Worksheet for practicing division of fractions with mixed numbers using the inversion method.

You're asked to divide fractions and mixed numbers using the inversion method. The “inversion method” means:
> To divide by a fraction, multiply by its reciprocal (flip the divisor).

Let’s solve each problem step-by-step.

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A. $ 1\frac{1}{8} \div \frac{3}{4} $

Step 1: Convert mixed number to improper fraction.
$ 1\frac{1}{8} = \frac{8 \cdot 1 + 1}{8} = \frac{9}{8} $

Step 2: Invert the divisor ($\frac{3}{4}$ → $\frac{4}{3}$) and multiply:
$ \frac{9}{8} \times \frac{4}{3} $

Step 3: Simplify before multiplying:
- 9 and 3 → divide both by 3: 9÷3=3, 3÷3=1
- 4 and 8 → divide both by 4: 4÷4=1, 8÷4=2
So: $ \frac{3}{2} \times \frac{1}{1} = \frac{3}{2} $

Step 4: Convert to mixed number if needed:
$ \frac{3}{2} = 1\frac{1}{2} $

✔ Answer A: $ \boxed{1\frac{1}{2}} $

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B. $ 2\frac{3}{5} \div \frac{7}{10} $

Step 1: Convert mixed number:
$ 2\frac{3}{5} = \frac{5 \cdot 2 + 3}{5} = \frac{13}{5} $

Step 2: Invert divisor ($\frac{7}{10}$ → $\frac{10}{7}$) and multiply:
$ \frac{13}{5} \times \frac{10}{7} $

Step 3: Simplify:
- 10 and 5 → divide by 5: 10÷5=2, 5÷5=1
So: $ \frac{13}{1} \times \frac{2}{7} = \frac{26}{7} $

Step 4: Convert to mixed number:
$ \frac{26}{7} = 3\frac{5}{7} $ (since 7×3=21, 26−21=5)

✔ Answer B: $ \boxed{3\frac{5}{7}} $

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C. $ 3\frac{4}{9} \div \frac{2}{9} $

Step 1: Convert mixed number:
$ 3\frac{4}{9} = \frac{9 \cdot 3 + 4}{9} = \frac{31}{9} $

Step 2: Invert divisor ($\frac{2}{9}$ → $\frac{9}{2}$) and multiply:
$ \frac{31}{9} \times \frac{9}{2} $

Step 3: Simplify:
- 9 in numerator and denominator cancel out → leaves $ \frac{31}{1} \times \frac{1}{2} = \frac{31}{2} $

Step 4: Convert to mixed number:
$ \frac{31}{2} = 15\frac{1}{2} $

✔ Answer C: $ \boxed{15\frac{1}{2}} $

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D. $ 5\frac{1}{4} \div \frac{7}{8} $

Step 1: Convert mixed number:
$ 5\frac{1}{4} = \frac{4 \cdot 5 + 1}{4} = \frac{21}{4} $

Step 2: Invert divisor ($\frac{7}{8}$ → $\frac{8}{7}$) and multiply:
$ \frac{21}{4} \times \frac{8}{7} $

Step 3: Simplify:
- 21 and 7 → divide by 7: 21÷7=3, 7÷7=1
- 8 and 4 → divide by 4: 8÷4=2, 4÷4=1
So: $ \frac{3}{1} \times \frac{2}{1} = 6 $

✔ Answer D: $ \boxed{6} $

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E. $ \frac{10}{11} \div 5 $

Step 1: Write 5 as a fraction: $ 5 = \frac{5}{1} $

Step 2: Invert divisor ($\frac{5}{1}$ → $\frac{1}{5}$) and multiply:
$ \frac{10}{11} \times \frac{1}{5} $

Step 3: Simplify:
- 10 and 5 → divide by 5: 10÷5=2, 5÷5=1
So: $ \frac{2}{11} \times \frac{1}{1} = \frac{2}{11} $

✔ Answer E: $ \boxed{\frac{2}{11}} $

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## ✔ Final Answers:

A. $ \boxed{1\frac{1}{2}} $
B. $ \boxed{3\frac{5}{7}} $
C. $ \boxed{15\frac{1}{2}} $
D. $ \boxed{6} $
E. $ \boxed{\frac{2}{11}} $

Let me know if you’d like to see visual diagrams or further explanation!