Multiplying Fractions Worksheet - Free Printable

Let's solve each of the multiplication problems step by step. We'll multiply the fractions together and simplify the results to their simplest form.

---

1)

$$
\frac{3}{5} \times \frac{2}{3} \times \frac{4}{3}
$$

Multiply numerators: $3 \times 2 \times 4 = 24$
Multiply denominators: $5 \times 3 \times 3 = 45$

So:
$$
\frac{24}{45}
$$

Simplify: Divide numerator and denominator by GCF (3):
$$
\frac{24 \div 3}{45 \div 3} = \frac{8}{15}
$$

✔ Answer: $\boxed{\frac{8}{15}}$

---

2)

$$
\frac{4}{7} \times \frac{2}{3} \times \frac{7}{4}
$$

Multiply numerators: $4 \times 2 \times 7 = 56$
Denominators: $7 \times 3 \times 4 = 84$

$$
\frac{56}{84}
$$

Simplify: GCF is 28 → $56 \div 28 = 2$, $84 \div 28 = 3$

✔ Answer: $\boxed{\frac{2}{3}}$

---

3)

$$
\frac{3}{8} \times 8 \times \frac{5}{4}
$$

First, write 8 as $\frac{8}{1}$

Now:
$$
\frac{3}{8} \times \frac{8}{1} \times \frac{5}{4}
$$

Cancel 8 in numerator and denominator:
$$
\frac{3}{\cancel{8}} \times \frac{\cancel{8}}{1} = 3
$$

Then: $3 \times \frac{5}{4} = \frac{15}{4}$

✔ Answer: $\boxed{\frac{15}{4}}$ or $3\frac{3}{4}$

---

4)

$$
\frac{2}{3} \times \frac{3}{4} \times \frac{4}{5}
$$

Multiply numerators: $2 \times 3 \times 4 = 24$
Denominators: $3 \times 4 \times 5 = 60$

$$
\frac{24}{60}
$$

Simplify: GCF = 12 → $24 \div 12 = 2$, $60 \div 12 = 5$

✔ Answer: $\boxed{\frac{2}{5}}$

---

5)

$$
\frac{7}{4} \times \frac{4}{5} \times \frac{2}{3}
$$

Cancel 4 in numerator and denominator:
$$
\frac{7}{\cancel{4}} \times \frac{\cancel{4}}{5} = \frac{7}{5}
$$

Now: $\frac{7}{5} \times \frac{2}{3} = \frac{14}{15}$

✔ Answer: $\boxed{\frac{14}{15}}$

---

6)

$$
6 \times \frac{3}{4} \times \frac{9}{3}
$$

Write 6 as $\frac{6}{1}$, and note that $\frac{9}{3} = 3$

So:
$$
\frac{6}{1} \times \frac{3}{4} \times 3
= \frac{6 \times 3 \times 3}{1 \times 4} = \frac{54}{4}
$$

Simplify: divide numerator and denominator by 2 → $\frac{27}{2}$

✔ Answer: $\boxed{\frac{27}{2}}$ or $13\frac{1}{2}$

---

7)

$$
\frac{10}{7} \times \frac{4}{5} \times \frac{5}{3}
$$

Note: 10 and 5 → 10 ÷ 5 = 2, 5 ÷ 5 = 1
Also, 5 in numerator and denominator cancel.

So:
$$
\frac{10}{7} \times \frac{4}{5} \times \frac{5}{3} = \frac{10 \times 4 \times 5}{7 \times 5 \times 3}
$$

Cancel 5s:
$$
\frac{10 \times 4}{7 \times 3} = \frac{40}{21}
$$

✔ Answer: $\boxed{\frac{40}{21}}$ or $1\frac{19}{21}$

---

8)

$$
\frac{10}{6} \times 7 \times \frac{2}{7}
$$

First, simplify $\frac{10}{6} = \frac{5}{3}$

Now:
$$
\frac{5}{3} \times 7 \times \frac{2}{7}
$$

The 7s cancel:
$$
\frac{5}{3} \times \cancel{7} \times \frac{2}{\cancel{7}} = \frac{5}{3} \times 2 = \frac{10}{3}
$$

✔ Answer: $\boxed{\frac{10}{3}}$ or $3\frac{1}{3}$

---

9)

$$
11 \times \frac{3}{5} \times \frac{2}{3}
$$

Write 11 as $\frac{11}{1}$

Now:
$$
\frac{11}{1} \times \frac{3}{5} \times \frac{2}{3}
$$

Cancel 3s:
$$
\frac{11}{1} \times \frac{\cancel{3}}{5} \times \frac{2}{\cancel{3}} = \frac{11 \times 2}{5} = \frac{22}{5}
$$

✔ Answer: $\boxed{\frac{22}{5}}$ or $4\frac{2}{5}$

---

10)

$$
\frac{4}{9} \times 12 \times \frac{2}{3}
$$

Write 12 as $\frac{12}{1}$

$$
\frac{4}{9} \times \frac{12}{1} \times \frac{2}{3}
$$

Break down 12: $12 = 3 \times 4$

So:
$$
\frac{4}{9} \times \frac{3 \times 4}{1} \times \frac{2}{3}
$$

Now cancel:

- 4 in numerator and denominator
- 3 in numerator and denominator

So:
$$
\frac{1}{9} \times \frac{4}{1} \times \frac{2}{1} = \frac{1 \times 4 \times 2}{9} = \frac{8}{9}
$$

Wait — let’s do it carefully:

Original:
$$
\frac{4}{9} \times \frac{12}{1} \times \frac{2}{3}
= \frac{4 \times 12 \times 2}{9 \times 1 \times 3} = \frac{96}{27}
$$

Simplify: divide numerator and denominator by 3 → $\frac{32}{9}$

✔ Answer: $\boxed{\frac{32}{9}}$ or $3\frac{5}{9}$

---

✔ Final Answers:

1) $\frac{8}{15}$
2) $\frac{2}{3}$
3) $\frac{15}{4}$
4) $\frac{2}{5}$
5) $\frac{14}{15}$
6) $\frac{27}{2}$
7) $\frac{40}{21}$
8) $\frac{10}{3}$
9) $\frac{22}{5}$
10) $\frac{32}{9}$

All answers are in simplest form.

Let me know if you'd like a printed version or explanation for any specific problem!