Adding and Subtracting Fractions
Grade 5 · Math · Study Guide
Master adding and subtracting fractions with unlike denominators using the least common denominator method.
When adding or subtracting fractions, both fractions must share the same denominator — called a common denominator. If the denominators are different, you need to find the Least Common Denominator (LCD) before you can add or subtract.
To find the LCD, list multiples of each denominator until you find a number that appears in both lists. Then rewrite each fraction as an equivalent fraction using that denominator before adding or subtracting the numerators.
After computing, always simplify your answer to lowest terms by dividing both the numerator and denominator by their Greatest Common Factor (GCF).
| Fraction 1 | Fraction 2 | LCD | Result |
|---|---|---|---|
| 1/2 | 1/3 | 6 | 3/6 + 2/6 = 5/6 |
| 2/5 | 1/4 | 20 | 8/20 + 5/20 = 13/20 |
| 3/4 | 1/6 | 12 | 9/12 - 2/12 = 7/12 |
| Unsimplified | GCF | Simplified |
|---|---|---|
| 6/8 | 2 | 3/4 |
| 10/15 | 5 | 2/3 |
| 4/12 | 4 | 1/3 |
Key terms
- Numerator
- The top number of a fraction, showing how many parts are selected.
- Denominator
- The bottom number of a fraction, showing the total equal parts.
- Least Common Denominator (LCD)
- The smallest number that is a multiple of both denominators.
- Equivalent Fraction
- A fraction with a different numerator and denominator but the same value.
Practice questions
What is 1/3 + 1/4?
- 2/7
- 5/12
- 7/12
- 2/12
Show answer
Answer: 7/12
LCD of 3 and 4 is 12. 1/3 = 4/12, 1/4 = 3/12. 4/12 + 3/12 = 7/12.
What is 3/4 - 1/3?
- 2/1
- 5/12
- 7/12
- 2/7
Show answer
Answer: 5/12
LCD is 12. 3/4 = 9/12, 1/3 = 4/12. 9/12 - 4/12 = 5/12.
1/2 + 2/5 = ___
Show answer
Answer: 9/10
LCD is 10. 1/2 = 5/10, 2/5 = 4/10. 5/10 + 4/10 = 9/10.
5/6 - 1/4 = ___
Show answer
Answer: 7/12
LCD is 12. 5/6 = 10/12, 1/4 = 3/12. 10/12 - 3/12 = 7/12.
Which fraction is equivalent to 4/6?
- 1/2
- 2/3
- 3/4
- 4/5
Show answer
Answer: 2/3
Divide numerator and denominator by GCF of 2: 4÷2=2, 6÷2=3, giving 2/3.
Fun facts
- Ancient Egyptians only used fractions with 1 in the numerator (called unit fractions), so they wrote 3/4 as 1/2 + 1/4!
- The word 'fraction' comes from the Latin word 'fractus,' meaning broken.
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