Grade 6 Multiplying Fractions Worksheets | Free Worksheets ... - Free Printable

Let's solve each of the fraction multiplication problems step by step. The rule for multiplying fractions is:

> Multiply the numerators together, and multiply the denominators together, then simplify if possible.

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First Set (Problems 1–12)

#### 1. $ \frac{1}{2} \times \frac{1}{2} $
$$
= \frac{1 \times 1}{2 \times 2} = \frac{1}{4}
$$

#### 2. $ \frac{3}{4} \times \frac{1}{5} $
$$
= \frac{3 \times 1}{4 \times 5} = \frac{3}{20}
$$

#### 3. $ \frac{9}{10} \times \frac{5}{6} $
$$
= \frac{9 \times 5}{10 \times 6} = \frac{45}{60} = \frac{3}{4} \quad \text{(simplified by dividing numerator and denominator by 15)}
$$

#### 4. $ \frac{1}{5} \times \frac{10}{11} $
$$
= \frac{1 \times 10}{5 \times 11} = \frac{10}{55} = \frac{2}{11} \quad \text{(divided by 5)}
$$

#### 5. $ \frac{3}{7} \times \frac{1}{9} $
$$
= \frac{3 \times 1}{7 \times 9} = \frac{3}{63} = \frac{1}{21} \quad \text{(divided by 3)}
$$

#### 6. $ \frac{4}{9} \times \frac{3}{8} $
$$
= \frac{4 \times 3}{9 \times 8} = \frac{12}{72} = \frac{1}{6} \quad \text{(divided by 12)}
$$

#### 7. $ \frac{5}{6} \times \frac{10}{15} $
Simplify $ \frac{10}{15} = \frac{2}{3} $, so:
$$
\frac{5}{6} \times \frac{2}{3} = \frac{10}{18} = \frac{5}{9}
$$

#### 8. $ \frac{9}{10} \times \frac{8}{9} $
$$
= \frac{9 \times 8}{10 \times 9} = \frac{72}{90} = \frac{4}{5} \quad \text{(divided by 18)}
$$

#### 9. $ \frac{4}{9} \times \frac{1}{8} $
$$
= \frac{4 \times 1}{9 \times 8} = \frac{4}{72} = \frac{1}{18}
$$

#### 10. $ \frac{6}{7} \times \frac{4}{5} $
$$
= \frac{6 \times 4}{7 \times 5} = \frac{24}{35} \quad \text{(already simplified)}
$$

#### 11. $ \frac{14}{20} \times \frac{10}{12} $
Simplify first:
$ \frac{14}{20} = \frac{7}{10} $, $ \frac{10}{12} = \frac{5}{6} $

So:
$$
\frac{7}{10} \times \frac{5}{6} = \frac{35}{60} = \frac{7}{12} \quad \text{(divided by 5)}
$$

#### 12. $ \frac{5}{7} \times \frac{1}{2} $
$$
= \frac{5 \times 1}{7 \times 2} = \frac{5}{14}
$$

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Second Set (Problems 1–12)

#### 1. $ \frac{12}{15} \times \frac{5}{6} $
Simplify $ \frac{12}{15} = \frac{4}{5} $, so:
$$
\frac{4}{5} \times \frac{5}{6} = \frac{20}{30} = \frac{2}{3}
$$

#### 2. $ \frac{8}{9} \times \frac{9}{10} $
$$
= \frac{8 \times 9}{9 \times 10} = \frac{72}{90} = \frac{4}{5} \quad \text{(divided by 18)}
$$

#### 3. $ \frac{1}{2} \times \frac{3}{4} $
$$
= \frac{1 \times 3}{2 \times 4} = \frac{3}{8}
$$

#### 4. $ \frac{7}{8} \times \frac{2}{5} $
$$
= \frac{7 \times 2}{8 \times 5} = \frac{14}{40} = \frac{7}{20} \quad \text{(divided by 2)}
$$

#### 5. $ \frac{6}{7} \times \frac{1}{7} $
$$
= \frac{6 \times 1}{7 \times 7} = \frac{6}{49}
$$

#### 6. $ \frac{8}{10} \times \frac{5}{7} $
Simplify $ \frac{8}{10} = \frac{4}{5} $, so:
$$
\frac{4}{5} \times \frac{5}{7} = \frac{20}{35} = \frac{4}{7}
$$

#### 7. $ \frac{1}{10} \times \frac{1}{5} $
$$
= \frac{1 \times 1}{10 \times 5} = \frac{1}{50}
$$

#### 8. $ \frac{7}{8} \times \frac{2}{5} $
Same as problem 4 above:
$$
= \frac{14}{40} = \frac{7}{20}
$$

#### 9. $ \frac{8}{11} \times \frac{3}{4} $
$$
= \frac{8 \times 3}{11 \times 4} = \frac{24}{44} = \frac{6}{11} \quad \text{(divided by 4)}
$$

#### 10. $ \frac{5}{9} \times \frac{3}{4} $
$$
= \frac{5 \times 3}{9 \times 4} = \frac{15}{36} = \frac{5}{12} \quad \text{(divided by 3)}
$$

#### 11. $ \frac{3}{4} \times \frac{3}{4} $
$$
= \frac{3 \times 3}{4 \times 4} = \frac{9}{16}
$$

#### 12. $ \frac{4}{5} \times \frac{8}{10} $
Simplify $ \frac{8}{10} = \frac{4}{5} $, so:
$$
\frac{4}{5} \times \frac{4}{5} = \frac{16}{25}
$$

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✔ Final Answers:

#### First Set:
1. $ \frac{1}{4} $
2. $ \frac{3}{20} $
3. $ \frac{3}{4} $
4. $ \frac{2}{11} $
5. $ \frac{1}{21} $
6. $ \frac{1}{6} $
7. $ \frac{5}{9} $
8. $ \frac{4}{5} $
9. $ \frac{1}{18} $
10. $ \frac{24}{35} $
11. $ \frac{7}{12} $
12. $ \frac{5}{14} $

#### Second Set:
1. $ \frac{2}{3} $
2. $ \frac{4}{5} $
3. $ \frac{3}{8} $
4. $ \frac{7}{20} $
5. $ \frac{6}{49} $
6. $ \frac{4}{7} $
7. $ \frac{1}{50} $
8. $ \frac{7}{20} $
9. $ \frac{6}{11} $
10. $ \frac{5}{12} $
11. $ \frac{9}{16} $
12. $ \frac{16}{25} $

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✔ All answers are simplified to lowest terms. Let me know if you'd like this formatted as a printable answer key!