# Substitute Numbers for Letters in Complex Calculations (No Division)

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!

If A = 10, B = 4, C = 3, D = 9, what is B + D - A + C?

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

4 + 9 - 10 + 3

10 + 9 - 4 + 3

4 + 9 - 3 + 10

9 + 4 - 10 - 3

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

Copy and complete the table with each of the steps you would take to solve the problem. Don't forget to use a space between each number, letter or symbol to be marked correctly.

 Letters Numbers Answer Step 1 b + d 4 + 9 13 Step 2 b + d - a 13 - 10 Step 3 b + d - a + c

 Letters Numbers Answer Step 1 Step 2 Step 3

If A = 12, B = 5, C = 4 and D = 7, what is B + D - A + C?

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

12 + 5 - 7 + 3

5 + 7 - 12 + 4

5 + 7 - 4 + 12

12 + 4 - 5 + 7

If a = 12, b = 5, c = 4 and d = 7, what is b + d - a + c?

Copy and complete the table with each of the steps you would take to solve the problem. Don't forget to use a space between each number, letter or symbol to be marked correctly.

Remember to start Step 2 with the answer from Step 1 and Step 3 with the answer from Step 2. Part of the table has been completed here to help you get started.

 Letters Numbers Answer Step 1 b + d 5 + 7 12 Step 2 b + d - a 12 - Step 3 b + d - a + c

 Letters Numbers Answer Step 1 Step 2 Step 3

If a = 5, b = 12, c = 7 and d = 8, what is b + d - a + c?

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

12 + 8 - 7 + 5

8 + 7 - 12 + 5

5 + 8 - 7 + 12

12 + 8 - 5 + 7

If A = 5, B = 12, C = 7 and D = 8, what is B + D - A + C?

Copy and complete the table with each of the steps you would take to solve the problem. Don't forget to use a space between each number, letter or symbol to be marked correctly.

Remember to start Step 2 with the answer from Step 1 and Step 3 with the answer from Step 2. Part of the table has been completed here to help you get started.

 Letters Numbers Answer Step 1 B + D 12 + 8 Step 2 B + D - A Step 3 B + D - A + C

 Letters Numbers Answer Step 1 Step 2 Step 3

If a = 9, b = 15, c = 6 and d = 3, what is b + d - a + c?

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

9 + 15 - 6 + 3

6 + 15 - 9 + 3

15 + 3 - 9 + 6

15 + 9 - 3 + 6

If A = 9, B = 15, C = 6 and D = 3, what is B + D - A + C?

Copy and complete the table with each of the steps you would take to solve the problem. Don't forget to use a space between each number, letter or symbol to be marked correctly.

Remember to start Step 2 with the answer from Step 1 and Step 3 with the answer from Step 2. Part of the table has been completed here to help you get started.

 Letters Numbers Answer Step 1 B + D Step 2 B + D - A Step 3 B + D - A + C

 Letters Numbers Answer Step 1 Step 2 Step 3

If A = 3, B = 17, C = 4 and D = 6, what is B + D - A + C?

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

17 + 6 - 4 + 3

17 + 6 - 3 + 4

17 + 4 - 6 + 3

17 + 3 - 4 + 6

If a = 3, b = 17, c = 4 and d = 6, what is b + d - a + c?

Copy and complete the table with each of the steps you would take to solve the problem. Don't forget to use a space between each number, letter or symbol to be marked correctly.

Remember to start Step 2 with the answer from Step 1 and Step 3 with the answer from Step 2. Part of the table has been completed here to help you get started.

 Letters Numbers Answer Step 1 b + d Step 2 b + d - c Step 3 b + d - c + a

 Letters Numbers Answer Step 1 Step 2 Step 3
• Question 1

If A = 10, B = 4, C = 3, D = 9, what is B + D - A + C?

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

4 + 9 - 10 + 3
EDDIE SAYS
The question tells us that B = 4, D = 9, A = 10 and C = 3.
If we swap the letters for the numbers they represent, we find that B + D - A + C becomes 4 + 9 - 10 + 3.
As this question has both addition (+) and subtraction (-) in it, we must do the calculations in order to reach the correct answer.
• Question 2

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

Copy and complete the table with each of the steps you would take to solve the problem. Don't forget to use a space between each number, letter or symbol to be marked correctly.

 Letters Numbers Answer Step 1 b + d 4 + 9 13 Step 2 b + d - a 13 - 10 Step 3 b + d - a + c

 Letters Numbers Answer Step 1 Step 2 Step 3
EDDIE SAYS
Completing all the steps in the correct order leaves you with the answer 6.
We will build on this technique in the next few questions so that you can answer all maths codes questions independently using these steps.
• Question 3

If A = 12, B = 5, C = 4 and D = 7, what is B + D - A + C?

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

5 + 7 - 12 + 4
EDDIE SAYS
The question tells us that B = 5, D = 7, A = 12 and C = 4.
If we swap the letters for the numbers they represent, we find that B + D - A + C becomes 5 + 7 - 12 + 4.
As this question has both addition (+) and subtraction (-) in it, we must do the calculations in order to reach the correct answer.
• Question 4

If a = 12, b = 5, c = 4 and d = 7, what is b + d - a + c?

Copy and complete the table with each of the steps you would take to solve the problem. Don't forget to use a space between each number, letter or symbol to be marked correctly.

Remember to start Step 2 with the answer from Step 1 and Step 3 with the answer from Step 2. Part of the table has been completed here to help you get started.

 Letters Numbers Answer Step 1 b + d 5 + 7 12 Step 2 b + d - a 12 - Step 3 b + d - a + c

 Letters Numbers Answer Step 1 Step 2 Step 3
EDDIE SAYS
Completing all the steps in the correct order leaves you with the answer 4.
Did you feel more confident completing the grid this time?
We will practise using it more in the rest of the questions in this activity.
• Question 5

If a = 5, b = 12, c = 7 and d = 8, what is b + d - a + c?

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

12 + 8 - 5 + 7
EDDIE SAYS
The question tells us that b = 12, d = 8, a = 5 and c = 7.
If we swap the letters for the numbers they represent, we find that b + d - a + c becomes 12 + 8 - 5 + 7.
As this question has both addition (+) and subtraction (-) in it, we must do the calculations in order to reach the correct answer.
• Question 6

If A = 5, B = 12, C = 7 and D = 8, what is B + D - A + C?

Copy and complete the table with each of the steps you would take to solve the problem. Don't forget to use a space between each number, letter or symbol to be marked correctly.

Remember to start Step 2 with the answer from Step 1 and Step 3 with the answer from Step 2. Part of the table has been completed here to help you get started.

 Letters Numbers Answer Step 1 B + D 12 + 8 Step 2 B + D - A Step 3 B + D - A + C

 Letters Numbers Answer Step 1 Step 2 Step 3
EDDIE SAYS
Completing all the steps in the correct order leaves you with the answer 22.
Hopefully you are feeling more an more confident using the grid and these steps to help you reach the correct answer.
Let's practice some more...
• Question 7

If a = 9, b = 15, c = 6 and d = 3, what is b + d - a + c?

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

15 + 3 - 9 + 6
EDDIE SAYS
The question tells us that b = 15, d = 3, a = 9 and c = 6.
If we swap the letters for the numbers they represent, we find that b + d - a + c becomes 15 + 3 - 9 + 6.
As this question has both an addition (+) and subtraction (-) in it, we must do the calculations in order to reach the correct answer.
• Question 8

If A = 9, B = 15, C = 6 and D = 3, what is B + D - A + C?

Copy and complete the table with each of the steps you would take to solve the problem. Don't forget to use a space between each number, letter or symbol to be marked correctly.

Remember to start Step 2 with the answer from Step 1 and Step 3 with the answer from Step 2. Part of the table has been completed here to help you get started.

 Letters Numbers Answer Step 1 B + D Step 2 B + D - A Step 3 B + D - A + C

 Letters Numbers Answer Step 1 Step 2 Step 3
EDDIE SAYS
Completing all the steps in the correct order leaves you with the answer 15.
• Question 9

If A = 3, B = 17, C = 4 and D = 6, what is B + D - A + C?

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

17 + 6 - 3 + 4
EDDIE SAYS
The question tells us that B = 17, D = 6, A = 3 and C = 4.
If we swap the letters for the numbers they represent, we find that B + D - A + C becomes 17 + 6 - 3 + 4.
As this question has both an addition (+) and subtraction (-) in it, we must do the calculations in order to reach the correct answer.
• Question 10

If a = 3, b = 17, c = 4 and d = 6, what is b + d - a + c?

Copy and complete the table with each of the steps you would take to solve the problem. Don't forget to use a space between each number, letter or symbol to be marked correctly.

Remember to start Step 2 with the answer from Step 1 and Step 3 with the answer from Step 2. Part of the table has been completed here to help you get started.

 Letters Numbers Answer Step 1 b + d Step 2 b + d - c Step 3 b + d - c + a

 Letters Numbers Answer Step 1 Step 2 Step 3
EDDIE SAYS
Completing all the steps in the correct order leaves you with the answer 24.
Hopefully you are feeling grid-tastic now, and ready to apply this technique to more maths codes soon!
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