2
Subtracting fractions with unlike denominators
Discover Mathematics P5: Term 2, Unit 7, Lessons 4–6
GoalSubtract fractions with different denominators in the same four steps, and check the answer by adding.
New words
difference · the result of subtractingcheck by adding · adding the difference to the smaller number to get the bigger oneleast common denominator · the LCM of the denominators
Explanation
Subtracting works like adding. Find the least common denominator, rewrite both fractions, subtract the numerators, keep the denominator, then simplify. For example 5/6 − 1/4: the LCM of 6 and 4 is 12, so 10/12 − 3/12 = 7/12. We can check the answer by adding: 7/12 + 1/4 = 7/12 + 3/12 = 10/12 = 5/6, the number we started with. The answer of a subtraction is always smaller than the number we start from, so an estimate with benchmarks quickly shows a wrong result.
| Subtraction | Common denominator | Difference |
|---|---|---|
| 5/6 − 1/4 | 10/12 − 3/12 | 7/12 |
| 7/8 − 1/6 | 21/24 − 4/24 | 17/24 |
| 3/4 − 1/12 | 9/12 − 1/12 | 8/12 = 2/3 |
Worked examples
Subtract 5/6 − 1/4. In twelfths: 10/12 − 3/12 = 7/12. Check by adding: 7/12 + 3/12 = 10/12 = 5/6.
Subtract 7/8 − 1/6. The LCM of 8 and 6 is 24. 21/24 − 4/24 = 17/24.
Subtract 3/4 − 1/12. 3/4 = 9/12, so 9/12 − 1/12 = 8/12. Simplify by dividing top and bottom by 4: 2/3.
Class activity
Check-by-adding game. The grown-up writes a subtraction of two unlike fractions (for example 3/4 − 2/5). The child solves it and then proves the answer by adding the difference to the smaller fraction. Score a point when the proof returns the first fraction.
Practice
1
Work out 3/4 − 2/5.
15/20 − 8/20 = 7/20.
2
Work out 5/6 − 3/10 and simplify.
25/30 − 9/30 = 16/30 = 8/15.
3
Work out 2/3 − 1/2.
4/6 − 3/6 = 1/6.
4
Work out 9/10 − 1/2 and simplify.
9/10 − 5/10 = 4/10 = 2/5.
5
Work out 11/12 − 3/8 and check by adding.
22/24 − 9/24 = 13/24. Check: 13/24 + 9/24 = 22/24 = 11/12.