Let’s solve each problem step by step. We’re adding fractions with different denominators, so we need to find a common denominator first — usually the least common multiple (LCM) of the two denominators.
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1. 3/5 + 1/10
- Denominators: 5 and 10 → LCM is 10
- Convert 3/5 to tenths: multiply numerator and denominator by 2 → 6/10
- Now add: 6/10 + 1/10 = 7/10
✔ Answer:
7/10
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2. 1/4 + 1/2
- Denominators: 4 and 2 → LCM is 4
- Convert 1/2 to fourths: multiply by 2 → 2/4
- Add: 1/4 + 2/4 = 3/4
✔ Answer:
3/4
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3. 2/5 + 4/15
- Denominators: 5 and 15 → LCM is 15
- Convert 2/5 to fifteenths: multiply by 3 → 6/15
- Add: 6/15 + 4/15 = 10/15 → simplify by dividing top and bottom by 5 → 2/3
✔ Answer:
2/3
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4. 3/7 + 1/14
- Denominators: 7 and 14 → LCM is 14
- Convert 3/7 to fourteenths: multiply by 2 → 6/14
- Add: 6/14 + 1/14 = 7/14 → simplify → 1/2
✔ Answer:
1/2
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5. 2/3 + 2/9
- Denominators: 3 and 9 → LCM is 9
- Convert 2/3 to ninths: multiply by 3 → 6/9
- Add: 6/9 + 2/9 = 8/9
✔ Answer:
8/9
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6. 4/5 + 3/20
- Denominators: 5 and 20 → LCM is 20
- Convert 4/5 to twentieths: multiply by 4 → 16/20
- Add: 16/20 + 3/20 = 19/20
✔ Answer:
19/20
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7. 1/4 + 1/8
- Denominators: 4 and 8 → LCM is 8
- Convert 1/4 to eighths: multiply by 2 → 2/8
- Add: 2/8 + 1/8 = 3/8
✔ Answer:
3/8
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8. 1/9 + 1/18
- Denominators: 9 and 18 → LCM is 18
- Convert 1/9 to eighteenths: multiply by 2 → 2/18
- Add: 2/18 + 1/18 = 3/18 → simplify → 1/6
✔ Answer:
1/6
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9. 3/4 + 1/12
- Denominators: 4 and 12 → LCM is 12
- Convert 3/4 to twelfths: multiply by 3 → 9/12
- Add: 9/12 + 1/12 = 10/12 → simplify → 5/6
✔ Answer:
5/6
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10. 3/6 + 1/3
- First, simplify 3/6 → 1/2
- Now: 1/2 + 1/3
- Denominators: 2 and 3 → LCM is 6
- Convert: 1/2 = 3/6, 1/3 = 2/6
- Add: 3/6 + 2/6 = 5/6
✔ Answer:
5/6
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Final Answer:
1. 7/10
2. 3/4
3. 2/3
4. 1/2
5. 8/9
6. 19/20
7. 3/8
8. 1/6
9. 5/6
10. 5/6
Parent Tip: Review the logic above to help your child master the concept of adding fractions different denominators worksheet.
