Math worksheet for practicing division of fractions by mixed numbers, featuring ten problems with step-by-step solutions.

Let's solve each problem step by step. The key concept here is dividing a fraction by a mixed number.

🔁 General Rule:

To divide a fraction by a mixed number:

1. Convert the mixed number to an improper fraction.
2. Change the division into multiplication by taking the reciprocal of the second fraction.
3. Multiply the fractions.
4. Simplify the result and convert to a mixed number if needed.

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Let’s go through each problem.

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① $ \frac{13}{12} \div 1\frac{3}{8} $

Step 1: Convert $ 1\frac{3}{8} $ to improper fraction
$ 1\frac{3}{8} = \frac{8 \times 1 + 3}{8} = \frac{11}{8} $

Step 2: Change division to multiplication by reciprocal
$ \frac{13}{12} \div \frac{11}{8} = \frac{13}{12} \times \frac{8}{11} $

Step 3: Multiply
$ \frac{13 \times 8}{12 \times 11} = \frac{104}{132} $

Step 4: Simplify
Divide numerator and denominator by 4:
$ \frac{104 \div 4}{132 \div 4} = \frac{26}{33} $

✔ Answer: $ \boxed{\frac{26}{33}} $

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② $ \frac{2}{9} \div 3\frac{1}{3} $

Step 1: Convert $ 3\frac{1}{3} $
$ 3\frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{10}{3} $

Step 2: $ \frac{2}{9} \div \frac{10}{3} = \frac{2}{9} \times \frac{3}{10} $

Step 3: Multiply
$ \frac{2 \times 3}{9 \times 10} = \frac{6}{90} $

Step 4: Simplify
$ \frac{6}{90} = \frac{1}{15} $

✔ Answer: $ \boxed{\frac{1}{15}} $

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③ $ \frac{3}{8} \div 2\frac{2}{4} $

Step 1: Simplify $ 2\frac{2}{4} $ → $ 2\frac{1}{2} $ (since $ \frac{2}{4} = \frac{1}{2} $)
Now convert: $ 2\frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{5}{2} $

Step 2: $ \frac{3}{8} \div \frac{5}{2} = \frac{3}{8} \times \frac{2}{5} $

Step 3: Multiply
$ \frac{3 \times 2}{8 \times 5} = \frac{6}{40} $

Step 4: Simplify
$ \frac{6}{40} = \frac{3}{20} $

✔ Answer: $ \boxed{\frac{3}{20}} $

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④ $ \frac{3}{12} \div 2\frac{1}{3} $

Step 1: Simplify $ \frac{3}{12} = \frac{1}{4} $
Convert $ 2\frac{1}{3} = \frac{7}{3} $

Step 2: $ \frac{1}{4} \div \frac{7}{3} = \frac{1}{4} \times \frac{3}{7} = \frac{3}{28} $

✔ Answer: $ \boxed{\frac{3}{28}} $

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⑤ $ \frac{5}{6} \div 2\frac{2}{3} $

Step 1: Convert $ 2\frac{2}{3} = \frac{8}{3} $

Step 2: $ \frac{5}{6} \div \frac{8}{3} = \frac{5}{6} \times \frac{3}{8} $

Step 3: Multiply
$ \frac{5 \times 3}{6 \times 8} = \frac{15}{48} $

Step 4: Simplify
$ \frac{15}{48} = \frac{5}{16} $

✔ Answer: $ \boxed{\frac{5}{16}} $

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⑥ $ \frac{5}{2} \div 4\frac{3}{4} $

Step 1: Convert $ 4\frac{3}{4} = \frac{19}{4} $

Step 2: $ \frac{5}{2} \div \frac{19}{4} = \frac{5}{2} \times \frac{4}{19} $

Step 3: Multiply
$ \frac{5 \times 4}{2 \times 19} = \frac{20}{38} $

Step 4: Simplify
$ \frac{20}{38} = \frac{10}{19} $

✔ Answer: $ \boxed{\frac{10}{19}} $

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⑦ $ \frac{6}{10} \div 4\frac{1}{2} $

Step 1: Simplify $ \frac{6}{10} = \frac{3}{5} $
Convert $ 4\frac{1}{2} = \frac{9}{2} $

Step 2: $ \frac{3}{5} \div \frac{9}{2} = \frac{3}{5} \times \frac{2}{9} = \frac{6}{45} $

Step 3: Simplify
$ \frac{6}{45} = \frac{2}{15} $

✔ Answer: $ \boxed{\frac{2}{15}} $

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⑧ $ \frac{5}{8} \div 7\frac{3}{4} $

Step 1: Convert $ 7\frac{3}{4} = \frac{31}{4} $

Step 2: $ \frac{5}{8} \div \frac{31}{4} = \frac{5}{8} \times \frac{4}{31} $

Step 3: Multiply
$ \frac{5 \times 4}{8 \times 31} = \frac{20}{248} $

Step 4: Simplify
Divide numerator and denominator by 4:
$ \frac{20 \div 4}{248 \div 4} = \frac{5}{62} $

✔ Answer: $ \boxed{\frac{5}{62}} $

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⑨ $ \frac{4}{6} \div 4\frac{1}{3} $

Step 1: Simplify $ \frac{4}{6} = \frac{2}{3} $
Convert $ 4\frac{1}{3} = \frac{13}{3} $

Step 2: $ \frac{2}{3} \div \frac{13}{3} = \frac{2}{3} \times \frac{3}{13} $

Step 3: Multiply
$ \frac{2 \times 3}{3 \times 13} = \frac{6}{39} $

Step 4: Simplify
$ \frac{6}{39} = \frac{2}{13} $

✔ Answer: $ \boxed{\frac{2}{13}} $

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⑩ $ \frac{7}{10} \div 3\frac{4}{5} $

Step 1: Convert $ 3\frac{4}{5} = \frac{19}{5} $

Step 2: $ \frac{7}{10} \div \frac{19}{5} = \frac{7}{10} \times \frac{5}{19} $

Step 3: Multiply
$ \frac{7 \times 5}{10 \times 19} = \frac{35}{190} $

Step 4: Simplify
Divide numerator and denominator by 5:
$ \frac{35 \div 5}{190 \div 5} = \frac{7}{38} $

✔ Answer: $ \boxed{\frac{7}{38}} $

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✔ Final Answers:

1. $ \frac{26}{33} $
2. $ \frac{1}{15} $
3. $ \frac{3}{20} $
4. $ \frac{3}{28} $
5. $ \frac{5}{16} $
6. $ \frac{10}{19} $
7. $ \frac{2}{15} $
8. $ \frac{5}{62} $
9. $ \frac{2}{13} $
10. $ \frac{7}{38} $

Let me know if you'd like these as decimals or visual models!