# Recognise the Correct Number Operation

In this worksheet, students will learn about addition, multiplication, division and subtraction facts and use these facts to work out a missing number.

Key stage:  KS 2

Curriculum topic:   Verbal Reasoning

Curriculum subtopic:   Number Logic

Difficulty level:

### QUESTION 1 of 10

Hi number detective! We’ve got a challenge that we need your help with. Are you ready?

6 (18) 3

How could the two outside numbers (6 and 3), make the inside number (18)?

We can use any of the four main number operations to make our number.

These are: addition, subtraction, multiplication and division.

If we return to our problem, we can see that 6 x 3 = 18.

So the rule here is that the outside numbers multiply together to make the inside number.

For this question, we need to work out the rule for the first set of numbers and then use that rule to work out the missing number in the next set.

Let’s look at a problem with two sets of numbers now:

3 (7) 4        6 ( __ ) 10

First, let’s work out how the numbers 3 and 4 make 7.

They add together to make 7.

We need to use the rule of adding the outside numbers for 6 and 10 to work out the missing number.

6 and 10 add together to make 16 so the missing number is 16.

Let’s try another one:

12 (7) 5        20 ( __ ) 4

First, we need to work out how the numbers 12 and 5 can make 7.

12 - 5 = 7. This means we are taking away the number on the right from the number on the left.

We need to apply this rule to the second pair of numbers giving us 20 - 4 which is 16.

Does that make sense?

It’s now your turn to put your skills to the test and be a number detective, hunting down those missing numbers!

Hi detective, I need your help with these number puzzles.

Which rule do the outside numbers below follow to make the inside number?

4 (28) 7

Left number x right number

Left number + right number

Left number - right number

Right number - left number

Are you ready for another one, number detective?

Which rule do the outside numbers follow to make the inside number?

3 (12) 15

Left number x right number

Right number - left number

Left number - right number

Left number + right number

How do the two outside numbers here make the inside number?

32 (8) 4

Left number x right number

Left number ÷ right number

Right number ÷ left number

Right number + left number

Your mission here is to match the number puzzles below to their rules.

The rules tell us how the outside numbers make the inside number.

## Column B

7 (16) 9
Right number - left number
5 (15) 20
Left number + right number
3 (21) 7
Left number x right number
4 (8) 32
Right number ÷ left number

Here's a new challenge for you.

Look at the sets of numbers below. Work out the rule to make the middle number for the first set of numbers and use this rule to help you work out the middle number in the second set. Type the number in as digits below.

11 (19) 8        21 (?) 4

17

84

25

5.25

Look at the two sets of numbers below. Work out the rule for the first set of numbers and use this to help you work out the middle number in the second set. Type the number in as digits below.

48 (12) 4         30 (?) 3

90

33

10

27

Look at the two sets of numbers below. Work out the rule for the first set of numbers and use this rule to work out the mystery middle number in the second set. Type the number as digits below.

6 (18) 3        4 (?) 7

28

11

3

1.75

Look at the number sets below.

Work out the rule for the first set of numbers and use this rule to work out the mystery number in the second set.

5 (17) 22        9 (?) 19

28

10

171

2.11

Look at the number sets below.

Work out the rule for the first set of numbers and use this rule to work out the missing number in the second set.

20 (31) 11        17 (?) 7

119

10

2.43

24

It's time for your final number puzzle mission- hooray!

Work out the rule for the first set of numbers below and use this to work out the mystery number in the second set.

41 (44) 3        27 (?) 4

23

6.75

31

108

• Question 1

Hi detective, I need your help with these number puzzles.

Which rule do the outside numbers below follow to make the inside number?

4 (28) 7

Left number x right number
EDDIE SAYS
I hope you've got your lefts and rights in order for this set of questions! Did you check all the different options to see if they would give you the answer of 28? If you did, you would have found that only one option gave you the correct answer and that was the first one. Here, the left number (4) multiplies by the right number (7) to make the middle number (28). 4 x 7 = 28. We could have also said the right number multiplies by the left number, as when we times it doesn't matter which order the numbers are in.
• Question 2

Are you ready for another one, number detective?

Which rule do the outside numbers follow to make the inside number?

3 (12) 15

Right number - left number
EDDIE SAYS
Did you go through all the options and find the correct rule here? It was the second option: the right number (15) subtracts the left number (3), to give us the middle number. 15 - 3 = 12 Remember to try out all four number operations until you can successfully calculate the middle number using the two outside numbers.
• Question 3

How do the two outside numbers here make the inside number?

32 (8) 4

Left number ÷ right number
EDDIE SAYS
Did you spot the rule here? We need to divide the left number (32) by the right number (4) to get the middle number (8). Remember your lefts and rights: <--- this arrow points left ---> this arrow points right Great work, detective - on to the next one!
• Question 4

Your mission here is to match the number puzzles below to their rules.

The rules tell us how the outside numbers make the inside number.

## Column B

7 (16) 9
Left number + right number
5 (15) 20
Right number - left number
3 (21) 7
Left number x right number
4 (8) 32
Right number ÷ left number
EDDIE SAYS
How many puzzles did you solve, detective? 7 (16) 9 --> In this puzzle, we do 'Left number + right number' to work out the middle number: 7 + 9 = 16. 5 (15) 20 --> In this puzzle we do 'Right number - left number' to work out the middle number: 20 - 5 = 15. 3 (21) 7 --> In this puzzle we do 'Left number x right number' to work out the middle number: 3 x 7 = 21. (We may not know our 7 times table but we can count up in 3s 7 times because 7 x 3 means the same thing.) 4 (8) 32 --> In this puzzle we do 'Right number ÷ left number' to work out the middle number: 32 ÷ 4 = 8 (There are 8 fours in 32). It's time for your next number challenge, detective...
• Question 5

Here's a new challenge for you.

Look at the sets of numbers below. Work out the rule to make the middle number for the first set of numbers and use this rule to help you work out the middle number in the second set. Type the number in as digits below.

11 (19) 8        21 (?) 4

25
EDDIE SAYS
Did you find this a bit more challenging? First, we need to work out the rule for the first set of numbers: how do the outside numbers (11 and 8) make the inside number (19)? The rule is that we add the left number and the right number together. We then use this rule for the next set of numbers: 21 (left number) + 4 (right number) = 25 (middle number). This makes 25 the mystery number. Puzzle solved!
• Question 6

Look at the two sets of numbers below. Work out the rule for the first set of numbers and use this to help you work out the middle number in the second set. Type the number in as digits below.

48 (12) 4         30 (?) 3

10
EDDIE SAYS
Did you work out the rule for the first set of numbers? To get the middle number (12), we need to divide the left number (48) by the right number (4): 48 ÷ 4 = 12. Let's follow this rule (left number ÷ right number) for the next set of numbers: 30 (left number) ÷ 3 (right number) = 10 (middle and mystery number). Are you getting the hang of it yet? You've passed halfway in this activity, let's push on!
• Question 7

Look at the two sets of numbers below. Work out the rule for the first set of numbers and use this rule to work out the mystery middle number in the second set. Type the number as digits below.

6 (18) 3        4 (?) 7

28
EDDIE SAYS
For this question, we need to work out how the two outside numbers in the first set (6 and 3) make the inside number (18). Can you see how these numbers are related? 6 x 3 = 18 The rule here is left number (6) x right number (3) = middle number (18). Let's use this rule to work out the middle number in the second set. Left number (4) x right number (7) = middle number (28). This makes 28 our mystery number. How high can you count up in 4s?
• Question 8

Look at the number sets below.

Work out the rule for the first set of numbers and use this rule to work out the mystery number in the second set.

5 (17) 22        9 (?) 19

10
EDDIE SAYS
Did you work out the rule for the first set of numbers? How do the numbers 5 and 22 make 17? The rule here is: right number (22) - left number (5) = middle number (17). Let's use this rule to work out the middle number of the next set: 19 (right number) - 9 (left number) = 10 (mystery middle number). You must be an expert at your lefts and rights by now!
• Question 9

Look at the number sets below.

Work out the rule for the first set of numbers and use this rule to work out the missing number in the second set.

20 (31) 11        17 (?) 7

24
EDDIE SAYS
Did you notice the adding rule here? We need to add the left and right numbers together to work out the middle number. Let's do the same with the next set of numbers: 17 + 7 = 24 This makes 24 the missing middle number. Last question coming up!
• Question 10

It's time for your final number puzzle mission- hooray!

Work out the rule for the first set of numbers below and use this to work out the mystery number in the second set.

41 (44) 3        27 (?) 4

31
EDDIE SAYS
The rule for the first set of numbers was: left number + right number. 41 + 3 = 44 Let's follow this rule for the next set of numbers: 27 + 4 = 31. This makes 31 the missing number. Excellent number puzzle skills here, detective! I love a good puzzle. You should now feel super confident when asked to recognise, apply and inverse basic operations.
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