6th Grade Fractions Worksheets - Math Monks - Free Printable

Let’s solve each problem step by step. We’ll convert mixed numbers to improper fractions when needed, find common denominators, add or subtract, and then simplify back to mixed numbers if necessary.

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Problem 1: 2 1/8 + 11/3

Convert 2 1/8 → (2×8 + 1)/8 = 17/8
Now: 17/8 + 11/3
LCM of 8 and 3 is 24
17/8 = (17×3)/(8×3) = 51/24
11/3 = (11×8)/(3×8) = 88/24
Add: 51/24 + 88/24 = 139/24
Convert to mixed number: 139 ÷ 24 = 5 with remainder 19 → 5 19/24

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Problem 2: 2 2/4 - 1 1/3

Simplify 2 2/4 → 2 1/2 = (2×2 + 1)/2 = 5/2
1 1/3 = (1×3 + 1)/3 = 4/3
Now: 5/2 - 4/3
LCM of 2 and 3 is 6
5/2 = 15/6, 4/3 = 8/6
Subtract: 15/6 - 8/6 = 7/6 → 1 1/6

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Problem 3: 4/7 + 2 7/14

Simplify 2 7/14 → 2 1/2 = (2×2 + 1)/2 = 5/2
Now: 4/7 + 5/2
LCM of 7 and 2 is 14
4/7 = 8/14, 5/2 = 35/14
Add: 8/14 + 35/14 = 43/14 → 43 ÷ 14 = 3 rem 1 → 3 1/14

Wait — let me double-check that.

Actually, 2 7/14 simplifies to 2 1/2, yes. But maybe we should keep it as 2 7/14 for now? No, better to simplify first.

But 7/14 = 1/2, so 2 1/2 is correct.

4/7 + 5/2 = 8/14 + 35/14 = 43/14 = 3 1/14 ✔

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Problem 4: 4 8/9 - 2 1/6

Convert both to improper fractions:

4 8/9 = (4×9 + 8)/9 = 44/9
2 1/6 = (2×6 + 1)/6 = 13/6
LCM of 9 and 6 is 18
44/9 = 88/18, 13/6 = 39/18
Subtract: 88/18 - 39/18 = 49/18 → 49 ÷ 18 = 2 rem 13 → 2 13/18

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Problem 5: 2/4 + 8 1/5

Simplify 2/4 → 1/2
8 1/5 = (8×5 + 1)/5 = 41/5
Now: 1/2 + 41/5
LCM of 2 and 5 is 10
1/2 = 5/10, 41/5 = 82/10
Add: 5/10 + 82/10 = 87/10 → 8 7/10 → 8 7/10

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Problem 6: 10 1/6 - 5/18

Convert 10 1/6 → (10×6 + 1)/6 = 61/6
Now: 61/6 - 5/18
LCM of 6 and 18 is 18
61/6 = 183/18
Subtract: 183/18 - 5/18 = 178/18
Simplify: divide numerator and denominator by 2 → 89/9
89 ÷ 9 = 9 rem 8 → 9 8/9

Wait — let me check: 178 ÷ 2 = 89, 18 ÷ 2 = 9 → yes. 89/9 = 9 8/9 ✔

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Problem 7: 3/4 + 5 2/6

Simplify 5 2/6 → 5 1/3 = (5×3 + 1)/3 = 16/3
Now: 3/4 + 16/3
LCM of 4 and 3 is 12
3/4 = 9/12, 16/3 = 64/12
Add: 9/12 + 64/12 = 73/12 → 73 ÷ 12 = 6 rem 1 → 6 1/12

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Problem 8: 12 3/8 - 8 2/9

Convert both:

12 3/8 = (12×8 + 3)/8 = 99/8
8 2/9 = (8×9 + 2)/9 = 74/9
LCM of 8 and 9 is 72
99/8 = (99×9)/72 = 891/72
74/9 = (74×8)/72 = 592/72
Subtract: 891 - 592 = 299 → 299/72
Divide: 299 ÷ 72 = 4 rem 11 → 4 11/72

Check: 72×4=288, 299-288=11 → yes.

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Problem 9: 2/8 + 9 3/8

Simplify 2/8 → 1/4, but since denominator matches the other fraction, better to keep as 2/8.

9 3/8 = (9×8 + 3)/8 = 75/8
Now: 2/8 + 75/8 = 77/8 → 77 ÷ 8 = 9 rem 5 → 9 5/8

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Problem 10: 7 2/3 - 2 5/9

Convert:

7 2/3 = (7×3 + 2)/3 = 23/3
2 5/9 = (2×9 + 5)/9 = 23/9
LCM of 3 and 9 is 9
23/3 = 69/9
Subtract: 69/9 - 23/9 = 46/9 → 46 ÷ 9 = 5 rem 1 → 5 1/9

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Problem 11: 7 3/5 + 8 2/7

Convert:

7 3/5 = (7×5 + 3)/5 = 38/5
8 2/7 = (8×7 + 2)/7 = 58/7
LCM of 5 and 7 is 35
38/5 = (38×7)/35 = 266/35
58/7 = (58×5)/35 = 290/35
Add: 266 + 290 = 556 → 556/35
Divide: 556 ÷ 35 = 15 rem 31 → because 35×15=525, 556-525=31 → 15 31/35

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Problem 12: 15 1/6 - 4/15

Convert 15 1/6 → (15×6 + 1)/6 = 91/6
Now: 91/6 - 4/15
LCM of 6 and 15 is 30
91/6 = (91×5)/30 = 455/30
4/15 = (4×2)/30 = 8/30
Subtract: 455 - 8 = 447 → 447/30
Simplify: divide numerator and denominator by 3 → 149/10
149 ÷ 10 = 14 rem 9 → 14 9/10

Wait — let me verify:

447 ÷ 3 = 149, 30 ÷ 3 = 10 → yes. 149/10 = 14 9/10 ✔

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Final Answers:

1. 5 19/24
2. 1 1/6
3. 3 1/14
4. 2 13/18
5. 8 7/10
6. 9 8/9
7. 6 1/12
8. 4 11/72
9. 9 5/8
10. 5 1/9
11. 15 31/35
12. 14 9/10

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Final Answer:
1. 5 19/24
2. 1 1/6
3. 3 1/14
4. 2 13/18
5. 8 7/10
6. 9 8/9
7. 6 1/12
8. 4 11/72
9. 9 5/8
10. 5 1/9
11. 15 31/35
12. 14 9/10