FREE Operation With Fractions Worksheets [PDFs] Brighterly - Free Printable

Let's solve each problem step by step in the worksheet titled "Fractions multiplied by a whole number". We'll use basic fraction multiplication rules:

> When multiplying a fraction by a whole number:
> $$
> \frac{a}{b} \times c = \frac{a \times c}{b}
> $$

We can also simplify before multiplying.

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1) $\frac{1}{9} \times 36 =$

$$
\frac{1}{9} \times 36 = \frac{36}{9} = 4
$$

✔ Answer: 4

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2) $49 \times \frac{3}{7} =$

$$
49 \times \frac{3}{7} = \frac{49 \times 3}{7} = \frac{147}{7} = 21
$$

✔ Answer: 21

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3) $\frac{4}{11} \times 55 =$

$$
\frac{4}{11} \times 55 = \frac{4 \times 55}{11} = \frac{220}{11} = 20
$$

✔ Answer: 20

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4) $\boxed{} \times \frac{5}{12} = \frac{25}{6}$

Let the missing number be $x$. So:
$$
x \times \frac{5}{12} = \frac{25}{6}
$$

Solve for $x$:
$$
x = \frac{25}{6} \div \frac{5}{12} = \frac{25}{6} \times \frac{12}{5} = \frac{25 \times 12}{6 \times 5} = \frac{300}{30} = 10
$$

✔ Answer: 10

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5) $\boxed{} \times 63 = \frac{45}{2}$

Let $x$ be the missing number:
$$
x \times 63 = \frac{45}{2}
\Rightarrow x = \frac{45}{2} \div 63 = \frac{45}{2} \times \frac{1}{63} = \frac{45}{126} = \frac{5}{14}
$$

(Simplify: $ \frac{45}{126} \div 9 = \frac{5}{14} $)

✔ Answer: $\frac{5}{14}$

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6) $\boxed{} \times 15 = \frac{9}{4}$

Let $x$ be the missing number:
$$
x \times 15 = \frac{9}{4}
\Rightarrow x = \frac{9}{4} \div 15 = \frac{9}{4} \times \frac{1}{15} = \frac{9}{60} = \frac{3}{20}
$$

✔ Answer: $\frac{3}{20}$

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7) $\frac{6}{5} \times \boxed{} = 54$

Let $x$ be the missing number:
$$
\frac{6}{5} \times x = 54
\Rightarrow x = 54 \div \frac{6}{5} = 54 \times \frac{5}{6} = \frac{270}{6} = 45
$$

✔ Answer: 45

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8) $85 \times \boxed{} = 34$

Let $x$ be the missing number:
$$
85 \times x = 34
\Rightarrow x = \frac{34}{85} = \frac{2}{5}
$$

(Simplify: divide numerator and denominator by 17 → $ \frac{34 \div 17}{85 \div 17} = \frac{2}{5} $)

✔ Answer: $\frac{2}{5}$

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9) $32 \times \boxed{} = \frac{40}{3}$

Let $x$ be the missing number:
$$
32 \times x = \frac{40}{3}
\Rightarrow x = \frac{40}{3} \div 32 = \frac{40}{3} \times \frac{1}{32} = \frac{40}{96} = \frac{5}{12}
$$

(Simplify: $ \frac{40}{96} \div 8 = \frac{5}{12} $)

✔ Answer: $\frac{5}{12}$

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10) $\boxed{} \times \frac{4}{13} = 16$

Let $x$ be the missing number:
$$
x \times \frac{4}{13} = 16
\Rightarrow x = 16 \div \frac{4}{13} = 16 \times \frac{13}{4} = \frac{208}{4} = 52
$$

✔ Answer: 52

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11) $\boxed{} \times 72 = 27$

Let $x$ be the missing number:
$$
x \times 72 = 27
\Rightarrow x = \frac{27}{72} = \frac{3}{8}
$$

(Simplify: divide numerator and denominator by 9 → $ \frac{3}{8} $)

✔ Answer: $\frac{3}{8}$

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12) $\boxed{} \times \frac{2}{27} = \frac{4}{3}$

Let $x$ be the missing number:
$$
x \times \frac{2}{27} = \frac{4}{3}
\Rightarrow x = \frac{4}{3} \div \frac{2}{27} = \frac{4}{3} \times \frac{27}{2} = \frac{108}{6} = 18
$$

✔ Answer: 18

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✔ Final Answers:

| Problem | Answer |
|--------|---------------|
| 1) | 4 |
| 2) | 21 |
| 3) | 20 |
| 4) | 10 |
| 5) | $\frac{5}{14}$ |
| 6) | $\frac{3}{20}$ |
| 7) | 45 |
| 8) | $\frac{2}{5}$ |
| 9) | $\frac{5}{12}$ |
| 10) | 52 |
| 11) | $\frac{3}{8}$ |
| 12) | 18 |

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Let me know if you'd like this formatted as a printable answer sheet!