Multiplying Fractions online worksheet for Grade 6 - Free Printable

Let's solve each problem step by step. We will multiply the fractions and mixed numbers, simplify the results, and write answers as improper fractions in simplest form.

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1. $ \frac{1}{6} \times \frac{5}{9} $

Multiply numerators: $ 1 \times 5 = 5 $
Multiply denominators: $ 6 \times 9 = 54 $
So: $ \frac{5}{54} $ — already in simplest form.

✔ Answer: $ \frac{5}{54} $

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2. $ \frac{2}{5} \times \frac{7}{8} $

$ 2 \times 7 = 14 $
$ 5 \times 8 = 40 $
So: $ \frac{14}{40} $

Simplify: divide numerator and denominator by 2 → $ \frac{7}{20} $

✔ Answer: $ \frac{7}{20} $

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3. $ \frac{6}{7} \times \frac{2}{9} $

$ 6 \times 2 = 12 $
$ 7 \times 9 = 63 $
So: $ \frac{12}{63} $

Simplify: divide by 3 → $ \frac{4}{21} $

✔ Answer: $ \frac{4}{21} $

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4. $ 18 \times \frac{5}{6} $

Write 18 as a fraction: $ \frac{18}{1} $

$ \frac{18}{1} \times \frac{5}{6} = \frac{90}{6} $

Simplify: $ 90 \div 6 = 15 $

✔ Answer: $ \frac{15}{1} $ or just $ 15 $ → but since it says "write as improper fraction", we write $ \frac{15}{1} $

But usually, $ 15 $ is acceptable unless specified otherwise. However, per instructions: "Mixed numbers should be written as improper fractions", so if answer is a whole number, we can write it as $ \frac{15}{1} $. But often, whole numbers are acceptable.

But let's follow strictly: $ \boxed{\frac{15}{1}} $

✔ Answer: $ \frac{15}{1} $

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5. $ \frac{5}{24} \times \frac{8}{15} $

Multiply: $ 5 \times 8 = 40 $, $ 24 \times 15 = 360 $

So: $ \frac{40}{360} $

Simplify: divide numerator and denominator by 40 → $ \frac{1}{9} $

✔ Answer: $ \frac{1}{9} $

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6. $ \frac{16}{7} \times \frac{21}{8} $

Multiply: $ 16 \times 21 = 336 $, $ 7 \times 8 = 56 $

So: $ \frac{336}{56} $

Now simplify: $ 336 \div 56 = 6 $

✔ Answer: $ \frac{6}{1} $ or $ \boxed{6} $

But again, per instruction: write as improper fraction → $ \boxed{\frac{6}{1}} $

Wait — actually, $ \frac{6}{1} $ is correct, but it’s redundant. Still, technically an improper fraction.

✔ Answer: $ \frac{6}{1} $

But let's check simplification:

We can cancel before multiplying:

$ \frac{16}{7} \times \frac{21}{8} $

- 16 and 8: $ 16 \div 8 = 2 $, $ 8 \div 8 = 1 $
- 21 and 7: $ 21 \div 7 = 3 $, $ 7 \div 7 = 1 $

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

Yes, same result.

✔ Answer: $ \frac{6}{1} $

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7. $ 2\frac{11}{12} \times \frac{2}{5} $

First, convert mixed number to improper fraction:

$ 2\frac{11}{12} = \frac{(2 \times 12) + 11}{12} = \frac{24 + 11}{12} = \frac{35}{12} $

Now: $ \frac{35}{12} \times \frac{2}{5} $

Multiply: $ 35 \times 2 = 70 $, $ 12 \times 5 = 60 $

So: $ \frac{70}{60} $

Simplify: divide numerator and denominator by 10 → $ \frac{7}{6} $

✔ Answer: $ \frac{7}{6} $

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8. $ 1\frac{3}{4} \times \frac{20}{21} $

Convert $ 1\frac{3}{4} $ to improper fraction:

$ 1 \times 4 + 3 = 7 $ → $ \frac{7}{4} $

Now: $ \frac{7}{4} \times \frac{20}{21} $

Multiply: $ 7 \times 20 = 140 $, $ 4 \times 21 = 84 $

So: $ \frac{140}{84} $

Simplify: divide numerator and denominator by 28?

Check GCD of 140 and 84.

- 140 ÷ 28 = 5
- 84 ÷ 28 = 3 → $ \frac{5}{3} $

Alternatively: divide by 4 → $ \frac{35}{21} $, then by 7 → $ \frac{5}{3} $

✔ Answer: $ \frac{5}{3} $

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9. $ 4\frac{9}{10} \times 1\frac{1}{7} $

Convert both to improper fractions:

- $ 4\frac{9}{10} = \frac{4 \times 10 + 9}{10} = \frac{49}{10} $
- $ 1\frac{1}{7} = \frac{7 + 1}{7} = \frac{8}{7} $

Now: $ \frac{49}{10} \times \frac{8}{7} $

Multiply: $ 49 \times 8 = 392 $, $ 10 \times 7 = 70 $

So: $ \frac{392}{70} $

Simplify: divide numerator and denominator by 14?

- 392 ÷ 14 = 28
- 70 ÷ 14 = 5 → $ \frac{28}{5} $

Check: 392 ÷ 14 = 28? $ 14 \times 28 = 392 $ → yes
70 ÷ 14 = 5 → yes

✔ Answer: $ \frac{28}{5} $

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10. $ 8\frac{1}{3} \times 4\frac{1}{2} $

Convert both:

- $ 8\frac{1}{3} = \frac{8 \times 3 + 1}{3} = \frac{25}{3} $
- $ 4\frac{1}{2} = \frac{4 \times 2 + 1}{2} = \frac{9}{2} $

Now: $ \frac{25}{3} \times \frac{9}{2} $

Multiply: $ 25 \times 9 = 225 $, $ 3 \times 2 = 6 $

So: $ \frac{225}{6} $

Simplify: divide numerator and denominator by 3 → $ \frac{75}{2} $

✔ Answer: $ \frac{75}{2} $

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✔ Final Answers:

1. $ \frac{5}{54} $
2. $ \frac{7}{20} $
3. $ \frac{4}{21} $
4. $ \frac{15}{1} $
5. $ \frac{1}{9} $
6. $ \frac{6}{1} $
7. $ \frac{7}{6} $
8. $ \frac{5}{3} $
9. $ \frac{28}{5} $
10. $ \frac{75}{2} $

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✔ Summary (Boxed):

$$
\begin{aligned}
1.\ & \frac{5}{54} \\
2.\ & \frac{7}{20} \\
3.\ & \frac{4}{21} \\
4.\ & \frac{15}{1} \\
5.\ & \frac{1}{9} \\
6.\ & \frac{6}{1} \\
7.\ & \frac{7}{6} \\
8.\ & \frac{5}{3} \\
9.\ & \frac{28}{5} \\
10.\ & \frac{75}{2} \\
\end{aligned}
$$

All answers are in simplest form and improper fractions as required.