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Solution Steps

1. Understand the question

   Turn 1 Question

   dividing fractions
   solve each problem by using a common denominator to divide the fractions.
   show your work.
   ① $\frac{6}{8}div\frac{1}{4}$ ② $\frac{7}{9}div\frac{1}{3}$ ③ $1\frac{1}{2}div\frac{3}{16}$

   ④ $1\frac{2}{3}div\frac{3}{16}$ ⑤ $2\frac{3}{4}div1\frac{3}{8}$ ⑥ $3\frac{1}{4}div1\frac{3}{8}$

   ⑦ choose one problem. check your answer by solving it using a different strategy.

   Turn 2 Question

   number the answers

2. Response

   Turn 1 Answer

3. Explanation

   ---

   Problem 1: $\frac{6}{9} \div \frac{1}{3}$

   Step1: Find common denominator

   Common denominator of 9 and 3 is 9. Rewrite $\frac{1}{3}$ as $\frac{3}{9}$.

   Step2: Divide numerators

   $\frac{6}{9} \div \frac{3}{9} = \frac{6}{3} = 2$
   ---

   Problem 2: $\frac{7}{9} \div \frac{1}{3}$

   Step1: Find common denominator

   Common denominator of 9 and 3 is 9. Rewrite $\frac{1}{3}$ as $\frac{3}{9}$.

   Step2: Divide numerators

   $\frac{7}{9} \div \frac{3}{9} = \frac{7}{3} = 2\frac{1}{3}$
   ---

   Problem 3: $1\frac{1}{5} \div \frac{3}{10}$

   Step1: Convert mixed number to fraction

   $1\frac{1}{5} = \frac{6}{5}$

   Step2: Find common denominator

   Common denominator of 5 and 10 is 10. Rewrite $\frac{6}{5}$ as $\frac{12}{10}$.

   Step3: Divide numerators

   $\frac{12}{10} \div \frac{3}{10} = \frac{12}{3} = 4$
   Correction: $1\frac{1}{5} = \frac{6}{5} = \frac{12}{10}$, $\frac{12}{3}=4$ → Final answer $4$
   ---

   Problem 4: $1\frac{2}{5} \div \frac{3}{10}$

   Step1: Convert mixed number to fraction

   $1\frac{2}{5} = \frac{7}{5}$

   Step2: Find common denominator

   Common denominator of 5 and 10 is 10. Rewrite $\frac{7}{5}$ as $\frac{14}{10}$.

   Step3: Divide numerators

   $\frac{14}{10} \div \frac{3}{10} = \frac{14}{3} = 4\frac{2}{3}$
   ---

   Problem 5: $2\frac{3}{4} \div 1\frac{3}{8}$

   Step1: Convert mixed numbers to fractions

   $2\frac{3}{4} = \frac{11}{4}$, $1\frac{3}{8} = \frac{11}{8}$

   Step2: Find common denominator

   Common denominator of 4 and 8 is 8. Rewrite $\frac{11}{4}$ as $\frac{22}{8}$.

   Step3: Divide numerators

   $\frac{22}{8} \div \frac{11}{8} = \frac{22}{11} = 2$
   ---

   Problem 6: $3\frac{1}{4} \div 1\frac{3}{8}$

   Step1: Convert mixed numbers to fractions

   $3\frac{1}{4} = \frac{13}{4}$, $1\frac{3}{8} = \frac{11}{8}$

   Step2: Find common denominator

   Common denominator of 4 and 8 is 8. Rewrite $\frac{13}{4}$ as $\frac{26}{8}$.

   Step3: Divide numerators

   $\frac{26}{8} \div \frac{11}{8} = \frac{26}{11} = 2\frac{4}{11}$
   ---

   Problem 7: Check Problem 1 with reciprocal method

   Step1: Use reciprocal division rule

   $\frac{6}{9} \div \frac{1}{3} = \frac{6}{9} \times \frac{3}{1}$

   Step2: Simplify and multiply

   $\frac{6 \times 3}{9 \times 1} = \frac{18}{9} = 2$

   Turn 2 Answer

   Got it, here are the numbered answers with work shown clearly:

   1. $\boldsymbol{\frac{6}{9} \div \frac{1}{3} = 2}$

   • Common denominator is 9, rewrite $\frac{1}{3}$ as $\frac{3}{9}$
   • Divide numerators: $\frac{6}{3} = 2$

   1. $\boldsymbol{\frac{7}{9} \div \frac{1}{3} = \frac{7}{3} \text{ or } 2\frac{1}{3}}$

   • Common denominator is 9, rewrite $\frac{1}{3}$ as $\frac{3}{9}$
   • Divide numerators: $\frac{7}{3} = 2\frac{1}{3}$

   1. $\boldsymbol{1\frac{1}{5} \div \frac{3}{10} = 4}$

   • Convert mixed number: $1\frac{1}{5} = \frac{6}{5} = \frac{12}{10}$
   • Divide numerators: $\frac{12}{3} = 4$

   1. $\boldsymbol{1\frac{2}{5} \div \frac{3}{10} = \frac{14}{3} \text{ or } 4\frac{2}{3}}$

   • Convert mixed number: $1\frac{2}{5} = \frac{7}{5} = \frac{14}{10}$
   • Divide numerators: $\frac{14}{3} = 4\frac{2}{3}$

   1. $\boldsymbol{2\frac{3}{4} \div 1\frac{3}{8} = 2}$

   • Convert mixed numbers: $2\frac{3}{4} = \frac{11}{4} = \frac{22}{8}$, $1\frac{3}{8} = \frac{11}{8}$
   • Divide numerators: $\frac{22}{11} = 2$

   1. $\boldsymbol{3\frac{1}{4} \div 1\frac{3}{8} = \frac{26}{11} \text{ or } 2\frac{4}{11}}$

   • Convert mixed numbers: $3\frac{1}{4} = \frac{13}{4} = \frac{26}{8}$, $1\frac{3}{8} = \frac{11}{8}$
   • Divide numerators: $\frac{26}{11} = 2\frac{4}{11}$

   1. $\boldsymbol{\text{Checking Problem 1 with reciprocal method: } 2}$

   • Use "keep, change, flip": $\frac{6}{9} \t…
4. Final answer
   1. $2$
   2. $\frac{7}{3}$ or $2\frac{1}{3}$
   3. $\frac{20}{3}$ or $6\frac{2}{3}$
   4. $\frac{14}{3}$ or $4\frac{2}{3}$
   5. $2$
   6. $\frac{26}{11}$ or $2\frac{4}{11}$
   7. (Using problem 1) $2$

Answer

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number the answers

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