9 - 7 = 17. Option 3 becomes 3 x 7 - 9 = 12. Option 4 becomes 7 + 9 - 3 = 13.
As we are trying to reach 13, option 4 (b + d - a) is the correct answer.
---- OR ----

Sign up for a £1 trial so you can track and measure your child's progress on this activity.

### What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Get started