1
Finding the unknown factor
Discover Mathematics P3: Term 2, Lessons 61–70
GoalFind a missing factor in an equation with three factors, including equations that multiply by 10.
New words
unknown · a number we do not know yet, shown by ? or a boxmissing factor · a factor that is not given in a multiplicationequation · a number sentence with an equals sign
Explanation
An equation can have an unknown factor. To find it, first multiply the factors you know. For 2 × ? × 5 = 60, multiply 2 × 5 = 10. Now the equation says 10 × ? = 60, so the unknown is 60 ÷ 10 = 6. Check by putting the answer back: 2 × 6 × 5 = 12 × 5 = 60. When one factor is 10, think of tens. For ? × 10 = 600, the answer is 600 ÷ 10 = 60, because 60 tens make 600. Always check that the product is correct.
| Step | Work |
|---|---|
| 1 | 2 × 5 = 10 |
| 2 | 10 × ? = 60 |
| 3 | 60 ÷ 10 = 6 |
| 4 | 2 × 6 × 5 = 60 |
Worked examples
Find the unknown in 2 × ? × 5 = 60. Since 2 × 5 = 10, we need 10 × ? = 60. Six tens make 60, so ? = 6.
| Step | Work |
|---|---|
| 1 | 4 × 3 = 12 |
| 2 | 12 × ? = 48 |
| 3 | 48 ÷ 12 = 4 |
| Multiplication | Product |
|---|---|
| 6 × 10 | 60 |
| 60 × 10 | 600 |
Class activity
Mystery number. Write five equations with three factors, such as 3 × ? × 2 = 36, each with one factor hidden. Swap with a partner. Solve each one by multiplying the known factors first, then check by putting the answer back.
Practice
1
Find the unknown: 3 × ? × 2 = 36.
3 × 2 = 6, and 6 × ? = 36, so ? = 6. Check: 3 × 6 × 2 = 36.
2
Find the unknown: ? × 10 = 800.
800 ÷ 10 = 80.
3
Find the unknown: 5 × ? × 10 = 400.
5 × 10 = 50, and 50 × ? = 400, so ? = 8. Check: 5 × 8 × 10 = 400.
4
Find the unknown: 2 × 4 × ? = 40.
2 × 4 = 8, and 8 × ? = 40, so ? = 5.
5
A farmer has 3 fields. Each field has 4 rows of orange trees, and there are 60 trees in all. How many trees are in each row?
3 × 4 × ? = 60. 3 × 4 = 12, and 12 × ? = 60, so ? = 5 trees in a row.