Grade 5 Adding and Subtracting Fractions Worksheets | Free Printables - Free Printable

Sure! Let’s solve each of these 12 mixed number addition problems, and then reduce the sum to lowest terms as requested.

We’ll follow this process for each problem:
1. Convert mixed numbers to improper fractions (if needed).
2. Find a common denominator.
3. Add the fractions.
4. Convert back to a mixed number if necessary.
5. Reduce the fractional part to lowest terms.

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Problem 1:

2 5/6 + 1/4

- Convert 2 5/6 → (2×6 + 5)/6 = 17/6
- LCD of 6 and 4 is 12.
- 17/6 = 34/12; 1/4 = 3/12
- Sum: 34/12 + 3/12 = 37/12
- Convert to mixed: 37 ÷ 12 = 3 with remainder 1 → 3 1/12
- Already reduced.

✔ Answer: 3 1/12

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Problem 2:

6 3/5 + 4/5

- 6 3/5 = 33/5
- 4/5 = 4/5
- Same denominator: 33/5 + 4/5 = 37/5
- 37 ÷ 5 = 7 R2 → 7 2/5
- Reduced.

✔ Answer: 7 2/5

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Problem 3:

2 4/6 + 1/3

- First, simplify 4/6 → 2/3
- So 2 4/6 = 2 2/3 = 8/3
- 1/3 = 1/3
- Sum: 8/3 + 1/3 = 9/3 = 3
- Whole number → 3

✔ Answer: 3

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Problem 4:

3 1/5 + 4/10

- Simplify 4/10 → 2/5
- 3 1/5 = 16/5
- 2/5 = 2/5
- Sum: 16/5 + 2/5 = 18/5
- 18 ÷ 5 = 3 R3 → 3 3/5

✔ Answer: 3 3/5

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Problem 5:

8 2/3 + 2/3

- 8 2/3 = 26/3
- 2/3 = 2/3
- Sum: 26/3 + 2/3 = 28/3
- 28 ÷ 3 = 9 R1 → 9 1/3

✔ Answer: 9 1/3

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Problem 6:

7 2/6 + 2/4

- Simplify: 2/6 → 1/3; 2/4 → 1/2
- 7 1/3 = 22/3
- 1/2 = 1/2
- LCD of 3 and 2 is 6
- 22/3 = 44/6; 1/2 = 3/6
- Sum: 44/6 + 3/6 = 47/6
- 47 ÷ 6 = 7 R5 → 7 5/6

✔ Answer: 7 5/6

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Problem 7:

4 1/3 + 2/3

- 4 1/3 = 13/3
- 2/3 = 2/3
- Sum: 13/3 + 2/3 = 15/3 = 5

✔ Answer: 5

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Problem 8:

5 2/4 + 5/6

- Simplify 2/4 → 1/2
- 5 1/2 = 11/2
- 5/6 = 5/6
- LCD of 2 and 6 is 6
- 11/2 = 33/6; 5/6 = 5/6
- Sum: 33/6 + 5/6 = 38/6
- Simplify: divide numerator and denominator by 2 → 19/3
- 19 ÷ 3 = 6 R1 → 6 1/3

✔ Answer: 6 1/3

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Problem 9:

6 1/8 + 3/5

- 6 1/8 = 49/8
- 3/5 = 3/5
- LCD of 8 and 5 is 40
- 49/8 = 245/40; 3/5 = 24/40
- Sum: 245/40 + 24/40 = 269/40
- 269 ÷ 40 = 6 R29 → 6 29/40
- 29 and 40 have no common factors → already reduced.

✔ Answer: 6 29/40

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Problem 10:

6 4/6 + 3/4

- Simplify 4/6 → 2/3
- 6 2/3 = 20/3
- 3/4 = 3/4
- LCD of 3 and 4 is 12
- 20/3 = 80/12; 3/4 = 9/12
- Sum: 80/12 + 9/12 = 89/12
- 89 ÷ 12 = 7 R5 → 7 5/12

✔ Answer: 7 5/12

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Problem 11:

5 1/3 + 7/8

- 5 1/3 = 16/3
- 7/8 = 7/8
- LCD of 3 and 8 is 24
- 16/3 = 128/24; 7/8 = 21/24
- Sum: 128/24 + 21/24 = 149/24
- 149 ÷ 24 = 6 R5 → 6 5/24

✔ Answer: 6 5/24

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Problem 12:

7 2/3 + 9/10

- 7 2/3 = 23/3
- 9/10 = 9/10
- LCD of 3 and 10 is 30
- 23/3 = 230/30; 9/10 = 27/30
- Sum: 230/30 + 27/30 = 257/30
- 257 ÷ 30 = 8 R17 → 8 17/30
- 17 and 30 coprime → reduced.

✔ Answer: 8 17/30

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## ✔ Final Answers:

1. 3 1/12
2. 7 2/5
3. 3
4. 3 3/5
5. 9 1/3
6. 7 5/6
7. 5
8. 6 1/3
9. 6 29/40
10. 7 5/12
11. 6 5/24
12. 8 17/30

All sums are in lowest terms as required.

Let me know if you’d like to see the work written out differently or need help checking your own answers!