Adding Fractions with Unlike Denominators - Worksheet Digital - Free Printable

Let’s solve each fraction addition problem step by step. Remember, when adding fractions with different denominators (unlike fractions), we need to find a common denominator first — usually the least common multiple (LCM) of the two denominators. Then we convert each fraction so they have that same denominator, add the numerators, and simplify if needed.

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Problem 1: 1/2 + 1/3

- Denominators: 2 and 3 → LCM = 6
- Convert:
1/2 = 3/6
1/3 = 2/6
- Add: 3/6 + 2/6 = 5/6
✔ Final: 5/6

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Problem 2: 1/3 + 3/5

- Denominators: 3 and 5 → LCM = 15
- Convert:
1/3 = 5/15
3/5 = 9/15
- Add: 5/15 + 9/15 = 14/15
✔ Final: 14/15

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Problem 3: 1/2 + 2/3

- Denominators: 2 and 3 → LCM = 6
- Convert:
1/2 = 3/6
2/3 = 4/6
- Add: 3/6 + 4/6 = 7/6 → This is an improper fraction. We can write it as mixed number: 1 1/6
✔ Final: 7/6 or 1 1/6

*(We’ll keep it as improper unless told otherwise — but both are correct. Let’s use 7/6 for consistency.)*

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Problem 4: 2/5 + 5/6

- Denominators: 5 and 6 → LCM = 30
- Convert:
2/5 = 12/30
5/6 = 25/30
- Add: 12/30 + 25/30 = 37/30 → Improper → 1 7/30
✔ Final: 37/30 or 1 7/30

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Problem 5: 5/6 + 2/5

- Denominators: 6 and 5 → LCM = 30
- Convert:
5/6 = 25/30
2/5 = 12/30
- Add: 25/30 + 12/30 = 37/30 → Same as above → 1 7/30
✔ Final: 37/30 or 1 7/30

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Problem 6: 1/4 + 1/6

- Denominators: 4 and 6 → LCM = 12
- Convert:
1/4 = 3/12
1/6 = 2/12
- Add: 3/12 + 2/12 = 5/12
✔ Final: 5/12

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Problem 7: 3/7 + 3/5

- Denominators: 7 and 5 → LCM = 35
- Convert:
3/7 = 15/35
3/5 = 21/35
- Add: 15/35 + 21/35 = 36/35 → Improper → 1 1/35
✔ Final: 36/35 or 1 1/35

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Problem 8: 2/5 + 5/9

- Denominators: 5 and 9 → LCM = 45
- Convert:
2/5 = 18/45
5/9 = 25/45
- Add: 18/45 + 25/45 = 43/45
✔ Final: 43/45

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Problem 9: 5/8 + 1/2

- Denominators: 8 and 2 → LCM = 8
- Convert:
5/8 stays
1/2 = 4/8
- Add: 5/8 + 4/8 = 9/8 → Improper → 1 1/8
✔ Final: 9/8 or 1 1/8

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Problem 10: 1/6 + 3/4

- Denominators: 6 and 4 → LCM = 12
- Convert:
1/6 = 2/12
3/4 = 9/12
- Add: 2/12 + 9/12 = 11/12
✔ Final: 11/12

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Final Answer:
1. 5/6
2. 14/15
3. 7/6
4. 37/30
5. 37/30
6. 5/12
7. 36/35
8. 43/45
9. 9/8
10. 11/12