Let’s solve each problem one by one. We’re adding mixed numbers — that means we add the whole numbers together and then add the fractions. If the fractions don’t have the same bottom number (denominator), we need to find a common denominator first.
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Problem 1: 4 1/8 + 2 4/5
Step 1: Add whole numbers → 4 + 2 = 6
Step 2: Add fractions → 1/8 + 4/5
Find common denominator of 8 and 5 → it’s 40
Convert: 1/8 = 5/40, 4/5 = 32/40
Add: 5/40 + 32/40 = 37/40
Final answer: 6 37/40
✔ Check: No simplification needed since 37 is prime and doesn’t divide 40.
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Problem 2: 3 1/6 + 7 1/4
Whole numbers: 3 + 7 = 10
Fractions: 1/6 + 1/4 → LCD of 6 and 4 is 12
1/6 = 2/12, 1/4 = 3/12 → 2/12 + 3/12 = 5/12
Final: 10 5/12
✔ Check: 5 and 12 share no common factors → done.
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Problem 3: 5 7/9 + 8 1/3
Whole: 5 + 8 = 13
Fractions: 7/9 + 1/3 → convert 1/3 to 3/9 → 7/9 + 3/9 = 10/9 = 1 1/9
So total: 13 + 1 1/9 = 14 1/9
✔ Check: 10/9 becomes 1 whole and 1/9 left over → correct.
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Problem 4: 9 8/9 + 4 1/5
Whole: 9 + 4 = 13
Fractions: 8/9 + 1/5 → LCD of 9 and 5 is 45
8/9 = 40/45, 1/5 = 9/45 → 40+9=49/45 = 1 4/45
Total: 13 + 1 4/45 = 14 4/45
✔ Check: 49 ÷ 45 = 1 remainder 4 → correct.
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Problem 5: 5 2/3 + 2 4/5
Whole: 5 + 2 = 7
Fractions: 2/3 + 4/5 → LCD = 15
2/3 = 10/15, 4/5 = 12/15 → 10+12=22/15 = 1 7/15
Total: 7 + 1 7/15 = 8 7/15
✔ Check: 22/15 = 1 7/15 → yes.
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Problem 6: 8 7/10 + 8 5/8
Whole: 8 + 8 = 16
Fractions: 7/10 + 5/8 → LCD of 10 and 8 is 40
7/10 = 28/40, 5/8 = 25/40 → 28+25=53/40 = 1 13/40
Total: 16 + 1 13/40 = 17 13/40
✔ Check: 53 - 40 = 13 → correct.
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Problem 7: 11 8/9 + 5 1/4
Whole: 11 + 5 = 16
Fractions: 8/9 + 1/4 → LCD = 36
8/9 = 32/36, 1/4 = 9/36 → 32+9=41/36 = 1 5/36
Total: 16 + 1 5/36 = 17 5/36
✔ Check: 41 - 36 = 5 → correct.
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Problem 8: 7 1/3 + 11 1/2
Whole: 7 + 11 = 18
Fractions: 1/3 + 1/2 → LCD = 6
1/3 = 2/6, 1/2 = 3/6 → 2+3=5/6
Total: 18 5/6
✔ Check: Already simplified → good.
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Problem 9: 15 5/6 + 8 3/8
Whole: 15 + 8 = 23
Fractions: 5/6 + 3/8 → LCD = 24
5/6 = 20/24, 3/8 = 9/24 → 20+9=29/24 = 1 5/24
Total: 23 + 1 5/24 = 24 5/24
✔ Check: 29 - 24 = 5 → correct.
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Problem 10: 12 3/7 + 6 5/6
Whole: 12 + 6 = 18
Fractions: 3/7 + 5/6 → LCD = 42
3/7 = 18/42, 5/6 = 35/42 → 18+35=53/42 = 1 11/42
Total: 18 + 1 11/42 = 19 11/42
✔ Check: 53 - 42 = 11 → correct.
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Final Answer:
1. 6 37/40
2. 10 5/12
3. 14 1/9
4. 14 4/45
5. 8 7/15
6. 17 13/40
7. 17 5/36
8. 18 5/6
9. 24 5/24
10. 19 11/42
Parent Tip: Review the logic above to help your child master the concept of fractions worksheet grade 6.
