FREE Dividing Fractions Worksheets 6Th Grade [PDFs] Brighterly - Free Printable

Here are the step-by-step solutions for each problem on the worksheet.

1. $12 \frac{5}{7} \div \frac{6}{7}$
* Convert the mixed number to an improper fraction: $12 \times 7 = 84$, plus $5$ is $89$. So, $\frac{89}{7}$.
* Change division to multiplication by the reciprocal: $\frac{89}{7} \times \frac{7}{6}$.
* The $7$s cancel out.
* Result: $\frac{89}{6}$ or $14 \frac{5}{6}$.

2. $14 \frac{1}{5} \div \frac{4}{5}$
* Convert to improper fraction: $14 \times 5 = 70$, plus $1$ is $71$. So, $\frac{71}{5}$.
* Multiply by reciprocal: $\frac{71}{5} \times \frac{5}{4}$.
* The $5$s cancel out.
* Result: $\frac{71}{4}$ or $17 \frac{3}{4}$.

3. $10 \frac{2}{6} \div \frac{2}{6}$
* Simplify the fractions first: $\frac{2}{6}$ is the same as $\frac{1}{3}$. So the problem is $10 \frac{1}{3} \div \frac{1}{3}$.
* Convert to improper fraction: $10 \times 3 = 30$, plus $1$ is $31$. So, $\frac{31}{3}$.
* Multiply by reciprocal: $\frac{31}{3} \times \frac{3}{1}$.
* The $3$s cancel out.
* Result: $31$.

4. $4 \frac{5}{10} \div \frac{7}{10}$
* Simplify the mixed number: $\frac{5}{10}$ is $\frac{1}{2}$. So, $4 \frac{1}{2}$.
* Convert to improper fraction: $4 \times 2 = 8$, plus $1$ is $9$. So, $\frac{9}{2}$.
* To divide by $\frac{7}{10}$, multiply by $\frac{10}{7}$: $\frac{9}{2} \times \frac{10}{7}$.
* Simplify: $10 \div 2 = 5$. So, $9 \times \frac{5}{7} = \frac{45}{7}$.
* Result: $\frac{45}{7}$ or $6 \frac{3}{7}$.

5. $4 \frac{4}{8} \div \frac{2}{8}$
* Simplify fractions: $\frac{4}{8} = \frac{1}{2}$ and $\frac{2}{8} = \frac{1}{4}$. Problem becomes $4 \frac{1}{2} \div \frac{1}{4}$.
* Convert to improper fraction: $4 \frac{1}{2} = \frac{9}{2}$.
* Multiply by reciprocal: $\frac{9}{2} \times \frac{4}{1}$.
* Simplify: $4 \div 2 = 2$. So, $9 \times 2 = 18$.
* Result: $18$.

6. $12 \frac{6}{9} \div \frac{5}{9}$
* Simplify the mixed number: $\frac{6}{9} = \frac{2}{3}$. So, $12 \frac{2}{3}$.
* Convert to improper fraction: $12 \times 3 = 36$, plus $2$ is $38$. So, $\frac{38}{3}$.
* We are dividing by $\frac{5}{9}$. Multiply by $\frac{9}{5}$: $\frac{38}{3} \times \frac{9}{5}$.
* Simplify: $9 \div 3 = 3$. So, $38 \times \frac{3}{5}$.
* $38 \times 3 = 114$. Denominator is $5$.
* Result: $\frac{114}{5}$ or $22 \frac{4}{5}$.

7. $13 \frac{1}{3} \div \frac{1}{5}$
* Convert to improper fraction: $13 \times 3 = 39$, plus $1$ is $40$. So, $\frac{40}{3}$.
* Multiply by reciprocal: $\frac{40}{3} \times \frac{5}{1}$.
* $40 \times 5 = 200$. Denominator is $3$.
* Result: $\frac{200}{3}$ or $66 \frac{2}{3}$.

8. $11 \frac{4}{11} \div \frac{5}{11}$
* Convert to improper fraction: $11 \times 11 = 121$, plus $4$ is $125$. So, $\frac{125}{11}$.
* Multiply by reciprocal: $\frac{125}{11} \times \frac{11}{5}$.
* The $11$s cancel out. We have $\frac{125}{5}$.
* $125 \div 5 = 25$.
* Result: $25$.

9. $2 \frac{1}{2} \div \frac{1}{2}$
* Convert to improper fraction: $2 \times 2 = 4$, plus $1$ is $5$. So, $\frac{5}{2}$.
* Multiply by reciprocal: $\frac{5}{2} \times \frac{2}{1}$.
* The $2$s cancel out.
* Result: $5$.

10. $6 \frac{6}{8} \div \frac{3}{8}$
* Simplify the mixed number: $\frac{6}{8} = \frac{3}{4}$. So, $6 \frac{3}{4}$.
* Convert to improper fraction: $6 \times 4 = 24$, plus $3$ is $27$. So, $\frac{27}{4}$.
* Multiply by reciprocal of $\frac{3}{8}$, which is $\frac{8}{3}$: $\frac{27}{4} \times \frac{8}{3}$.
* Simplify: $27 \div 3 = 9$ and $8 \div 4 = 2$.
* $9 \times 2 = 18$.
* Result: $18$.

Final Answer:
1. $14 \frac{5}{6}$
2. $17 \frac{3}{4}$
3. $31$
4. $6 \frac{3}{7}$
5. $18$
6. $22 \frac{4}{5}$
7. $66 \frac{2}{3}$
8. $25$
9. $5$
10. $18$