What you need to know

Things to remember:

  • It doesn’t matter what order you add or subtract numbers, so you can move them all around.

Find the missing number in the following equation:

5 + [?] - 2 = 7

Before we start, it is important to remember that the order we do additions and subtractions doesn’t matter.

2+9-3=8

9+2-3=8

-3+2+8=8

Now, back to our question

5 + [?] - 2 = 7

We will do this in 3 steps.

Step 1: Move what we are looking for to the start of the equation.

5 + [?] - 2 = 7

[?] + 5 - 2 = 7

Step 2: Do the addition or subtraction for the numbers next to each other

 

[?] + 5 - 2 = 7

5-2 =3

[?] + 3 = 7

 

Step 3: Find your missing number.

We can do this in two ways:

Step 3a: Try thinking about what the question is saying.

[?] + 3 = 7

This is telling us that “something plus 3 is 7”. But, we know that we add 3 to 4 to make 7, so 4 must be our answer!

Step 3b: Rearrange to get what we are looking for by itself.

Hint: Remember, we do the opposite to get something by itself.

 

[?] + 3 = 7

[?] = 7 - 3

[?] = 4

So, as we can see, it doesn’t matter if we use 3a or 3b, we get the same answer!

Example Questions

Question 1: Find the missing number in the following equation:

 

12 + [?] + 9 = 33

Answer

Step 1: Move what we are looking for to the start of the equation.

 

12 + [?] + 9 = 33

 

[?] + 12 +  9 = 33

 

Step 2: Do the addition or subtraction for the numbers next to each other

 

 

[?] + 12 +  9 = 33

 

 12+9 =21

 

[?] + 21 = 33

 

 

Step 3: Find your missing number.

 

We can do this in two ways:

 

Step 3a: Try thinking about what the question is saying.

 

[?] + 21 = 33

 

This is telling us that “something plus 21 is 12”. We can make 33 by adding 12 to 21, so 12 must be our missing number.

 

Step 3b: Rearrange to get what we are looking for by itself.

 

Hint: Remember, we do the opposite to get something by itself.

 

 

[?] + 21 = 33

 

[?] = 33 - 21

 

[?] = 12

Question 2: Find the missing number in the following equation:

 

11 + [?] -15 = 1

Answer

Step 1: Move what we are looking for to the start of the equation.

 

11 + [?] + -15 = 1

 

[?] + 11 -  15 = 1

 

Step 2: Do the addition or subtraction for the numbers next to each other

 

 

[?] + 11 -  15 = 1

 

 11-15 =-4

 

[?] -4 = 1

 

 

Step 3: Find your missing number.

 

We can do this in two ways:

 

Step 3a: Try thinking about what the question is saying.

 

[?] + 21 = 33

 

This is telling us that “something subtract 4 is 11”. We can make 1 by subtracting 4  from 5, so 5 must be our missing number.

 

Step 3b: Rearrange to get what we are looking for by itself.

 

Hint: Remember, we do the opposite to get something by itself.

 

 

[?] -4 = 1

 

[?] = 1 + 4

 

[?] = 5