Adding And Subtracting Fractions With Unlike Denominators Worksheets - Free Printable

Let's solve each of these problems step by step. The task is to add mixed numbers with unlike denominators (denominators less than 30). We'll convert the mixed numbers to improper fractions, find a common denominator, add them, and then simplify or convert back to mixed numbers if needed.

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Problem 1: $13\frac{4}{10} + 9\frac{2}{10}$

- Both have the same denominator (10), so we can add directly.
- Add whole numbers: $13 + 9 = 22$
- Add fractions: $\frac{4}{10} + \frac{2}{10} = \frac{6}{10}$
- Simplify $\frac{6}{10} = \frac{3}{5}$
- Final answer: $22\frac{3}{5}$

✔ Answer: $22\frac{3}{5}$

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Problem 2: $1\frac{7}{11} + 2\frac{9}{11}$

- Same denominator (11)
- Whole numbers: $1 + 2 = 3$
- Fractions: $\frac{7}{11} + \frac{9}{11} = \frac{16}{11}$
- $\frac{16}{11} = 1\frac{5}{11}$
- Add to whole number: $3 + 1\frac{5}{11} = 4\frac{5}{11}$

✔ Answer: $4\frac{5}{11}$

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Problem 3: $17\frac{1}{8} + 19\frac{10}{16}$

- Denominators: 8 and 16 → LCM is 16
- Convert $\frac{1}{8} = \frac{2}{16}$
- So $17\frac{1}{8} = 17\frac{2}{16}$
- Now add: $17\frac{2}{16} + 19\frac{10}{16}$
- Whole numbers: $17 + 19 = 36$
- Fractions: $\frac{2}{16} + \frac{10}{16} = \frac{12}{16} = \frac{3}{4}$
- Final answer: $36\frac{3}{4}$

✔ Answer: $36\frac{3}{4}$

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Problem 4: $6\frac{5}{6} + 2\frac{1}{3}$

- Denominators: 6 and 3 → LCM is 6
- Convert $\frac{1}{3} = \frac{2}{6}$
- So $2\frac{1}{3} = 2\frac{2}{6}$
- Add: $6\frac{5}{6} + 2\frac{2}{6}$
- Whole numbers: $6 + 2 = 8$
- Fractions: $\frac{5}{6} + \frac{2}{6} = \frac{7}{6} = 1\frac{1}{6}$
- Add to whole: $8 + 1\frac{1}{6} = 9\frac{1}{6}$

✔ Answer: $9\frac{1}{6}$

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Problem 5: $19\frac{1}{4} + 13\frac{3}{8}$

- Denominators: 4 and 8 → LCM is 8
- Convert $\frac{1}{4} = \frac{2}{8}$
- So $19\frac{1}{4} = 19\frac{2}{8}$
- Add: $19\frac{2}{8} + 13\frac{3}{8}$
- Whole numbers: $19 + 13 = 32$
- Fractions: $\frac{2}{8} + \frac{3}{8} = \frac{5}{8}$
- Final answer: $32\frac{5}{8}$

✔ Answer: $32\frac{5}{8}$

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Problem 6: $1\frac{1}{11} + 4\frac{10}{11}$

- Same denominator (11)
- Whole numbers: $1 + 4 = 5$
- Fractions: $\frac{1}{11} + \frac{10}{11} = \frac{11}{11} = 1$
- Add to whole: $5 + 1 = 6$

✔ Answer: $6$

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Problem 7: $6\frac{1}{6} + 13\frac{10}{12}$

- Denominators: 6 and 12 → LCM is 12
- Convert $\frac{1}{6} = \frac{2}{12}$
- So $6\frac{1}{6} = 6\frac{2}{12}$
- Convert $\frac{10}{12}$ stays as is
- Add: $6\frac{2}{12} + 13\frac{10}{12}$
- Whole numbers: $6 + 13 = 19$
- Fractions: $\frac{2}{12} + \frac{10}{12} = \frac{12}{12} = 1$
- Add to whole: $19 + 1 = 20$

✔ Answer: $20$

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Problem 8: $19\frac{10}{12} + 4\frac{6}{12}$

- Same denominator (12)
- Whole numbers: $19 + 4 = 23$
- Fractions: $\frac{10}{12} + \frac{6}{12} = \frac{16}{12} = 1\frac{4}{12} = 1\frac{1}{3}$
- Add to whole: $23 + 1\frac{1}{3} = 24\frac{1}{3}$

✔ Answer: $24\frac{1}{3}$

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Problem 9: $6\frac{1}{5} + 5\frac{1}{10}$

- Denominators: 5 and 10 → LCM is 10
- Convert $\frac{1}{5} = \frac{2}{10}$
- So $6\frac{1}{5} = 6\frac{2}{10}$
- Add: $6\frac{2}{10} + 5\frac{1}{10}$
- Whole numbers: $6 + 5 = 11$
- Fractions: $\frac{2}{10} + \frac{1}{10} = \frac{3}{10}$
- Final answer: $11\frac{3}{10}$

✔ Answer: $11\frac{3}{10}$

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Problem 10: $4\frac{1}{4} + 1\frac{3}{8}$

- Denominators: 4 and 8 → LCM is 8
- Convert $\frac{1}{4} = \frac{2}{8}$
- So $4\frac{1}{4} = 4\frac{2}{8}$
- Add: $4\frac{2}{8} + 1\frac{3}{8}$
- Whole numbers: $4 + 1 = 5$
- Fractions: $\frac{2}{8} + \frac{3}{8} = \frac{5}{8}$
- Final answer: $5\frac{5}{8}$

✔ Answer: $5\frac{5}{8}$

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✔ Final Answers:

1. $22\frac{3}{5}$
2. $4\frac{5}{11}$
3. $36\frac{3}{4}$
4. $9\frac{1}{6}$
5. $32\frac{5}{8}$
6. $6$
7. $20$
8. $24\frac{1}{3}$
9. $11\frac{3}{10}$
10. $5\frac{5}{8}$

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🔍 Summary Tips:

- Always convert mixed numbers to improper fractions (or work with mixed numbers carefully).
- Find the least common denominator (LCD) when denominators differ.
- Add whole parts and fractional parts separately.
- Simplify fractions and convert improper fractions back to mixed numbers if needed.

Let me know if you'd like this in printable format or with steps shown!