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. Then convert each fraction, add them, and simplify if needed.
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1) 2/5 + 5/10
- LCM of 5 and 10 is 10.
- Convert 2/5 → 4/10
- 4/10 + 5/10 = 9/10
✔
2) 4/9 + 3/12
- LCM of 9 and 12 is 36.
- 4/9 = 16/36; 3/12 = 9/36
- 16/36 + 9/36 = 25/36
✔
3) 1/4 + 3/5
- LCM of 4 and 5 is 20.
- 1/4 = 5/20; 3/5 = 12/20
- 5/20 + 12/20 = 17/20
✔
4) 2/5 + 1/3
- LCM of 5 and 3 is 15.
- 2/5 = 6/15; 1/3 = 5/15
- 6/15 + 5/15 = 11/15
✔
5) 2/5 + 3/10
- LCM of 5 and 10 is 10.
- 2/5 = 4/10
- 4/10 + 3/10 = 7/10
✔
6) 5/14 + 3/7
- LCM of 14 and 7 is 14.
- 3/7 = 6/14
- 5/14 + 6/14 = 11/14
✔
7) 5/9 + 1/3
- LCM of 9 and 3 is 9.
- 1/3 = 3/9
- 5/9 + 3/9 = 8/9
✔
8) 1/6 + 2/9
- LCM of 6 and 9 is 18.
- 1/6 = 3/18; 2/9 = 4/18
- 3/18 + 4/18 = 7/18
✔
9) 5/15 + 3/5
- Simplify 5/15 → 1/3
- LCM of 3 and 5 is 15.
- 1/3 = 5/15; 3/5 = 9/15
- 5/15 + 9/15 = 14/15
✔
*(Alternatively: 5/15 + 9/15 = 14/15)*
10) 3/9 + 1/5
- Simplify 3/9 → 1/3
- LCM of 3 and 5 is 15.
- 1/3 = 5/15; 1/5 = 3/15
- 5/15 + 3/15 = 8/15
✔
11) 4/10 + 7/20
- Simplify 4/10 → 2/5
- LCM of 5 and 20 is 20.
- 2/5 = 8/20
- 8/20 + 7/20 = 15/20 → simplify to 3/4
✔
*(Or directly: 4/10 = 8/20 → 8+7=15 → 15/20 = 3/4)*
12) 3/10 + 2/15
- LCM of 10 and 15 is 30.
- 3/10 = 9/30; 2/15 = 4/30
- 9/30 + 4/30 = 13/30
✔
13) 6/15 + 3/20
- Simplify 6/15 → 2/5
- LCM of 5 and 20 is 20.
- 2/5 = 8/20
- 8/20 + 3/20 = 11/20
✔
*(Directly: 6/15 = 8/20? Wait — let's recalculate properly:
6/15 = ? / 60? Better use LCM of 15 and 20 = 60.
6/15 = 24/60; 3/20 = 9/60 → 24+9=33/60 = 11/20
✔ Same answer.)*
14) 1/4 + 4/10
- Simplify 4/10 → 2/5
- LCM of 4 and 5 is 20.
- 1/4 = 5/20; 2/5 = 8/20
- 5/20 + 8/20 = 13/20
✔
*(Direct: 1/4 = 5/20; 4/10 = 8/20 → same)*
15) 3/15 + 7/12
- Simplify 3/15 → 1/5
- LCM of 5 and 12 is 60.
- 1/5 = 12/60; 7/12 = 35/60
- 12/60 + 35/60 = 47/60
✔
16) 4/15 + 3/25
- LCM of 15 and 25 is 75.
- 4/15 = 20/75; 3/25 = 9/75
- 20/75 + 9/75 = 29/75
✔
17) 4/10 + 7/15
- Simplify 4/10 → 2/5
- LCM of 5 and 15 is 15.
- 2/5 = 6/15
- 6/15 + 7/15 = 13/15
✔
*(Direct: 4/10 = 6/15? 4/10 = 12/30; 7/15 = 14/30 → 26/30 = 13/15
✔)*
18) 3/10 + 2/15
- LCM of 10 and 15 is 30.
- 3/10 = 9/30; 2/15 = 4/30
- 9/30 + 4/30 = 13/30
✔
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Final Answer:
1) 9/10
2) 25/36
3) 17/20
4) 11/15
5) 7/10
6) 11/14
7) 8/9
8) 7/18
9) 14/15
10) 8/15
11) 3/4
12) 13/30
13) 11/20
14) 13/20
15) 47/60
16) 29/75
17) 13/15
18) 13/30
Parent Tip: Review the logic above to help your child master the concept of subtract fractions with unlike denominators worksheet.
