Balance the sum

The idea

In these questions, a sum has a missing number, and the two sides of the equals sign must balance — they must be worth exactly the same.

First, add up all the numbers you can see on the side with the gap. In 10 + ? + 36 = 52, the numbers shown add to 46. Then find what the gap must be to reach the total on the other side: 52 − 46 = 6.

If the missing number comes after a minus sign, work backwards carefully: in 55 − ? = 18, the missing number is 55 − 18 = 37. Always check by putting your answer back into the sum and making sure both sides really are equal.

Worked example

10 + ? + 36 = 52. Find the missing number.

1. Add the numbers shown on the left: 10 + 36 = 46.
2. The left side must reach 52, so the missing number is 52 − 46 = 6.
3. Check: 10 + 6 + 36 = 52. The two sides balance.

Answer: 6

Watch out

• Adding the total on the right to the numbers on the left instead of subtracting.
• Forgetting to check by putting the answer back into the sum.
• In a take-away sum like 55 − ? = 18, adding 55 and 18 instead of subtracting.