Finding the missing number
A missing-number equation has a number we don’t know yet, called the unknown. It’s shown by a box, a blank, a question mark or a symbol such as a letter:
- 7 + □ = 12
- __ × 4 = 28
- 30 − ? = 18
Your job is to find the number that makes the equation true.
Think of a balance
The equal sign means both sides have the same value, like a balanced scale. 7 + □ must weigh the same as 12. What makes it balance? □ = 5.
Use the inverse operation
An inverse operation undoes another one.
| Operation | Inverse |
|---|---|
| Addition | Subtraction |
| Subtraction | Addition |
| Multiplication | Division |
| Division | Multiplication |
Solving each type
| Equation | Think | Answer |
|---|---|---|
| 7 + □ = 12 | 12 − 7 | 5 |
| □ + 9 = 15 | 15 − 9 | 6 |
| 20 − □ = 13 | 20 − 13 | 7 |
| □ − 8 = 6 | 6 + 8 | 14 |
| 6 × □ = 42 | 42 ÷ 6 | 7 |
| □ ÷ 3 = 9 | 9 × 3 | 27 |
| 36 ÷ □ = 4 | 36 ÷ 4 | 9 |
Notice: when the unknown is the number being subtracted or divided by, you use the same operation (20 − 13, 36 ÷ 4).
Unknowns on the left
The unknown can be anywhere, and so can the equal sign:
- 15 = □ + 8 → □ = 7
- 12 + 5 = □ + 10 → 17 = □ + 10 → □ = 7
The second one trips many people up: the answer is not 17! Work out the side you know, then balance.
Always check
Put your answer back in. If 7 + 5 = 12 is true, you’re right.
Worked examples
Example 1: □ + 14 = 30
30 − 14 = 16. Check: 16 + 14 = 30 ✓
Example 2: 9 × □ = 72
72 ÷ 9 = 8.
Example 3: 25 + 10 = □ + 20
Left side = 35. 35 − 20 = 15.
Common mistakes
- Writing the answer to the left side instead of the unknown (writing 35 in Example 3).
- Using the wrong inverse: for □ − 8 = 6, the answer is 6 + 8 = 14, not 6 − 8.
- Not checking by substituting back.
Try it yourself
- □ + 23 = 50
- 45 − □ = 17
- □ × 7 = 63
- □ ÷ 5 = 12
- 8 + 9 = □ + 11
Answers: 1) 27 2) 28 3) 9 4) 60 5) 6
Quick recap
- The unknown makes the equation true.
- Use the inverse operation to find it.
- The equal sign means balance; check by putting your answer back in.