# 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 = 5, C = 3 and D = 8, what is B + D - A + C?

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

5 + 8 - 10 + 3

10 + 8 - 5 + 3

5 + 8 - 3 + 10

8 + 5 - 10 - 3

Following on from the previous question:

If A = 10, B = 5, C = 3 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 5 + 8 13 Step 2 B + D - A Step 3 B + D - A + C

 Letters Numbers Answer Step 1 Step 2 Step 3

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

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

12 + 5 - 8 + 7

5 + 8 - 12 + 7

5 + 8 - 7 + 12

12 + 7 - 5 + 8

Following on from the last question:

If a = 12, b = 5, 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 Step 2 b + d - a Step 3 b + d - a + c

 Letters Numbers Answer Step 1 Step 2 Step 3

If A = 6, B = 9, C = 7 and D = 8, what is B x D - A + C?

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

9 x 8 - 7 + 6

8 + 7 - 9 + 6

6 + 8 - 7 + 9

9 x 8 - 6 + 7

Following on from the last question:

If A = 6, B = 9, C = 7 and D = 8, what is B x 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 x D Step 2 B x D - A Step 3 B x D - A + C

 Letters Numbers Answer Step 1 Step 2 Step 3

If a = 7, b = 11, c = 6 and d = 4, what is b x d - a + c?

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

7 x 11 - 6 + 4

6 + 11 - 7 + 4

11 x 4 - 7 + 6

11 x 7 - 4 + 6

Following on from the previous question:

If a = 7, b = 11, c = 6 and d = 4, what is b x 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 x d Step 2 b x d - a Step 3 b x d - a + c

 Letters Numbers Answer Step 1 Step 2 Step 3

If A = 3, B = 12, C = 4 and D = 9, what is B x D - A + C?

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

12 x 9 - 4 + 3

12 x 9 - 3 + 4

12 x 9 - 6 + 3

12 x 9 - 4 + 6

Following on from the last question:

If A = 3, B = 12, C = 4 and D = 9, what is B x 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 x D Step 2 B x D - A Step 3 B x D - A + C

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

If A = 10, B = 5, C = 3 and D = 8, what is B + D - A + C?

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

5 + 8 - 10 + 3
EDDIE SAYS
The question tells us that B = 5, D = 8, A = 10 and C = 3.
If we swap the letters for the numbers they represent, we find that B + D - A + C becomes 5 + 8 - 10 + 3.
Remember that when we have both addition (+) and subtraction (-) within one calculation, we must complete the steps in the order they have been written to reach the correct answer.
• Question 2

Following on from the previous question:

If A = 10, B = 5, C = 3 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 5 + 8 13 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 6.
Using a step-by-step approach like this grid will make sure that you complete the sums in the right order to reach the correct answer.
• Question 3

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

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

5 + 8 - 12 + 7
EDDIE SAYS
The question tells us that b = 5, d = 8, a = 12 and c = 7.
If we swap the letters for the numbers they represent, we find that b + d - a + c becomes 5 + 8 - 12 + 7.
As we have both addition (+) and subtraction (-) steps in this sentence, we must complete them in the order they have been written to reach the correct answer.
• Question 4

Following on from the last question:

If a = 12, b = 5, 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 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 8.
• Question 5

If A = 6, B = 9, C = 7 and D = 8, what is B x D - A + C?

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

9 x 8 - 6 + 7
EDDIE SAYS
The question tells us that B = 9, D = 8, A = 6 and C = 7.
If we swap the letters for the numbers they represent, we find that B + D - A + C becomes 9 x 8 - 6 + 7.
Did you remember to keep the numbers and operations in the same order?
• Question 6

Following on from the last question:

If A = 6, B = 9, C = 7 and D = 8, what is B x 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 x D Step 2 B x D - A Step 3 B x 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 73.
• Question 7

If a = 7, b = 11, c = 6 and d = 4, what is b x d - a + c?

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

11 x 4 - 7 + 6
EDDIE SAYS
The question tells us that b = 11, d = 4, a = 7 and c = 6.
If we swap the letters for the numbers they represent, we find that b x d - a + c becomes 11 x 4 - 7 + 6.
Remember that we have to keep the numbers and operations in the same order to reach the correct answer.
• Question 8

Following on from the previous question:

If a = 7, b = 11, c = 6 and d = 4, what is b x 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 x d Step 2 b x d - a Step 3 b x 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 43.
Hopefully the grids are helping you to follow each step in the correct order - the answer won't stay hid, if you use a grid!
• Question 9

If A = 3, B = 12, C = 4 and D = 9, what is B x D - A + C?

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

12 x 9 - 3 + 4
EDDIE SAYS
The question tells us that B = 12, D = 9, A = 3 and C = 4.
If we swap the letters for the numbers they represent, we find that B x D - A + C becomes 12 x 9 - 3 + 4.
This is a real brain stretcher!
Let's use a grid to help us solve it...
• Question 10

Following on from the last question:

If A = 3, B = 12, C = 4 and D = 9, what is B x 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 x D Step 2 B x D - A Step 3 B x 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 109.
Are you feeling confident that you can solve any maths code using the grid method? We hope so!
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