Multiplying and Dividing Fractions Worksheets with Answer Key - Free Printable

Let's solve each of the 10 problems involving multiplication and division of fractions step by step.

We will follow these rules:
- Multiplication: Multiply numerators together and denominators together.
- Division: Change the division into multiplication by flipping (taking the reciprocal) of the second fraction.

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🔹 Problem 1:

$$
\frac{11}{3} \times \frac{9}{13} \div \frac{4}{6}
$$

Step 1: Convert division to multiplication:
$$
= \frac{11}{3} \times \frac{9}{13} \times \frac{6}{4}
$$

Step 2: Simplify before multiplying:

- $ \frac{9}{3} = 3 $ → So $ \frac{11}{3} \times \frac{9}{13} = \frac{11 \times 3}{13} = \frac{33}{13} $
- Now multiply by $ \frac{6}{4} = \frac{3}{2} $

So:
$$
\frac{33}{13} \times \frac{3}{2} = \frac{99}{26}
$$

✔ Final Answer: $ \frac{99}{26} $

---

🔹 Problem 2:

$$
\frac{7}{4} \div \frac{8}{3} \div \frac{9}{14}
$$

Convert both divisions to multiplications:
$$
= \frac{7}{4} \times \frac{3}{8} \times \frac{14}{9}
$$

Now simplify:

- $ \frac{7}{4} \times \frac{3}{8} = \frac{21}{32} $
- $ \frac{21}{32} \times \frac{14}{9} $

Simplify cross terms:
- 21 and 9: $ \frac{21}{9} = \frac{7}{3} $
- 14 and 32: $ \frac{14}{32} = \frac{7}{16} $

So:
$$
= \frac{7}{3} \times \frac{7}{16} = \frac{49}{48}
$$

✔ Final Answer: $ \frac{49}{48} $

---

🔹 Problem 3:

$$
\frac{3}{5} \div \frac{17}{6} \times \frac{15}{9}
$$

Convert division:
$$
= \frac{3}{5} \times \frac{6}{17} \times \frac{15}{9}
$$

Simplify:
- $ \frac{15}{9} = \frac{5}{3} $
- So now: $ \frac{3}{5} \times \frac{6}{17} \times \frac{5}{3} $

Now cancel:
- $ \frac{3}{5} \times \frac{5}{3} = 1 $
- So left with: $ 1 \times \frac{6}{17} = \frac{6}{17} $

✔ Final Answer: $ \frac{6}{17} $

---

🔹 Problem 4:

$$
\frac{16}{5} \times \frac{3}{11} \times \frac{10}{16}
$$

Cancel common factors:
- $ \frac{16}{16} = 1 $, so cancel 16 in numerator and denominator
- $ \frac{10}{5} = 2 $, so $ \frac{10}{5} = 2 $

So:
$$
= \frac{1}{1} \times \frac{3}{11} \times \frac{2}{1} = \frac{6}{11}
$$

✔ Final Answer: $ \frac{6}{11} $

---

🔹 Problem 5:

$$
\frac{20}{9} \times \frac{2}{6} \times \frac{12}{58}
$$

Simplify:
- $ \frac{2}{6} = \frac{1}{3} $
- $ \frac{12}{58} = \frac{6}{29} $

Now:
$$
= \frac{20}{9} \times \frac{1}{3} \times \frac{6}{29}
$$

Multiply:
- Numerator: $ 20 \times 1 \times 6 = 120 $
- Denominator: $ 9 \times 3 \times 29 = 783 $

So: $ \frac{120}{783} $

Simplify:
- GCF of 120 and 783: Let's divide both by 3:
- $ 120 ÷ 3 = 40 $
- $ 783 ÷ 3 = 261 $
- $ \frac{40}{261} $ — check if reducible: 40 and 261 share no common factors (261 = 3×87, 40 = 2³×5)

✔ Final Answer: $ \frac{40}{261} $

---

🔹 Problem 6:

$$
\frac{19}{9} \div \frac{13}{6} \times \frac{24}{76}
$$

Convert division:
$$
= \frac{19}{9} \times \frac{6}{13} \times \frac{24}{76}
$$

Simplify:
- $ \frac{24}{76} = \frac{6}{19} $ (divide numerator and denominator by 4)

Now:
$$
= \frac{19}{9} \times \frac{6}{13} \times \frac{6}{19}
$$

Cancel:
- $ \frac{19}{19} = 1 $
- Left: $ \frac{1}{9} \times \frac{6}{13} \times 6 = \frac{36}{117} $

Simplify $ \frac{36}{117} $:
- Divide numerator and denominator by 3: $ \frac{12}{39} $
- Again by 3: $ \frac{4}{13} $

✔ Final Answer: $ \frac{4}{13} $

---

🔹 Problem 7:

$$
\frac{7}{6} \div \frac{15}{8} \times \frac{36}{35}
$$

Convert division:
$$
= \frac{7}{6} \times \frac{8}{15} \times \frac{36}{35}
$$

Simplify step-by-step:

Look for cancellations:
- $ \frac{7}{35} = \frac{1}{5} $
- $ \frac{8}{6} = \frac{4}{3} $
- $ \frac{36}{15} = \frac{12}{5} $

Better to write all together:

Numerator: $ 7 \times 8 \times 36 = ? $
Denominator: $ 6 \times 15 \times 35 $

But let’s cancel:

- 7 and 35 → $ \frac{7}{35} = \frac{1}{5} $
- 8 and 6 → $ \frac{8}{6} = \frac{4}{3} $
- 36 and 15 → $ \frac{36}{15} = \frac{12}{5} $

Wait — better to factor:

$$
\frac{7}{6} \times \frac{8}{15} \times \frac{36}{35}
= \frac{7 \times 8 \times 36}{6 \times 15 \times 35}
$$

Break down:
- $ 8 = 2^3 $
- $ 36 = 6 \times 6 = 2^2 \times 3^2 $
- $ 6 = 2 \times 3 $
- $ 15 = 3 \times 5 $
- $ 35 = 5 \times 7 $

Now:
Numerator: $ 7 \times 8 \times 36 = 7 \times 2^3 \times (2^2 \times 3^2) = 7 \times 2^5 \times 3^2 $
Denominator: $ 6 \times 15 \times 35 = (2 \times 3) \times (3 \times 5) \times (5 \times 7) = 2 \times 3^2 \times 5^2 \times 7 $

Now cancel:
- 7 cancels
- $ 2^5 / 2 = 2^4 $
- $ 3^2 / 3^2 = 1 $
- $ 5^2 $ remains in denominator

So: $ \frac{2^4}{5^2} = \frac{16}{25} $

✔ Final Answer: $ \frac{16}{25} $

---

🔹 Problem 8:

$$
\frac{13}{8} \times \frac{4}{3} \div \frac{26}{16}
$$

Convert division:
$$
= \frac{13}{8} \times \frac{4}{3} \times \frac{16}{26}
$$

Simplify:
- $ \frac{13}{26} = \frac{1}{2} $
- $ \frac{16}{8} = 2 $
- $ \frac{4}{3} $ stays

So:
$$
= \frac{13}{8} \times \frac{4}{3} \times \frac{16}{26}
= \frac{13}{8} \times \frac{4}{3} \times \frac{8}{13} \quad \text{(since } \frac{16}{26} = \frac{8}{13})
$$

Now:
- $ \frac{13}{13} = 1 $
- $ \frac{8}{8} = 1 $
- Left: $ \frac{4}{3} $

✔ Final Answer: $ \frac{4}{3} $

---

🔹 Problem 9:

$$
\frac{3}{8} \times \frac{18}{42} \div \frac{12}{16}
$$

First simplify:
- $ \frac{18}{42} = \frac{3}{7} $
- $ \frac{12}{16} = \frac{3}{4} $

So:
$$
= \frac{3}{8} \times \frac{3}{7} \div \frac{3}{4}
= \frac{3}{8} \times \frac{3}{7} \times \frac{4}{3}
$$

Cancel:
- $ \frac{3}{3} = 1 $
- $ \frac{4}{8} = \frac{1}{2} $

So:
$$
= \frac{1}{2} \times \frac{3}{7} = \frac{3}{14}
$$

✔ Final Answer: $ \frac{3}{14} $

---

🔹 Problem 10:

$$
\frac{29}{10} \div \frac{7}{2} \times \frac{5}{58}
$$

Convert division:
$$
= \frac{29}{10} \times \frac{2}{7} \times \frac{5}{58}
$$

Now simplify:

- $ \frac{29}{58} = \frac{1}{2} $
- $ \frac{2}{10} = \frac{1}{5} $
- $ \frac{5}{7} $ stays?

Let’s write it:

$$
= \frac{29}{10} \times \frac{2}{7} \times \frac{5}{58}
$$

Group:
- $ \frac{29}{58} = \frac{1}{2} $
- $ \frac{2}{10} = \frac{1}{5} $
- $ \frac{5}{7} $

So:
$$
= \frac{1}{2} \times \frac{1}{5} \times \frac{5}{7} = \frac{1}{2} \times \frac{1}{7} = \frac{1}{14}
$$

Because $ \frac{1}{5} \times \frac{5}{7} = \frac{1}{7} $

✔ Final Answer: $ \frac{1}{14} $

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✔ Final Answers Summary:

| Problem | Answer |
|--------|----------------|
| 1 | $ \frac{99}{26} $ |
| 2 | $ \frac{49}{48} $ |
| 3 | $ \frac{6}{17} $ |
| 4 | $ \frac{6}{11} $ |
| 5 | $ \frac{40}{261} $ |
| 6 | $ \frac{4}{13} $ |
| 7 | $ \frac{16}{25} $ |
| 8 | $ \frac{4}{3} $ |
| 9 | $ \frac{3}{14} $ |
| 10 | $ \frac{1}{14} $ |

Let me know if you'd like this formatted as a printable answer sheet!