1
Missing numbers in fact families
Discover Mathematics P3: Term 2, Lessons 101–110
GoalFind the missing number in a multiplication or division equation using a fact family.
New words
missing number · the number we must find, shown by ? or a boxfact family · equations that use the same three numbersinverse · the opposite operation, such as division for multiplication
Explanation
Three numbers such as 6, 7 and 42 make a fact family: 6 × 7 = 42, 7 × 6 = 42, 42 ÷ 6 = 7 and 42 ÷ 7 = 6. If one number is missing, look at which place it is in, then use the family. If a factor is missing, as in ? × 6 = 42, divide the product by the other factor: 42 ÷ 6 = 7. If the number we divide by is missing, as in 42 ÷ ? = 6, we also divide: 42 ÷ 6 = 7. If the total we divide is missing, as in ? ÷ 7 = 6, multiply: 7 × 6 = 42. Always check by putting the answer back in the equation.
| Where is the ? | What we do | Example |
|---|---|---|
| A factor | divide the product | ? × 6 = 42, 42 ÷ 6 = 7 |
| The divisor | divide the total by the quotient | 42 ÷ ? = 6, 42 ÷ 6 = 7 |
| The total | multiply | ? ÷ 7 = 6, 7 × 6 = 42 |
Worked examples
Find the missing number in the fact triangle. The product is 48 and one factor is 6, so the missing factor is 48 ÷ 6 = 8. The family is 6 × 8 = 48, 8 × 6 = 48, 48 ÷ 6 = 8 and 48 ÷ 8 = 6.
Solve ? × 7 = 63. Think of the family: 63 ÷ 7 = 9. Check: 9 × 7 = 63, so the missing number is 9.
| Equation | Think | Missing number |
|---|---|---|
| ? ÷ 4 = 9 | 4 × 9 | 36 |
| 45 ÷ ? = 5 | 45 ÷ 5 | 9 |
Class activity
Missing number cards. Write 10 equations like 56 ÷ ? = 8 or ? × 9 = 72, hiding one number in each with a card. Mix them up. A partner picks a card, finds the missing number and says the whole fact family aloud.
Practice
1
Find the missing number: ? × 6 = 42.
42 ÷ 6 = 7, so the missing number is 7.
2
Find the missing number in the fact triangle.
56 ÷ 8 = 7, so the missing number is 7. Check: 8 × 7 = 56.
3
Find the missing number: 63 ÷ ? = 9.
63 ÷ 9 = 7, so the missing number is 7.
4
Find the missing number: ? ÷ 5 = 8.
5 × 8 = 40, so the missing number is 40.
5
Write the four equations of the fact family of 6, 9 and 54.
6 × 9 = 54, 9 × 6 = 54, 54 ÷ 6 = 9 and 54 ÷ 9 = 6.