Mixed multiplication of fractions worksheets - Math Worksheets ... - Free Printable

Let's solve each of these multiplication problems step by step. The worksheet involves multiplying mixed numbers (a whole number and a fraction) by whole numbers. We’ll convert the mixed numbers to improper fractions, multiply, and then simplify or convert back to mixed numbers as needed.

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General Steps:

1. Convert the mixed number to an improper fraction.
2. Multiply the improper fraction by the whole number.
3. Simplify the result and convert back to a mixed number if necessary.

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Problem 1: $ 3\frac{1}{2} \times 8 $

- $ 3\frac{1}{2} = \frac{7}{2} $
- $ \frac{7}{2} \times 8 = \frac{7 \times 8}{2} = \frac{56}{2} = 28 $

✔ Answer: 28

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Problem 2: $ 10\frac{3}{9} \times 4 $

- First, simplify $ \frac{3}{9} = \frac{1}{3} $, so $ 10\frac{3}{9} = 10\frac{1}{3} $
- $ 10\frac{1}{3} = \frac{31}{3} $
- $ \frac{31}{3} \times 4 = \frac{124}{3} $
- $ \frac{124}{3} = 41\frac{1}{3} $

✔ Answer: $ 41\frac{1}{3} $

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Problem 3: $ 6\frac{7}{12} \times 6 $

- $ 6\frac{7}{12} = \frac{79}{12} $
- $ \frac{79}{12} \times 6 = \frac{79 \times 6}{12} = \frac{474}{12} $
- Simplify: $ \frac{474 \div 6}{12 \div 6} = \frac{79}{2} = 39\frac{1}{2} $

✔ Answer: $ 39\frac{1}{2} $

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Problem 4: $ 4\frac{2}{3} \times 7 $

- $ 4\frac{2}{3} = \frac{14}{3} $
- $ \frac{14}{3} \times 7 = \frac{98}{3} = 32\frac{2}{3} $

✔ Answer: $ 32\frac{2}{3} $

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Problem 5: $ 10\frac{4}{11} \times 6 $

- $ 10\frac{4}{11} = \frac{114}{11} $
- $ \frac{114}{11} \times 6 = \frac{684}{11} $
- $ \frac{684}{11} = 62\frac{2}{11} $ (since $ 11 \times 62 = 682 $, remainder 2)

✔ Answer: $ 62\frac{2}{11} $

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Problem 6: $ 4\frac{6}{10} \times 6 $

- Simplify $ \frac{6}{10} = \frac{3}{5} $, so $ 4\frac{3}{5} = \frac{23}{5} $
- $ \frac{23}{5} \times 6 = \frac{138}{5} = 27\frac{3}{5} $

✔ Answer: $ 27\frac{3}{5} $

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Problem 7: $ 10\frac{7}{8} \times 6 $

- $ 10\frac{7}{8} = \frac{87}{8} $
- $ \frac{87}{8} \times 6 = \frac{522}{8} = \frac{261}{4} = 65\frac{1}{4} $

✔ Answer: $ 65\frac{1}{4} $

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Problem 8: $ 6\frac{1}{2} \times 12 $

- $ 6\frac{1}{2} = \frac{13}{2} $
- $ \frac{13}{2} \times 12 = \frac{156}{2} = 78 $

✔ Answer: 78

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Problem 9: $ 6\frac{9}{12} \times 10 $

- Simplify $ \frac{9}{12} = \frac{3}{4} $, so $ 6\frac{3}{4} = \frac{27}{4} $
- $ \frac{27}{4} \times 10 = \frac{270}{4} = \frac{135}{2} = 67\frac{1}{2} $

✔ Answer: $ 67\frac{1}{2} $

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Problem 10: $ 10\frac{1}{2} \times 12 $

- $ 10\frac{1}{2} = \frac{21}{2} $
- $ \frac{21}{2} \times 12 = \frac{252}{2} = 126 $

✔ Answer: 126

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Problem 11: $ 3\frac{6}{8} \times 6 $

- Simplify $ \frac{6}{8} = \frac{3}{4} $, so $ 3\frac{3}{4} = \frac{15}{4} $
- $ \frac{15}{4} \times 6 = \frac{90}{4} = \frac{45}{2} = 22\frac{1}{2} $

✔ Answer: $ 22\frac{1}{2} $

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Problem 12: $ 7\frac{1}{2} \times 6 $

- $ 7\frac{1}{2} = \frac{15}{2} $
- $ \frac{15}{2} \times 6 = \frac{90}{2} = 45 $

✔ Answer: 45

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Problem 13: $ 1\frac{1}{9} \times 11 $

- $ 1\frac{1}{9} = \frac{10}{9} $
- $ \frac{10}{9} \times 11 = \frac{110}{9} = 12\frac{2}{9} $

✔ Answer: $ 12\frac{2}{9} $

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Problem 14: $ 5\frac{6}{11} \times 11 $

- $ 5\frac{6}{11} = \frac{61}{11} $
- $ \frac{61}{11} \times 11 = 61 $

✔ Answer: 61

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Problem 15: $ 4\frac{1}{8} \times 6 $

- $ 4\frac{1}{8} = \frac{33}{8} $
- $ \frac{33}{8} \times 6 = \frac{198}{8} = \frac{99}{4} = 24\frac{3}{4} $

✔ Answer: $ 24\frac{3}{4} $

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Problem 16: $ 18 \times 28 $

- $ 18 \times 28 = (20 - 2) \times 28 = 20 \times 28 - 2 \times 28 = 560 - 56 = 504 $

✔ Answer: 504

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Problem 17: $ 11 \times 22 $

- $ 11 \times 22 = 242 $

✔ Answer: 242

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Problem 18: $ 9 \times 3 $

- $ 9 \times 3 = 27 $

✔ Answer: 27

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✔ Final Answers:

1. $ 28 $
2. $ 41\frac{1}{3} $
3. $ 39\frac{1}{2} $
4. $ 32\frac{2}{3} $
5. $ 62\frac{2}{11} $
6. $ 27\frac{3}{5} $
7. $ 65\frac{1}{4} $
8. $ 78 $
9. $ 67\frac{1}{2} $
10. $ 126 $
11. $ 22\frac{1}{2} $
12. $ 45 $
13. $ 12\frac{2}{9} $
14. $ 61 $
15. $ 24\frac{3}{4} $
16. $ 504 $
17. $ 242 $
18. $ 27 $

Let me know if you'd like this in a printable format or with explanations for any specific problem!