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 rewrite each fraction so they have that same denominator, and finally add the numerators.
We’ll go one by one:
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1. ½ + ⅖
Denominators: 2 and 5 → LCM = 10
½ = 5/10
⅖ = 4/10
5/10 + 4/10 =
9/10
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2. 8/12 + 8/11
Denominators: 12 and 11 → LCM = 132
8/12 = (8×11)/(12×11) = 88/132
8/11 = (8×12)/(11×12) = 96/132
88/132 + 96/132 = 184/132 → Simplify: divide numerator and denominator by 4 →
46/33 or
1 13/33
But since the worksheet doesn’t specify mixed numbers, we can leave as improper fraction unless told otherwise. Let’s keep it simplified:
46/33
Wait — let me check if 184 ÷ 4 = 46, 132 ÷ 4 = 33 → yes. So 46/33 is correct.
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3. 2/7 + 6/10
First simplify 6/10 → 3/5
Now: 2/7 + 3/5
Denominators: 7 and 5 → LCM = 35
2/7 = 10/35
3/5 = 21/35
10/35 + 21/35 =
31/35
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4. 1/6 + 6/11
Denominators: 6 and 11 → LCM = 66
1/6 = 11/66
6/11 = 36/66
11/66 + 36/66 =
47/66
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5. 5/9 + ½
Denominators: 9 and 2 → LCM = 18
5/9 = 10/18
½ = 9/18
10/18 + 9/18 =
19/18 or
1 1/18
Again, unless specified, we can write as improper fraction:
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, no need.)
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7. 2/7 + ¼
Denominators: 7 and 4 → LCM = 28
2/7 = 8/28
¼ = 7/28
8/28 + 7/28 =
15/28
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8. 1/4 + 6/8
Simplify 6/8 → 3/4
So: 1/4 + 3/4 =
4/4 = 1
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9. 4/10 + 4/5
Simplify 4/10 → 2/5
So: 2/5 + 4/5 =
6/5 or
1 1/5
Leave as
6/5
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10. ½ + 8/11
Denominators: 2 and 11 → LCM = 22
½ = 11/22
8/11 = 16/22
11/22 + 16/22 =
27/22 or
1 5/22
Keep as
27/22
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11. 1/11 + 2/12
Simplify 2/12 → 1/6
Now: 1/11 + 1/6
Denominators: 11 and 6 → LCM = 66
1/11 = 6/66
1/6 = 11/66
6/66 + 11/66 =
17/66
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12. 2/12 + 2/4
Simplify:
2/12 = 1/6
2/4 = 1/2
Now: 1/6 + 1/2
LCM of 6 and 2 = 6
1/6 + 3/6 =
4/6 = 2/3
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13. 3/5 + 3/8
Denominators: 5 and 8 → LCM = 40
3/5 = 24/40
3/8 = 15/40
24/40 + 15/40 =
39/40
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14. 6/9 + ½
Simplify 6/9 → 2/3
Now: 2/3 + ½
LCM of 3 and 2 = 6
2/3 = 4/6
½ = 3/6
4/6 + 3/6 =
7/6 or
1 1/6
Keep as
7/6
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✔ All answers checked and verified.
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
Parent Tip: Review the logic above to help your child master the concept of add subtract unlike denominators worksheet.
