Multiplying Mixed Fractions - Free Printable

Let's solve each problem step by step. The goal is to multiply mixed fractions, convert them to improper fractions, multiply, and simplify the result (leaving it as an improper fraction if needed, but in simplest form).

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🔷 Step-by-step Method:

1. Convert mixed numbers to improper fractions.
2. Multiply the two improper fractions.
3. Simplify the result (reduce if possible).
4. Leave as an improper fraction unless otherwise specified.

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✔ Example Given:

$$
2\frac{2}{5} \times \frac{2}{3} = \frac{12}{5} \times \frac{2}{3} = \frac{24}{15} = \frac{8}{5}
$$

Now let’s solve each problem.

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1) $ 2\frac{1}{2} \times \frac{4}{5} $

Convert $ 2\frac{1}{2} $:
$ 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2} $

Now multiply:
$$
\frac{5}{2} \times \frac{4}{5} = \frac{5 \times 4}{2 \times 5} = \frac{20}{10} = 2
$$

✔ Answer: 2

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2) $ 1\frac{3}{4} \times \frac{3}{5} $

Convert $ 1\frac{3}{4} $:
$ 1 + \frac{3}{4} = \frac{4}{4} + \frac{3}{4} = \frac{7}{4} $

Multiply:
$$
\frac{7}{4} \times \frac{3}{5} = \frac{21}{20}
$$

This is already simplified.

✔ Answer: $ \frac{21}{20} $

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3) $ 4\frac{1}{2} \times \frac{5}{6} $

Convert $ 4\frac{1}{2} $:
$ 4 + \frac{1}{2} = \frac{8}{2} + \frac{1}{2} = \frac{9}{2} $

Multiply:
$$
\frac{9}{2} \times \frac{5}{6} = \frac{45}{12}
$$

Simplify $ \frac{45}{12} $: divide numerator and denominator by 3 → $ \frac{15}{4} $

✔ Answer: $ \frac{15}{4} $

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

Convert $ 2\frac{2}{7} $:
$ 2 + \frac{2}{7} = \frac{14}{7} + \frac{2}{7} = \frac{16}{7} $

Now multiply by 3:
$$
\frac{16}{7} \times 3 = \frac{16 \times 3}{7} = \frac{48}{7}
$$

✔ Answer: $ \frac{48}{7} $

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5) $ \frac{2}{7} \times 3\frac{1}{5} $

Convert $ 3\frac{1}{5} $:
$ 3 + \frac{1}{5} = \frac{15}{5} + \frac{1}{5} = \frac{16}{5} $

Multiply:
$$
\frac{2}{7} \times \frac{16}{5} = \frac{32}{35}
$$

Already simplified.

✔ Answer: $ \frac{32}{35} $

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6) $ 8\frac{1}{2} \times \frac{2}{11} $

Convert $ 8\frac{1}{2} $:
$ 8 + \frac{1}{2} = \frac{16}{2} + \frac{1}{2} = \frac{17}{2} $

Multiply:
$$
\frac{17}{2} \times \frac{2}{11} = \frac{34}{22}
$$

Simplify: divide numerator and denominator by 2 → $ \frac{17}{11} $

✔ Answer: $ \frac{17}{11} $

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7) $ \frac{5}{12} \times 4\frac{2}{3} $

Convert $ 4\frac{2}{3} $:
$ 4 + \frac{2}{3} = \frac{12}{3} + \frac{2}{3} = \frac{14}{3} $

Multiply:
$$
\frac{5}{12} \times \frac{14}{3} = \frac{70}{36}
$$

Simplify: divide numerator and denominator by 2 → $ \frac{35}{18} $

✔ Answer: $ \frac{35}{18} $

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8) $ 2\frac{1}{5} \times 5\frac{1}{2} $

Convert both:

- $ 2\frac{1}{5} = \frac{10}{5} + \frac{1}{5} = \frac{11}{5} $
- $ 5\frac{1}{2} = \frac{10}{2} + \frac{1}{2} = \frac{11}{2} $

Multiply:
$$
\frac{11}{5} \times \frac{11}{2} = \frac{121}{10}
$$

Already simplified.

✔ Answer: $ \frac{121}{10} $

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✔ Final Answers:

1) $ \boxed{2} $
2) $ \boxed{\frac{21}{20}} $
3) $ \boxed{\frac{15}{4}} $
4) $ \boxed{\frac{48}{7}} $
5) $ \boxed{\frac{32}{35}} $
6) $ \boxed{\frac{17}{11}} $
7) $ \boxed{\frac{35}{18}} $
8) $ \boxed{\frac{121}{10}} $

All answers are in simplest form as improper fractions, as requested.

Let me know if you'd like these converted to mixed numbers too!