# 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 and D = 7, what is B + D - A + C?

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

4 + 7 - 10 + 3

10 + 7 - 4 + 3

4 + 7 - 3 + 10

7 + 4 - 10 - 3

If a = 10, b = 4, c = 3 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.

 Letters Numbers Answer Step 1 b + d 4 + 7 11 Step 2 b + d - a 11 - 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 = 9, what is B + D - A + C?

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

12 + 5 - 9 + 3

5 + 9 - 12 + 4

5 + 9 - 4 + 12

12 + 4 - 5 + 9

If A=12, B=5, C=4 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.

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 + 9 14 Step 2 B + D - A 14 - 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 x d - a + c?

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

12 x 8 - 7 + 5

8 + 7 - 12 + 5

5 + 8 - 7 + 12

12 x 8 - 5 + 7

If a = 5, b = 12, 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 12 x 8 Step 2 b x d - a Step 3 b x d - a + c

 Letters Numbers Answer Step 1 Step 2 Step 3

If A = 9, B = 10, C = 6 and D = 3, what is B x D - A + C?

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

9 x 10 - 6 + 3

6 + 10 - 9 + 3

10 x 3 - 9 + 6

10 x 9 - 3 + 6

If A = 9, B = 10, C = 6 and D = 3, 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 = 6, what is b x d - a + c?

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

12 x 6 - 4 + 3

12 x 6 - 3 + 4

12 x 4 - 6 + 3

12 x 3 - 4 + 6

If a = 3, b = 12, c = 4 and d = 6, 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 = 4, C = 3 and D = 7, what is B + D - A + C?

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

CORRECT ANSWER
4 + 7 - 10 + 3
EDDIE SAYS
The question tells us that B = 4, D = 7, A = 10 and C = 3.
If we swap the letters for the numbers they represent, we find that B + D - A + C becomes 4 + 7 - 10 + 3.
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, but we MUST keep subtractions in the same place or we will reach the wrong answer.
• Question 2

If a = 10, b = 4, c = 3 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.

 Letters Numbers Answer Step 1 b + d 4 + 7 11 Step 2 b + d - a 11 - 10 Step 3 b + d - a + c

CORRECT ANSWER
 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.
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 = 9, what is B + D - A + C?

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

CORRECT ANSWER
5 + 9 - 12 + 4
EDDIE SAYS
The question tells us that B = 5, D = 9, A = 12 and C = 4.
If we swap the letters for the numbers they represent, we find that B + D - A + C becomes 5 + 9 - 12 + 4.
Remember that as we have both addition (+) and subtraction (-) in this calculation, we must do each step in order.
• Question 4

If A=12, B=5, C=4 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.

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 + 9 14 Step 2 B + D - A 14 - Step 3 B + D - A + C

CORRECT ANSWER
 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.
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 x d - a + c?

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

CORRECT ANSWER
12 x 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 x d - a + c becomes 12 x 8 - 5 + 7.
We have used multiplication (x), addition (+) and subtraction (-) in this question so we must be sure to do each step in order to reach the correct answer.
• Question 6

If a = 5, b = 12, 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 12 x 8 Step 2 b x d - a Step 3 b x d - a + c

CORRECT ANSWER
 Letters Numbers Answer Step 1 Step 2 Step 3
EDDIE SAYS
Completing all the steps in the correct order leaves you with the answer 98.
It gets a little more tricky when we have a multiplication step in the puzzle, and the numbers get larger too!
Let's practice this some more in the next questions.
• Question 7

If A = 9, B = 10, C = 6 and D = 3, what is B x D - A + C?

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

CORRECT ANSWER
10 x 3 - 9 + 6
EDDIE SAYS
The question tells us that B = 10, D = 3, A = 9 and C = 6.
If we swap the letters for the numbers they represent, we find that B x D - A + C becomes 10 x 3 - 9 + 6.
Remember that as we have multiplication (x), addition (+) and subtraction (-) in this calculation, we must do each step in order to get to the correct answer.
• Question 8

If A = 9, B = 10, C = 6 and D = 3, 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

CORRECT ANSWER
 Letters Numbers Answer Step 1 Step 2 Step 3
EDDIE SAYS
Completing all the steps in the correct order leaves you with the answer 27.
How are you getting on with the multiplication step?
Ask an adult to assign you some times tables activities if you would like to practise more questions like this.
• Question 9

If a = 3, b = 12, c = 4 and d = 6, what is b x d - a + c?

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

CORRECT ANSWER
12 x 6 - 3 + 4
EDDIE SAYS
The question tells us that b = 12, d = 6, 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 6 - 3 + 4.
Remember that as we have multiplication (x), addition (+) and subtraction (-) in this calculation, we must do each step in order to get to the correct answer.
• Question 10

If a = 3, b = 12, c = 4 and d = 6, 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

CORRECT ANSWER
 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.
Hopefully you are feeling much more confident with multiplications (x) in these types of questions!
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