 # Balance the Sum so that Both Sides are Equal

In this worksheet, students will complete a calculation by adding in the missing number so that both sides are equal. It will strengthen their number skills. Key stage:  KS 2

Curriculum topic:   Verbal Reasoning

Curriculum subtopic:   Complete the Calculation

Difficulty level:   ### QUESTION 1 of 10

Calling all number detectives!

Look at this symbol: We know it is the equals sign but what does it actually mean?

It means the same as and doesn’t just mean the answer.

Look at the following calculation:

43 - 7 = 12 x __

Both sides of the calculation are equal. The answer to 43 - 7 must be the same as the answer to 12 multiplied by something (our mystery number).

We need to work out the answer to the calculation on the left to help us work out the missing number on the right.

So 43 - 7 = 36.

We need to make the calculation on the right equal 36. 12 x 3 is 36. Therefore the missing number is 3. Let’s try another to check we understand what is happening:

3 x __ = 5 + 7

Here we must work out the right side of the calculation to help us work out the missing number on the left.

So 5 + 7 = 12.

3 x ? = 12

The missing number is 4 as 3 x 4 = 12.

3 x 4 = 5 + 7

Remember that equals means the same as and the answers on either side of the equals sign must be the same.

In this activity, you will be completing sums by finding the missing number.

Good luck!

Welcome number detective!

Below is a calculation, where both sides should be equal.

However, one of the numbers has been taken away by the cheeky number burglar! Can you work out what it is

4 x 11 = 31 + __ Ready for another one, number detective?

Below is a calculation where both sides should be equal.

Can you work out what the missing number is?

105 - 90 = 34 - __

Let's try another one, number detective.

Below is a calculation where both sides should be equal.

Can you find out what number has been missed out?

55 ÷ 5 = 96 - __

Are you getting the hang of this now?

Below is a calculation where both sides should be equal.

Can you use your detecting skills to work out what number has been missed out?

12 x 4 = 19 + __ Below is another calculation where both sides should be equal.

Can you work out what the mystery number is?

99 ÷ 11 = 109 - __ You're over halfway through now, number detective!

Below is a calculation where both sides should be equal.

Can you work out what number is missing?

67 + 53 = 10 x __

Keep going, number detective - you're doing really well!

Below is a calculation where both sides should be equal.

Can you see what number has been missed out?

78 - 68 = 110 ÷ __ Below is yet another calculation where both sides should be equal!

Once again, there is a gap in the sum - can you work out what number should be in the hole?

109 - 54 = 28 + __ Only two more to go now, number detective!

Below is a calculation where both sides should be equal.

Can you work out what number is missing?

8 x 4 = 78 - __

This is the last question in this activity, number detective! Yippee!

Below is a calculation where both sides should be equal.

So, for the last time, what is the missing number?

86 + 23 = 72 + __ • Question 1

Welcome number detective!

Below is a calculation, where both sides should be equal.

However, one of the numbers has been taken away by the cheeky number burglar! Can you work out what it is

4 x 11 = 31 + __ 13
EDDIE SAYS
Some fun and challenging questions in this activity! There are two steps to take in order to find the missing number. First, work out the answer to the calculation on the left. So 4 x 11 = 44. Then, you work out the answer to the calculation on the right. The answer must total 44 also. So, 31 + __ = 44 can be worked out as 44 - 31, which equals 13. Brilliant!
• Question 2

Ready for another one, number detective?

Below is a calculation where both sides should be equal.

Can you work out what the missing number is?

105 - 90 = 34 - __

19
EDDIE SAYS
You're doing great! Remember to take things slowly and work it out in two stages. First, you work out 105 - 90, which is 15. Then, you need to make sure that the answer to the right-hand side is also 15. So, you need to find out what the mystery number is in the sum 34 - __ = 15. This can be worked out as 34 - 15 which equals 19.
• Question 3

Let's try another one, number detective.

Below is a calculation where both sides should be equal.

Can you find out what number has been missed out?

55 ÷ 5 = 96 - __

85
EDDIE SAYS
Did you work this one out, detective? First, find out the answer to the left-hand side: 55 ÷ 5 = 11. Now you know that the right-hand side must also equal 11, so you need to solve the sum: 96 - __ = 11. This is the same as doing 96 - 11, which gives you 85.
• Question 4

Are you getting the hang of this now?

Below is a calculation where both sides should be equal.

Can you use your detecting skills to work out what number has been missed out?

12 x 4 = 19 + __ 29
EDDIE SAYS
Did you get this one sorted? Remember to work it out in stages! First, find the answer to the left-hand side - you have to work out 12 x 4, which is 48. The next step is to put 48 as the answer to the right-hand side so that your sum becomes 19 + __ = 48. Now, all you have to do is work out 48 - 19, which equals 29.
• Question 5

Below is another calculation where both sides should be equal.

Can you work out what the mystery number is?

99 ÷ 11 = 109 - __ 100
EDDIE SAYS
You're halfway through this activity! To work out the answer here, you do 99 ÷ 11 = 9. Secondly, you solve 109 - __ = 9. So the calculation would be 109 - 9, which makes 100. It's simple once you break it down into stages, isn't it?
• Question 6

You're over halfway through now, number detective!

Below is a calculation where both sides should be equal.

Can you work out what number is missing?

67 + 53 = 10 x __

12
EDDIE SAYS
Are you getting the hang of these types of calculations? For this question, you first do the sum 67 + 53 = 120. Then, 10 x __ = 120. The way you work this out is to work out how many tens are there in 120. 120 divided by 10 = 12.
• Question 7

Keep going, number detective - you're doing really well!

Below is a calculation where both sides should be equal.

Can you see what number has been missed out?

78 - 68 = 110 ÷ __ 11
EDDIE SAYS
First, you need to work out 78 - 68 = 10. Then, you need to put the number 10 into the answer on the right-hand side, making the sum: 110 ÷ __ = 10. Finally, you need to work out how many tens there are in 110. Excellent!
• Question 8

Below is yet another calculation where both sides should be equal!

Once again, there is a gap in the sum - can you work out what number should be in the hole?

109 - 54 = 28 + __ 27
EDDIE SAYS
You're finding so many of our missing numbers! This time, you need to work out 109 - 54 = 55. Then, 28 + __ = 55, which can be solved by doing 55 - 28. Did you follow all the stages, number detective?
• Question 9

Only two more to go now, number detective!

Below is a calculation where both sides should be equal.

Can you work out what number is missing?

8 x 4 = 78 - __

46
EDDIE SAYS
How are you getting on, detective? First, you need to work out 8 x 4, which is 32. Then, put 32 as the answer to the sum on the right-hand side: 78 - __ = 32, which can be solved by doing 78 - 32. Great number work!
• Question 10

This is the last question in this activity, number detective! Yippee!

Below is a calculation where both sides should be equal.

So, for the last time, what is the missing number?

86 + 23 = 72 + __ 37
EDDIE SAYS
This time you work out 86 + 23 = 109. Then, 72 + __ = 109 can be worked out by doing 109 - 72. You've collected heaps of missing numbers, but there are still plenty more to find! Please join us again soon so we can continue our number finding mission.
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