Do the opposite
An equation with a blank already tells you the result. To find the blank, do the opposite operation to that result.
If a × [ ] = c, then [ ] = c ÷ a. Multiplying made the result, so dividing takes you back.
Division needs more care, because it matters which side the blank is on. If a ÷ [ ] = c, then [ ] = a ÷ c. If [ ] ÷ b = c, then [ ] = c × b.
Divide only by nonzero numbers. Multiplication by zero cannot be undone by division.
When the equation has brackets, work from the outside in. Undo the operation outside the brackets first, which gives you the value of the bracket. Then undo the operation inside it.
Two worked equations
Take 36 ÷ [ ] = 4. The blank is the number you divide by. Read it as: 36 shared into groups of the blank gives 4. So the blank is 36 ÷ 4, which is 9. Check it: 36 ÷ 9 = 4.
Now take (12 + [ ]) × 3 = 60. The outside operation is × 3, so undo that first: the bracket is 60 ÷ 3, which is 20.
That leaves 12 + [ ] = 20. Undo the addition: the blank is 20 − 12, which is 8. Check it: (12 + 8) × 3 = 60.
One with brackets
Here is (5 + [ ]) × 4 = 32.
Undo the outside operation first to get the value of the bracket. Then undo the addition inside it.
Stopping after the first step is the usual slip. The bracket is not the blank.
Try it
In (5 + [ ]) × 4 = 32, what is the missing number?
- 3
- 8
Show the answer
3
Correct. The bracket is 32 ÷ 4 = 8, and then 8 − 5 = 3. Check it: (5 + 3) × 4 = 32.
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Practice Find the missing number