Grade 6 Adding Fractions with Unlike Denominators Worksheets 2024 - Free Printable

Let's solve the problem step by step.

The task is to add mixed numbers and fractions with unlike denominators. We'll go through each problem, convert mixed numbers to improper fractions if needed, find a common denominator, add the fractions, and simplify the result.

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Problem 1:

4⅖ + ⅔

- Convert 4⅖ to an improper fraction:
$ 4 \frac{2}{5} = \frac{4 \times 5 + 2}{5} = \frac{20 + 2}{5} = \frac{22}{5} $

- Now add $ \frac{22}{5} + \frac{1}{3} $

- Find the least common denominator (LCD) of 5 and 3 → 15

- Convert both fractions:
- $ \frac{22}{5} = \frac{22 \times 3}{5 \times 3} = \frac{66}{15} $
- $ \frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15} $

- Add: $ \frac{66}{15} + \frac{5}{15} = \frac{71}{15} $

- Convert back to mixed number:
$ \frac{71}{15} = 4 \frac{11}{15} $

✔ Answer: 4⅞? Wait — let’s check:
Wait! 71 ÷ 15 = 4 × 15 = 60 → remainder 11 → yes, $ 4\frac{11}{15} $

So: 4⅖ + ⅔ = 4⅛? No — it's 4¹¹⁄₁₅

Wait — I made a typo in my thought process. Let me fix:

✔ Answer: 4¹¹⁄₁₅

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Problem 2:

8½ + ⅓

- 8½ = $ \frac{17}{2} $

- $ \frac{17}{2} + \frac{1}{3} $

- LCD of 2 and 3 = 6

- $ \frac{17}{2} = \frac{51}{6}, \quad \frac{1}{3} = \frac{2}{6} $

- $ \frac{51}{6} + \frac{2}{6} = \frac{53}{6} $

- $ \frac{53}{6} = 8\frac{5}{6} $

✔ Answer: 8⅚

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Problem 3:

3⅕ + ⅖

- 3⅕ = $ \frac{16}{5} $

- $ \frac{16}{5} + \frac{2}{5} = \frac{18}{5} = 3\frac{3}{5} $

✔ Answer: 3⅗

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Problem 4:

1⅔ + ⅔

- 1⅔ = $ \frac{5}{3} $

- $ \frac{5}{3} + \frac{2}{3} = \frac{7}{3} = 2\frac{1}{3} $

✔ Answer: 2⅓

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Problem 5:

7⅕ + ¼

- 7⅕ = $ \frac{36}{5} $

- $ \frac{36}{5} + \frac{1}{4} $

- LCD of 5 and 4 = 20

- $ \frac{36}{5} = \frac{144}{20}, \quad \frac{1}{4} = \frac{5}{20} $

- $ \frac{144}{20} + \frac{5}{20} = \frac{149}{20} = 7\frac{9}{20} $

✔ Answer: 7⁹⁄₂₀

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Problem 6:

5⅜ + ⅜

- 5⅜ = $ \frac{43}{8} $

- $ \frac{43}{8} + \frac{3}{8} = \frac{46}{8} = \frac{23}{4} = 5\frac{3}{4} $

✔ Answer: 5¾

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Problem 7:

8⅓ + ⅙

- 8⅓ = $ \frac{25}{3} $

- $ \frac{25}{3} + \frac{1}{6} $

- LCD of 3 and 6 = 6

- $ \frac{25}{3} = \frac{50}{6}, \quad \frac{1}{6} = \frac{1}{6} $

- $ \frac{50}{6} + \frac{1}{6} = \frac{51}{6} = \frac{17}{2} = 8\frac{1}{2} $

✔ Answer: 8½

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Problem 8:

6⅝ + ⅛

- 6⅝ = $ \frac{53}{8} $

- $ \frac{53}{8} + \frac{1}{8} = \frac{54}{8} = \frac{27}{4} = 6\frac{3}{4} $

✔ Answer: 6¾

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Problem 9:

7⅘ + ⅘

- 7⅘ = $ \frac{39}{5} $

- $ \frac{39}{5} + \frac{4}{5} = \frac{43}{5} = 8\frac{3}{5} $

✔ Answer: 8⅗

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Problem 10:

8⅕ + ⅕

- 8⅕ = $ \frac{41}{5} $

- $ \frac{41}{5} + \frac{1}{5} = \frac{42}{5} = 8\frac{2}{5} $

✔ Answer: 8⅖

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Problem 11:

5⅓ + ⅔

- 5⅓ = $ \frac{16}{3} $

- $ \frac{16}{3} + \frac{2}{3} = \frac{18}{3} = 6 $

✔ Answer: 6

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Problem 12:

9⅙ + ⅙

- 9⅙ = $ \frac{55}{6} $

- $ \frac{55}{6} + \frac{1}{6} = \frac{56}{6} = \frac{28}{3} = 9\frac{1}{3} $

✔ Answer: 9⅓

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Problem 13:

3⅜ + ⅜

- 3⅜ = $ \frac{29}{8} $

- $ \frac{29}{8} + \frac{3}{8} = \frac{32}{8} = 4 $

✔ Answer: 4

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Final Answers:

| Problem | Answer |
|--------|--------|
| 1. 4⅖ + ⅔ | 4¹¹⁄₁₅ |
| 2. 8½ + ⅓ | 8⅚ |
| 3. 3⅕ + ⅖ | 3⅗ |
| 4. 1⅔ + ⅔ | 2⅓ |
| 5. 7⅕ + ¼ | 7⁹⁄₂₀ |
| 6. 5⅜ + ⅜ | 5¾ |
| 7. 8⅓ + ⅙ | 8½ |
| 8. 6⅝ + ⅛ | 6¾ |
| 9. 7⅘ + ⅘ | 8⅗ |
| 10. 8⅕ + ⅕ | 8⅖ |
| 11. 5⅓ + ⅔ | 6 |
| 12. 9⅙ + ⅙ | 9⅓ |
| 13. 3⅜ + ⅜ | 4 |

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Summary of Steps:

1. Convert mixed numbers to improper fractions.
2. Find the least common denominator (LCD).
3. Convert fractions to equivalent fractions with the LCD.
4. Add the numerators.
5. Simplify the result and convert back to a mixed number if needed.

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