Math worksheet for adding fractions with unlike denominators.

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 each fraction so they 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
- Add: 1/4 + 2/4 = 3/4
✔ Final: 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
- Add: 6/8 + 3/8 = 9/8
- Simplify: 9/8 = 1 1/8
✔ Final: 1 1/8

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Problem ③: 2/4 + 5/6

- First, simplify 2/4 = 1/2 (optional but helps)
- Denominators: 2 and 6 → LCM = 6
- Convert 1/2 to sixths: 1/2 = 3/6
- Add: 3/6 + 5/6 = 8/6
- Simplify: 8/6 = 4/3 = 1 1/3
✔ Final: 1 1/3

*(Alternatively, without simplifying first: 2/4 = 3/6? Wait — better to use original: 2/4 and 5/6 → LCM of 4 and 6 is 12)*

Wait — let me recalculate carefully:

Original: 2/4 + 5/6

LCM of 4 and 6 is 12.

2/4 = (2×3)/(4×3) = 6/12
5/6 = (5×2)/(6×2) = 10/12
Add: 6/12 + 10/12 = 16/12 = 4/3 = 1 1/3 ✔ Same answer.

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Problem ④: 3/6 + 1/3

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

*(Or directly: 3/6 + 1/3 → LCM 6 → 3/6 + 2/6 = 5/6)*

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Problem ⑤: 8/3 + 4/5

Denominators: 3 and 5 → LCM = 15
8/3 = (8×5)/(3×5) = 40/15
4/5 = (4×3)/(5×3) = 12/15
Add: 40/15 + 12/15 = 52/15
Convert to mixed number: 52 ÷ 15 = 3 remainder 7 → 3 7/15
✔ Final: 3 7/15

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Problem ⑥: 2/5 + 5/10

Simplify 5/10 = 1/2
Now: 2/5 + 1/2
LCM of 5 and 2 = 10
2/5 = 4/10, 1/2 = 5/10
Add: 4/10 + 5/10 = 9/10
✔ Final: 9/10

*(Or keep as is: 2/5 + 5/10 → LCM 10 → 4/10 + 5/10 = 9/10)*

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Problem ⑦: 2/3 + 1/2

LCM of 3 and 2 = 6
2/3 = 4/6, 1/2 = 3/6
Add: 4/6 + 3/6 = 7/6 = 1 1/6
✔ Final: 1 1/6

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Problem ⑧: 4/6 + 5/8

Simplify 4/6 = 2/3
Now: 2/3 + 5/8
LCM of 3 and 8 = 24
2/3 = 16/24, 5/8 = 15/24
Add: 16/24 + 15/24 = 31/24 = 1 7/24
✔ Final: 1 7/24

*(Without simplifying: 4/6 + 5/8 → LCM 24 → 4/6=16/24, 5/8=15/24 → same result)*

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Problem ⑨: 3/9 + 1/3

Simplify 3/9 = 1/3
So: 1/3 + 1/3 = 2/3
✔ Final: 2/3

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Problem ⑩: 6/4 + 5/12

Simplify 6/4 = 3/2
Now: 3/2 + 5/12
LCM of 2 and 12 = 12
3/2 = 18/12, 5/12 stays
Add: 18/12 + 5/12 = 23/12 = 1 11/12
✔ Final: 1 11/12

*(Without simplifying: 6/4 = 18/12, 5/12 → 23/12 → same)*

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Problem ⑪: 4/6 + 2/9

Simplify 4/6 = 2/3
Now: 2/3 + 2/9
LCM of 3 and 9 = 9
2/3 = 6/9, 2/9 stays
Add: 6/9 + 2/9 = 8/9
✔ Final: 8/9

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Problem ⑫: 9/2 + 2/8

Simplify 2/8 = 1/4
Now: 9/2 + 1/4
LCM of 2 and 4 = 4
9/2 = 18/4, 1/4 stays
Add: 18/4 + 1/4 = 19/4 = 4 3/4
✔ Final: 4 3/4

*(Without simplifying: 9/2 + 2/8 → LCM 8 → 9/2=36/8, 2/8 → 38/8 = 19/4 = 4 3/4)*

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Final Answer:
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