Adding unlike fractions worksheets | Worsheets library - Free Printable

Let’s solve each problem step by step. We’re adding fractions with different denominators (unlike fractions). To do that, we need to find a common denominator — usually the least common multiple (LCM) of the two denominators — then convert each fraction so they have the same bottom number, add the tops, and simplify if needed.

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1. ½ + ⅖

Denominators: 2 and 5 → LCM = 10
Convert:
½ = 5/10
⅖ = 4/10
Add: 5/10 + 4/10 = 9/10

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2. 8/12 + 8/11

Denominators: 12 and 11 → LCM = 132
Convert:
8/12 = (8×11)/(12×11) = 88/132
8/11 = (8×12)/(11×12) = 96/132
Add: 88/132 + 96/132 = 184/132
Simplify: Divide numerator and denominator by 4 → 46/33
Or as mixed number: 1 13/33 → but let’s keep improper unless asked.
Actually, 184 ÷ 4 = 46, 132 ÷ 4 = 33 → 46/33

Wait — can we reduce more? 46 and 33 share no common factors besides 1 → yes, 46/33

But maybe leave as is or check if simplifies further — nope. So answer is 46/33

Alternatively, we could write as mixed number: 1 13/33 — but since worksheet doesn’t specify, either is fine. Let’s go with simplified fraction: 46/33

Actually, let me double-check calculation:

8/12 = 2/3 → but better to use original for accuracy.

8/12 = 88/132 ✔️
8/11 = 96/132 ✔️
Sum: 184/132 → divide numerator and denominator by 4 → 46/33 ✔️

Yes.

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3. 2/7 + 6/10

First, simplify 6/10 = 3/5 → but let’s use original to avoid confusion.

Denominators: 7 and 10 → LCM = 70
Convert:
2/7 = 20/70
6/10 = 42/70
Add: 20/70 + 42/70 = 62/70
Simplify: divide by 2 → 31/35

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4. 1/6 + 6/11

Denominators: 6 and 11 → LCM = 66
Convert:
1/6 = 11/66
6/11 = 36/66
Add: 11/66 + 36/66 = 47/66 → already simplified → 47/66

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5. 5/9 + ½

Denominators: 9 and 2 → LCM = 18
Convert:
5/9 = 10/18
½ = 9/18
Add: 10/18 + 9/18 = 19/18 → improper fraction → 19/18 or 1 1/18 → we’ll write 19/18

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6. 9/12 + 2/12

Same denominator! Just add numerators:
9 + 2 = 11 → 11/12

(Also, 9/12 simplifies to 3/4, but since both are over 12, just add.)

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7. 2/7 + ¼

Denominators: 7 and 4 → LCM = 28
Convert:
2/7 = 8/28
¼ = 7/28
Add: 8/28 + 7/28 = 15/28 → already simplified → 15/28

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8. 1/4 + 6/8

Note: 6/8 = 3/4 → so 1/4 + 3/4 = 4/4 = 1

Or using common denominator:

Denominators: 4 and 8 → LCM = 8
1/4 = 2/8
6/8 = 6/8
Add: 2/8 + 6/8 = 8/8 = 1

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9. 4/10 + 4/5

Simplify 4/10 = 2/5 → so 2/5 + 4/5 = 6/5 → 6/5

Or using common denominator:

Denominators: 10 and 5 → LCM = 10
4/10 = 4/10
4/5 = 8/10
Add: 4/10 + 8/10 = 12/10 = 6/5 → 6/5

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10. ½ + 8/11

Denominators: 2 and 11 → LCM = 22
Convert:
½ = 11/22
8/11 = 16/22
Add: 11/22 + 16/22 = 27/22 → 27/22

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11. 1/11 + 2/12

Simplify 2/12 = 1/6 → now add 1/11 + 1/6

Denominators: 11 and 6 → LCM = 66
Convert:
1/11 = 6/66
1/6 = 11/66
Add: 6/66 + 11/66 = 17/66 → 17/66

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12. 2/12 + 2/4

Simplify first:
2/12 = 1/6
2/4 = 1/2
Now add 1/6 + 1/2

LCM of 6 and 2 = 6
1/6 = 1/6
1/2 = 3/6
Add: 1/6 + 3/6 = 4/6 = 2/3

Or without simplifying first:

Denominators: 12 and 4 → LCM = 12
2/12 = 2/12
2/4 = 6/12
Add: 2/12 + 6/12 = 8/12 = 2/3

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13. 3/5 + 3/8

Denominators: 5 and 8 → LCM = 40
Convert:
3/5 = 24/40
3/8 = 15/40
Add: 24/40 + 15/40 = 39/40 → already simplified → 39/40

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14. 6/9 + ½

Simplify 6/9 = 2/3 → now add 2/3 + ½

Denominators: 3 and 2 → LCM = 6
2/3 = 4/6
½ = 3/6
Add: 4/6 + 3/6 = 7/6 → 7/6

Or without simplifying:

6/9 = 6/9, ½ = ?
LCM of 9 and 2 = 18
6/9 = 12/18
½ = 9/18
Add: 12/18 + 9/18 = 21/18 = 7/6 → same → 7/6

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✔ All problems solved carefully.

Final Answer:
1. 9/10
2. 46/33
3. 31/35
4. 47/66
5. 19/18
6. 11/12
7. 15/28
8. 1
9. 6/5
10. 27/22
11. 17/66
12. 2/3
13. 39/40
14. 7/6