Adding Mixed Numbers: A math worksheet with 14 problems to practice adding mixed fractions.

Let’s solve each problem step by step. We’ll add the whole numbers first, then add the fractions. If the fraction part adds up to more than 1, we’ll convert it to a mixed number and add the whole number part to the total.

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Problem 1:
4 3/6 + 2 2/8
→ Whole numbers: 4 + 2 = 6
→ Fractions: 3/6 + 2/8
Simplify: 3/6 = 1/2, 2/8 = 1/4
Find common denominator for 1/2 and 1/4 → LCD is 4
1/2 = 2/4, so 2/4 + 1/4 = 3/4
Total: 6 + 3/4 = 6 3/4

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Problem 2:
5 1/5 + 2 2/4
→ Whole numbers: 5 + 2 = 7
→ Fractions: 1/5 + 2/4 = 1/5 + 1/2
LCD of 5 and 2 is 10
1/5 = 2/10, 1/2 = 5/10 → 2/10 + 5/10 = 7/10
Total: 7 + 7/10 = 7 7/10

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Problem 3:
4 6/7 + 5 3/5
→ Whole numbers: 4 + 5 = 9
→ Fractions: 6/7 + 3/5
LCD of 7 and 5 is 35
6/7 = 30/35, 3/5 = 21/35 → 30+21=51/35 = 1 16/35
Add to whole: 9 + 1 = 10, plus 16/35 → 10 16/35

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Problem 4:
2 5/10 + 3 2/5
→ Simplify 5/10 = 1/2
→ Whole numbers: 2 + 3 = 5
→ Fractions: 1/2 + 2/5
LCD of 2 and 5 is 10
1/2 = 5/10, 2/5 = 4/10 → 5+4=9/10
Total: 5 + 9/10 = 5 9/10

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Problem 5:
5 1/5 + 2 3/7
→ Whole numbers: 5 + 2 = 7
→ Fractions: 1/5 + 3/7
LCD of 5 and 7 is 35
1/5 = 7/35, 3/7 = 15/35 → 7+15=22/35
Total: 7 + 22/35 = 7 22/35

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Problem 6:
4 2/12 + 2 3/8
→ Simplify 2/12 = 1/6
→ Whole numbers: 4 + 2 = 6
→ Fractions: 1/6 + 3/8
LCD of 6 and 8 is 24
1/6 = 4/24, 3/8 = 9/24 → 4+9=13/24
Total: 6 + 13/24 = 6 13/24

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Problem 7:
7 1/9 + 5 2/6
→ Simplify 2/6 = 1/3
→ Whole numbers: 7 + 5 = 12
→ Fractions: 1/9 + 1/3
LCD of 9 and 3 is 9
1/3 = 3/9 → 1/9 + 3/9 = 4/9
Total: 12 + 4/9 = 12 4/9

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Problem 8:
5 4/7 + 1 3/4
→ Whole numbers: 5 + 1 = 6
→ Fractions: 4/7 + 3/4
LCD of 7 and 4 is 28
4/7 = 16/28, 3/4 = 21/28 → 16+21=37/28 = 1 9/28
Add to whole: 6 + 1 = 7, plus 9/28 → 7 9/28

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Problem 9:
2 6/9 + 2 5/8
→ Simplify 6/9 = 2/3
→ Whole numbers: 2 + 2 = 4
→ Fractions: 2/3 + 5/8
LCD of 3 and 8 is 24
2/3 = 16/24, 5/8 = 15/24 → 16+15=31/24 = 1 7/24
Add to whole: 4 + 1 = 5, plus 7/24 → 5 7/24

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Problem 10:
5 8/10 + 1 2/6
→ Simplify: 8/10 = 4/5, 2/6 = 1/3
→ Whole numbers: 5 + 1 = 6
→ Fractions: 4/5 + 1/3
LCD of 5 and 3 is 15
4/5 = 12/15, 1/3 = 5/15 → 12+5=17/15 = 1 2/15
Add to whole: 6 + 1 = 7, plus 2/15 → 7 2/15

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Problem 11:
4 2/7 + 2 5/9
→ Whole numbers: 4 + 2 = 6
→ Fractions: 2/7 + 5/9
LCD of 7 and 9 is 63
2/7 = 18/63, 5/9 = 35/63 → 18+35=53/63
Total: 6 + 53/63 = 6 53/63

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Problem 12:
2 4/8 + 2 7/9
→ Simplify 4/8 = 1/2
→ Whole numbers: 2 + 2 = 4
→ Fractions: 1/2 + 7/9
LCD of 2 and 9 is 18
1/2 = 9/18, 7/9 = 14/18 → 9+14=23/18 = 1 5/18
Add to whole: 4 + 1 = 5, plus 5/18 → 5 5/18

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Problem 13:
3 2/5 + 4 4/6
→ Simplify 4/6 = 2/3
→ Whole numbers: 3 + 4 = 7
→ Fractions: 2/5 + 2/3
LCD of 5 and 3 is 15
2/5 = 6/15, 2/3 = 10/15 → 6+10=16/15 = 1 1/15
Add to whole: 7 + 1 = 8, plus 1/15 → 8 1/15

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Problem 14:
4 1/7 + 1 2/6
→ Simplify 2/6 = 1/3
→ Whole numbers: 4 + 1 = 5
→ Fractions: 1/7 + 1/3
LCD of 7 and 3 is 21
1/7 = 3/21, 1/3 = 7/21 → 3+7=10/21
Total: 5 + 10/21 = 5 10/21

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Final Answer:
1. 6 3/4
2. 7 7/10
3. 10 16/35
4. 5 9/10
5. 7 22/35
6. 6 13/24
7. 12 4/9
8. 7 9/28
9. 5 7/24
10. 7 2/15
11. 6 53/63
12. 5 5/18
13. 8 1/15
14. 5 10/21