Missing number problems
A missing-number problem gives you the answer and asks for one of the numbers that made it, like 7 × ? = 56. The trick is to run the sum backwards with the opposite operation.
Every operation has an opposite
- Adding and taking away undo each other: if 15 + 8 = 23, then 23 − 8 = 15.
- Multiplying and dividing undo each other: if 7 × 8 = 56, then 56 ÷ 7 = 8.
So when a number is missing, ask “what would undo this?” Then always put your answer back into the sum to check it. This is the same thinking as the fact families on our 7 × 8 page.
7 × ? = 56
Multiplying is undone by dividing: 56 ÷ 7 = 8.
Check: 7 × 8 = 56 ✓
? ÷ 6 = 9
Dividing is undone by multiplying: 9 × 6 = 54.
Check: 54 ÷ 6 = 9 ✓
15 + ? = 23
Adding is undone by taking away: 23 − 15 = 8. Or count up from 15 to 23.
Check: 15 + 8 = 23 ✓
40 − ? = 28
How much was taken from 40 to leave 28? Count up from 28 to 40: 40 − 28 = 12.
Check: 40 − 12 = 28 ✓
Watch out for take-away and divide
With adding and multiplying, the order doesn't matter, so 15 + ? and ? + 15 work the same way. Taking away and dividing are different. In 40 − ? = 28 you take the answer away from the start (40 − 28), but in ? − 12 = 28 you add it back on (28 + 12). Checking your answer in the original sum catches any mix-up.
Try some
8 questions. If one is tricky, you'll see how to undo it and get another go.
Missing numbers get much easier when the times tables are quick to recall. Practice them with a beat in Times Tables Rhythm or Division DJ, or explore the multiplication chart.
Frequently asked questions
How do you solve 7 × ? = 56?
Divide the answer by the number you know: 56 ÷ 7 = 8. Then check: 7 × 8 = 56.
What age are missing-number problems for?
Children usually meet them with adding and taking away from about age 6 or 7, and with multiplication and division from about 8 or 9. They are an early step toward algebra.