Adding Fractions Worksheet with 10 Practice Problems

To solve these fraction addition problems, we need to find a common denominator for each pair of fractions. Once the denominators are the same, we can add the numerators and simplify if needed.

Let’s go through each one step by step:

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1. 1/2 + 1/4

- Common denominator of 2 and 4 is 4.
- Convert 1/2 → 2/4
- Now: 2/4 + 1/4 = 3/4

✔ Answer: 3/4

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2. 3/7 + 2/9

- Denominators: 7 and 9 → least common denominator is 63
- 3/7 = (3×9)/(7×9) = 27/63
- 2/9 = (2×7)/(9×7) = 14/63
- Add: 27/63 + 14/63 = 41/63
- 41 and 63 have no common factors → already simplified

✔ Answer: 41/63

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3. 3/5 + 1/15

- Denominators: 5 and 15 → LCD is 15
- 3/5 = (3×3)/(5×3) = 9/15
- 1/15 stays as is
- Add: 9/15 + 1/15 = 10/15
- Simplify: divide numerator and denominator by 5 → 2/3

✔ Answer: 2/3

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4. 1/9 + 7/8

- Denominators: 9 and 8 → LCD is 72
- 1/9 = (1×8)/(9×8) = 8/72
- 7/8 = (7×9)/(8×9) = 63/72
- Add: 8/72 + 63/72 = 71/72
- Already simplified

✔ Answer: 71/72

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5. 6/7 + 2/21

- Denominators: 7 and 21 → LCD is 21
- 6/7 = (6×3)/(7×3) = 18/21
- 2/21 stays as is
- Add: 18/21 + 2/21 = 20/21
- Already simplified

✔ Answer: 20/21

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6. 4/6 + 2/10

First, simplify both fractions:
- 4/6 = 2/3
- 2/10 = 1/5

Now add: 2/3 + 1/5

- LCD of 3 and 5 is 15
- 2/3 = 10/15
- 1/5 = 3/15
- Add: 10/15 + 3/15 = 13/15

✔ Answer: 13/15

*(Note: You could also use original denominators — 6 and 10 → LCD 30 — but simplifying first makes it easier.)*

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7. 1/11 + 3/22

- LCD of 11 and 22 is 22
- 1/11 = 2/22
- 3/22 stays
- Add: 2/22 + 3/22 = 5/22

✔ Answer: 5/22

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8. 1/4 + 8/20

Simplify 8/20 → 2/5

Now: 1/4 + 2/5

- LCD of 4 and 5 is 20
- 1/4 = 5/20
- 2/5 = 8/20
- Add: 5/20 + 8/20 = 13/20

✔ Answer: 13/20

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9. 4/7 + 2/9

- LCD of 7 and 9 is 63
- 4/7 = (4×9)/63 = 36/63
- 2/9 = (2×7)/63 = 14/63
- Add: 36/63 + 14/63 = 50/63
- Already simplified

✔ Answer: 50/63

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10. 7/10 + 2/30

Simplify 2/30 → 1/15

Now: 7/10 + 1/15

- LCD of 10 and 15 is 30
- 7/10 = 21/30
- 1/15 = 2/30
- Add: 21/30 + 2/30 = 23/30

✔ Answer: 23/30

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Final Answers:

1. 3/4
2. 41/63
3. 2/3
4. 71/72
5. 20/21
6. 13/15
7. 5/22
8. 13/20
9. 50/63
10. 23/30

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Final Answer:
1. $\frac{3}{4}$
2. $\frac{41}{63}$
3. $\frac{2}{3}$
4. $\frac{71}{72}$
5. $\frac{20}{21}$
6. $\frac{13}{15}$
7. $\frac{5}{22}$
8. $\frac{13}{20}$
9. $\frac{50}{63}$
10. $\frac{23}{30}$