Multiplying Fractions Sheet 4: A math worksheet with ten fraction multiplication problems for practice.

Let's solve each of these fraction multiplication problems step by step, simplifying the answers to their simplest form.

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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(24, 45) = 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: $4 \times 2 \times 7 = 56$
Multiply denominators: $7 \times 3 \times 4 = 84$

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

Simplify: GCF(56, 84) = 28
$$
\frac{56 \div 28}{84 \div 28} = \frac{2}{3}
$$

✔ Answer: $\boxed{\frac{2}{3}}$

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3)

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

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

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

Now multiply:

Numerator: $3 \times 8 \times 5 = 120$
Denominator: $8 \times 1 \times 4 = 32$

$$
\frac{120}{32}
$$

Simplify: GCF(120, 32) = 8
$$
\frac{120 \div 8}{32 \div 8} = \frac{15}{4}
$$

This is an improper fraction. Convert to mixed number:
$15 \div 4 = 3$ remainder $3$, so $\frac{15}{4} = 3\frac{3}{4}$

✔ Answer: $\boxed{3\frac{3}{4}}$

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4)

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

Numerator: $2 \times 3 \times 4 = 24$
Denominator: $3 \times 4 \times 5 = 60$

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

Simplify: GCF(24, 60) = 12
$$
\frac{24 \div 12}{60 \div 12} = \frac{2}{5}
$$

✔ Answer: $\boxed{\frac{2}{5}}$

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5)

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

Numerator: $7 \times 4 \times 2 = 56$
Denominator: $4 \times 5 \times 3 = 60$

$$
\frac{56}{60}
$$

Simplify: GCF(56, 60) = 4
$$
\frac{56 \div 4}{60 \div 4} = \frac{14}{15}
$$

✔ Answer: $\boxed{\frac{14}{15}}$

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6)

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

Note: $\frac{9}{3} = 3$, so we can simplify first:

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

Now compute:
$6 \times 3 = 18$, then $18 \times \frac{3}{4} = \frac{54}{4}$

Simplify: $\frac{54}{4} = \frac{27}{2} = 13\frac{1}{2}$

Alternatively, do it all at once:

Numerator: $6 \times 3 \times 9 = 162$
Denominator: $1 \times 4 \times 3 = 12$

$$
\frac{162}{12}
$$

Simplify: GCF(162, 12) = 6
$$
\frac{162 \div 6}{12 \div 6} = \frac{27}{2} = 13\frac{1}{2}
$$

✔ Answer: $\boxed{13\frac{1}{2}}$

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7)

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

Numerator: $10 \times 4 \times 5 = 200$
Denominator: $7 \times 5 \times 3 = 105$

$$
\frac{200}{105}
$$

Simplify: GCF(200, 105) = 5
$$
\frac{200 \div 5}{105 \div 5} = \frac{40}{21}
$$

Convert to mixed number: $40 \div 21 = 1$ remainder $19$, so $1\frac{19}{21}$

✔ Answer: $\boxed{1\frac{19}{21}}$

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8)

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

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

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

Notice: $7$ in numerator and denominator cancel out:

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

Convert: $\frac{10}{3} = 3\frac{1}{3}$

✔ Answer: $\boxed{3\frac{1}{3}}$

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9)

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

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

Numerator: $11 \times 3 \times 2 = 66$
Denominator: $1 \times 5 \times 3 = 15$

$$
\frac{66}{15}
$$

Simplify: GCF(66, 15) = 3
$$
\frac{66 \div 3}{15 \div 3} = \frac{22}{5} = 4\frac{2}{5}
$$

✔ Answer: $\boxed{4\frac{2}{5}}$

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10)

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

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

Numerator: $4 \times 12 \times 2 = 96$
Denominator: $9 \times 1 \times 3 = 27$

$$
\frac{96}{27}
$$

Simplify: GCF(96, 27) = 3
$$
\frac{96 \div 3}{27 \div 3} = \frac{32}{9} = 3\frac{5}{9}
$$

✔ Answer: $\boxed{3\frac{5}{9}}$

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✔ Final Answers:

1) $\frac{8}{15}$
2) $\frac{2}{3}$
3) $3\frac{3}{4}$
4) $\frac{2}{5}$
5) $\frac{14}{15}$
6) $13\frac{1}{2}$
7) $1\frac{19}{21}$
8) $3\frac{1}{3}$
9) $4\frac{2}{5}$
10) $3\frac{5}{9}$

Let me know if you'd like a printable version or explanation of any step!