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:$$12 + [?] + 9 = 33$$

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:$$11 + [?] -15 = 1$$

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.

$$[?] -4 = 1$$

$$[?] = 1 + 4$$

$$[?] = 5$$