Multiplying and Dividing Fractions worksheet with 12 practice problems for math students.

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

1. $\frac{3}{7} \times \frac{5}{2} \div \frac{3}{2}$
* First, change division to multiplication by flipping the last fraction (reciprocal): $\frac{3}{7} \times \frac{5}{2} \times \frac{2}{3}$
* Multiply straight across: Numerator $3 \times 5 \times 2 = 30$. Denominator $7 \times 2 \times 3 = 42$.
* Result: $\frac{30}{42}$
* Simplify by dividing top and bottom by 6: $\frac{5}{7}$

2. $\frac{35}{3} \times \frac{3}{3} \div \frac{10}{3}$
* Change division to multiplication: $\frac{35}{3} \times \frac{3}{3} \times \frac{3}{10}$
* Cancel out common numbers before multiplying. The $3$s in the denominators cancel with the $3$s in the numerators. We are left with $\frac{35}{1} \times \frac{1}{1} \times \frac{1}{10} = \frac{35}{10}$.
* Simplify $\frac{35}{10}$ by dividing by 5: $\frac{7}{2}$ (or $3 \frac{1}{2}$)

3. $\frac{15}{17} \times \frac{9}{13} \div \frac{2}{3}$
* Change division to multiplication: $\frac{15}{17} \times \frac{9}{13} \times \frac{3}{2}$
* Multiply numerators: $15 \times 9 \times 3 = 405$
* Multiply denominators: $17 \times 13 \times 2 = 442$
* Result: $\frac{405}{442}$ (This cannot be simplified further).

4. $\frac{1}{2} \times \frac{40}{75} \div \frac{40}{25}$
* Change division to multiplication: $\frac{1}{2} \times \frac{40}{75} \times \frac{25}{40}$
* Notice that $40$ is on top and bottom, so they cancel out completely.
* Now we have: $\frac{1}{2} \times \frac{25}{75}$
* Simplify $\frac{25}{75}$ to $\frac{1}{3}$.
* Multiply: $\frac{1}{2} \times \frac{1}{3} = \frac{1}{6}$

5. $\frac{5}{2} \div \frac{10}{14} \times \frac{3}{2}$
* Change division to multiplication: $\frac{5}{2} \times \frac{14}{10} \times \frac{3}{2}$
* Simplify $\frac{14}{10}$ to $\frac{7}{5}$.
* Equation becomes: $\frac{5}{2} \times \frac{7}{5} \times \frac{3}{2}$
* The $5$ on top and bottom cancel out.
* Multiply remaining: $\frac{1}{2} \times \frac{7}{1} \times \frac{3}{2} = \frac{21}{4}$ (or $5 \frac{1}{4}$)

6. $\frac{20}{48} \div \frac{25}{5} \div \frac{1}{8}$
* Simplify $\frac{25}{5}$ to just $5$ (or $\frac{5}{1}$).
* Change divisions to multiplications: $\frac{20}{48} \times \frac{1}{5} \times \frac{8}{1}$
* Simplify $\frac{20}{48}$ by dividing by 4: $\frac{5}{12}$.
* Equation: $\frac{5}{12} \times \frac{1}{5} \times \frac{8}{1}$
* The $5$s cancel out. We have $\frac{8}{12}$.
* Simplify $\frac{8}{12}$ by dividing by 4: $\frac{2}{3}$

7. $\frac{32}{50} \times \frac{16}{50} \times \frac{15}{7}$
* Simplify fractions first. $\frac{32}{50}$ becomes $\frac{16}{25}$. $\frac{16}{50}$ becomes $\frac{8}{25}$.
* Equation: $\frac{16}{25} \times \frac{8}{25} \times \frac{15}{7}$
* Cross-cancel: Divide 15 and 25 by 5. The 15 becomes 3, and one 25 becomes 5.
* Equation: $\frac{16}{5} \times \frac{8}{25} \times \frac{3}{7}$
* Multiply tops: $16 \times 8 \times 3 = 384$
* Multiply bottoms: $5 \times 25 \times 7 = 875$
* Result: $\frac{384}{875}$

8. $\frac{60}{120} \div \frac{5}{30} \div \frac{18}{14}$
* Simplify everything first.
* $\frac{60}{120} = \frac{1}{2}$
* $\frac{5}{30} = \frac{1}{6}$
* $\frac{18}{14} = \frac{9}{7}$
* Equation: $\frac{1}{2} \div \frac{1}{6} \div \frac{9}{7}$
* Flip both divisors: $\frac{1}{2} \times \frac{6}{1} \times \frac{7}{9}$
* Simplify $\frac{6}{2}$ to $3$. So, $3 \times \frac{7}{9} = \frac{21}{9}$.
* Simplify $\frac{21}{9}$ by dividing by 3: $\frac{7}{3}$ (or $2 \frac{1}{3}$)

9. $\frac{75}{9} \times \frac{9}{7} \times \frac{7}{15}$
* Cancel matching numbers diagonally.
* The $9$ on bottom (first fraction) cancels with $9$ on top (second fraction).
* The $7$ on bottom (second fraction) cancels with $7$ on top (third fraction).
* Left with: $\frac{75}{1} \times \frac{1}{1} \times \frac{1}{15} = \frac{75}{15}$
* $75 \div 15 = 5$

10. $\frac{4}{9} \times \frac{3}{9} \div \frac{7}{9}$
* Change division to multiplication: $\frac{4}{9} \times \frac{3}{9} \times \frac{9}{7}$
* One $9$ on bottom cancels with one $9$ on top.
* Left with: $\frac{4}{1} \times \frac{3}{9} \times \frac{1}{7}$
* Simplify $\frac{3}{9}$ to $\frac{1}{3}$.
* Multiply: $\frac{4 \times 1 \times 1}{1 \times 3 \times 7} = \frac{4}{21}$

11. $\frac{85}{30} \times \frac{40}{30} \times \frac{10}{13}$
* Simplify fractions.
* $\frac{85}{30}$ divide by 5 $\rightarrow \frac{17}{6}$
* $\frac{40}{30}$ divide by 10 $\rightarrow \frac{4}{3}$
* Equation: $\frac{17}{6} \times \frac{4}{3} \times \frac{10}{13}$
* Cross-cancel: Divide 4 and 6 by 2 $\rightarrow$ 2 and 3.
* Equation: $\frac{17}{3} \times \frac{2}{3} \times \frac{10}{13}$
* Multiply tops: $17 \times 2 \times 10 = 340$
* Multiply bottoms: $3 \times 3 \times 13 = 117$
* Result: $\frac{340}{117}$ (or $2 \frac{106}{117}$)

12. $\frac{160}{30} \times \frac{2}{15} \times \frac{5}{2}$
* Simplify $\frac{160}{30}$ to $\frac{16}{3}$.
* Equation: $\frac{16}{3} \times \frac{2}{15} \times \frac{5}{2}$
* The $2$s cancel out.
* Cross-cancel 5 and 15 (divide by 5) $\rightarrow$ 1 and 3.
* Equation: $\frac{16}{3} \times \frac{1}{3} \times \frac{1}{1}$
* Multiply: $\frac{16}{9}$ (or $1 \frac{7}{9}$)

Final Answer:
1. 5/7
2. 7/2
3. 405/442
4. 1/6
5. 21/4
6. 2/3
7. 384/875
8. 7/3
9. 5
10. 4/21
11. 340/117
12. 16/9