The idea, step by step
Find a missing factor or dividend
In □ × 8 = 96, the missing number counts groups of eight. Divide ninety-six by eight to get twelve. Check by replacing the square: 12 × 8 = 96.
In □ ÷ 7 = 15, the missing number is the starting total, called the dividend. Fifteen groups of seven make the total, so multiply: 15 × 7 = 105. The square's position matters; a single 'always divide' rule will not solve every equation.
Find a missing divisor
In 84 ÷ □ = 7, the missing number tells how large each of seven equal groups is, or how many groups give a quotient of seven. Use the fact 7 × □ = 84. The missing number is twelve.
Name the known product and factors before calculating. Once you find a number, substitute it into the original equation, not just into the fact you used along the way. This catches answers that fit a different equation.
| Missing-number equation | Useful calculation | Check |
|---|---|---|
| □ × 8 = 96 | 96 ÷ 8 = 12 | 12 × 8 = 96 |
| □ ÷ 7 = 15 | 15 × 7 = 105 | 105 ÷ 7 = 15 |
| 84 ÷ □ = 7 | 84 ÷ 7 = 12 | 84 ÷ 12 = 7 |
A common trap
Solving 72 ÷ □ = 8 by multiplying seventy-two by eight.
Instead: Use the related fact 8 × □ = 72, so the square is nine. Substitution confirms 72 ÷ 9 = 8.
See the thinking
Missing number of packs
Each pack holds twelve cards. There are 156 cards altogether. How many packs is this?
- Write □ × 12 = 156.
- Divide 156 by twelve: 12 × 13 = 156.
- Substitute thirteen into the multiplication sentence.
Missing starting amount
Find the square in □ ÷ 9 = 24.
- The square is the total before division.
- Multiply the quotient twenty-four by nine: 24 × 9 = 216.
- Check 216 ÷ 9 = 24.
Check your understanding
Find the square: 132 ÷ □ = 11.
Show answer
12.
11 × 12 = 132, so 132 ÷ 12 = 11.
Your turn
6 questions · 10 marks · Work at your own pace.
Read the questions online
- Find the square: □ × 6 = 78.1 mark
- Find the square: 9 × □ = 225.1 mark
- Find the square: □ ÷ 8 = 17.2 marks
- Find the square: 144 ÷ □ = 12.2 marks
- A school shares an unknown number of books equally among seven classes. Each class receives 23 books. How many books were shared?2 marks
- A learner puts 48 in the square in 96 ÷ □ = 2. Is the answer correct? Show the original equation with the number substituted.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Find the square: □ × 6 = 78.1 mark
78 ÷ 6 = 13; check 13 × 6 = 78.
13. - Find the square: 9 × □ = 225.1 mark
225 ÷ 9 = 25.
25. - Find the square: □ ÷ 8 = 17.2 marks
17 × 8 = 136; check 136 ÷ 8 = 17.
136. - Find the square: 144 ÷ □ = 12.2 marks
The related multiplication is 12 × □ = 144.
12. - A school shares an unknown number of books equally among seven classes. Each class receives 23 books. How many books were shared?2 marks
Write □ ÷ 7 = 23.
Multiply 23 × 7 = 161.
161 books. - A learner puts 48 in the square in 96 ÷ □ = 2. Is the answer correct? Show the original equation with the number substituted.2 marks
Two groups of forty-eight make ninety-six.
The answer satisfies the original equation.
Yes: 96 ÷ 48 = 2.
Curriculum reference & lesson scope
Australian Curriculum v9.0; SA Curriculum Mathematics 2026
One-/two-digit multipliers; division strategies; contextual remainders; inverse fact families; unknown factors/dividends/divisors.
Official curriculum source ↗