Adding fractions with unlike denominators worksheet for math practice.

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

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Problem ①:

1/4 + 1/2

- Denominators: 4 and 2 → LCM = 4
- Convert 1/2 to fourths: 1/2 = 2/4
- Now: 1/4 + 2/4 = 3/4

✔ Answer: 3/4

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Problem ②:

3/4 + 3/8

- Denominators: 4 and 8 → LCM = 8
- Convert 3/4 to eighths: 3/4 = 6/8
- Now: 6/8 + 3/8 = 9/8 → This is an improper fraction → 1 1/8

✔ Answer: 1 1/8 or 9/8

*(We’ll write as mixed number unless told otherwise — but since worksheet doesn’t specify, either is fine. Let’s use simplified form: 9/8 is acceptable, but 1 1/8 is more common for students.)*

Actually, let’s check instructions — it says “add each pair”, no simplification specified. But in school, we usually simplify. So:

→ 9/8 = 1 1/8

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Problem ③:

2/4 + 5/6

First, simplify 2/4 → 1/2? Wait — better to keep as is for now and find common denominator.

Denominators: 4 and 6 → LCM = 12

Convert:
- 2/4 = (2×3)/(4×3) = 6/12
- 5/6 = (5×2)/(6×2) = 10/12

Add: 6/12 + 10/12 = 16/12 → Simplify: divide numerator and denominator by 4 → 4/3 → or 1 1/3

✔ Answer: 1 1/3 or 4/3

Again, let’s go with 1 1/3

Wait — actually, 16/12 reduces to 4/3, which is 1 1/3. Correct.

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Problem ④:

3/6 + 1/3

Simplify 3/6 → 1/2? Or find common denominator.

Denominators: 6 and 3 → LCM = 6

Convert 1/3 to sixths: 1/3 = 2/6

Now: 3/6 + 2/6 = 5/6

✔ Answer: 5/6

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Problem ⑤:

8/3 + 4/5

Denominators: 3 and 5 → LCM = 15

Convert:
- 8/3 = (8×5)/(3×5) = 40/15
- 4/5 = (4×3)/(5×3) = 12/15

Add: 40/15 + 12/15 = 52/15 → Improper fraction → 3 7/15

✔ Answer: 3 7/15

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Problem ⑥:

2/5 + 5/10

Note: 5/10 = 1/2, but let’s use common denominator.

Denominators: 5 and 10 → LCM = 10

Convert 2/5 to tenths: 2/5 = 4/10

Now: 4/10 + 5/10 = 9/10

✔ Answer: 9/10

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Problem ⑦:

2/3 + 1/2

Denominators: 3 and 2 → LCM = 6

Convert:
- 2/3 = 4/6
- 1/2 = 3/6

Add: 4/6 + 3/6 = 7/6 → 1 1/6

✔ Answer: 1 1/6

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Problem ⑧:

4/6 + 5/8

First, simplify 4/6 → 2/3? Maybe easier to work with original.

Denominators: 6 and 8 → LCM = 24

Convert:
- 4/6 = (4×4)/(6×4) = 16/24
- 5/8 = (5×3)/(8×3) = 15/24

Add: 16/24 + 15/24 = 31/24 → 1 7/24

✔ Answer: 1 7/24

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Problem ⑨:

3/9 + 1/3

Simplify 3/9 → 1/3

So: 1/3 + 1/3 = 2/3

Or using common denominator:

Denominators: 9 and 3 → LCM = 9

Convert 1/3 to ninths: 1/3 = 3/9

Then: 3/9 + 3/9 = 6/9 → simplify → 2/3

✔ Answer: 2/3

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Problem ⑩:

6/4 + 5/12

First, 6/4 can be simplified to 3/2, but let’s use common denominator.

Denominators: 4 and 12 → LCM = 12

Convert 6/4 to twelfths: 6/4 = (6×3)/(4×3) = 18/12

Now: 18/12 + 5/12 = 23/12 → 1 11/12

✔ Answer: 1 11/12

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Problem ⑪:

4/6 + 2/9

Simplify 4/6 → 2/3? Let’s use common denominator.

Denominators: 6 and 9 → LCM = 18

Convert:
- 4/6 = (4×3)/(6×3) = 12/18
- 2/9 = (2×2)/(9×2) = 4/18

Add: 12/18 + 4/18 = 16/18 → simplify → 8/9

✔ Answer: 8/9

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Problem ⑫:

9/2 + 2/8

Simplify 2/8 → 1/4? Or use common denominator.

Denominators: 2 and 8 → LCM = 8

Convert 9/2 to eighths: 9/2 = (9×4)/(2×4) = 36/8

2/8 stays as is.

Add: 36/8 + 2/8 = 38/8 → simplify: divide by 2 → 19/4 → 4 3/4

✔ Answer: 4 3/4

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## Final Answers:

① 3/4
② 1 1/8
③ 1 1/3
④ 5/6
⑤ 3 7/15
⑥ 9/10
⑦ 1 1/6
⑧ 1 7/24
⑨ 2/3
⑩ 1 11/12
⑪ 8/9
⑫ 4 3/4