Multiply fractions and whole numbers worksheet with problems and instructions for canceling.

Problem: Multiply Fractions and Whole Numbers

The task is to multiply fractions by whole numbers, simplifying where possible. Let's solve each problem step by step.

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#### 1. \( \frac{1}{5} \times 4 \)

- Step 1: Write the whole number as a fraction: \( 4 = \frac{4}{1} \).
- Step 2: Multiply the numerators and the denominators:
\[
\frac{1}{5} \times \frac{4}{1} = \frac{1 \times 4}{5 \times 1} = \frac{4}{5}
\]
- Step 3: Simplify (if possible). In this case, \( \frac{4}{5} \) is already in its simplest form.

Answer: \( \frac{4}{5} \)

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#### 2. \( \frac{6}{8} \times 8 \)

- Step 1: Write the whole number as a fraction: \( 8 = \frac{8}{1} \).
- Step 2: Multiply the numerators and the denominators:
\[
\frac{6}{8} \times \frac{8}{1} = \frac{6 \times 8}{8 \times 1} = \frac{48}{8}
\]
- Step 3: Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 8:
\[
\frac{48 \div 8}{8 \div 8} = \frac{6}{1} = 6
\]

Answer: \( 6 \)

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#### 3. \( \frac{2}{9} \times 3 \)

- Step 1: Write the whole number as a fraction: \( 3 = \frac{3}{1} \).
- Step 2: Multiply the numerators and the denominators:
\[
\frac{2}{9} \times \frac{3}{1} = \frac{2 \times 3}{9 \times 1} = \frac{6}{9}
\]
- Step 3: Simplify the fraction by dividing both the numerator and the denominator by their GCD, which is 3:
\[
\frac{6 \div 3}{9 \div 3} = \frac{2}{3}
\]

Answer: \( \frac{2}{3} \)

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#### 4. \( \frac{3}{4} \times 10 \)

- Step 1: Write the whole number as a fraction: \( 10 = \frac{10}{1} \).
- Step 2: Multiply the numerators and the denominators:
\[
\frac{3}{4} \times \frac{10}{1} = \frac{3 \times 10}{4 \times 1} = \frac{30}{4}
\]
- Step 3: Simplify the fraction by dividing both the numerator and the denominator by their GCD, which is 2:
\[
\frac{30 \div 2}{4 \div 2} = \frac{15}{2}
\]
- Step 4: Convert the improper fraction to a mixed number (optional):
\[
\frac{15}{2} = 7 \frac{1}{2}
\]

Answer: \( \frac{15}{2} \) or \( 7 \frac{1}{2} \)

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#### 5. \( \frac{2}{3} \times 6 \)

- Step 1: Write the whole number as a fraction: \( 6 = \frac{6}{1} \).
- Step 2: Multiply the numerators and the denominators:
\[
\frac{2}{3} \times \frac{6}{1} = \frac{2 \times 6}{3 \times 1} = \frac{12}{3}
\]
- Step 3: Simplify the fraction by dividing both the numerator and the denominator by their GCD, which is 3:
\[
\frac{12 \div 3}{3 \div 3} = \frac{4}{1} = 4
\]

Answer: \( 4 \)

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#### 6. \( \frac{3}{5} \times 13 \)

- Step 1: Write the whole number as a fraction: \( 13 = \frac{13}{1} \).
- Step 2: Multiply the numerators and the denominators:
\[
\frac{3}{5} \times \frac{13}{1} = \frac{3 \times 13}{5 \times 1} = \frac{39}{5}
\]
- Step 3: The fraction \( \frac{39}{5} \) is already in its simplest form. Convert it to a mixed number (optional):
\[
\frac{39}{5} = 7 \frac{4}{5}
\]

Answer: \( \frac{39}{5} \) or \( 7 \frac{4}{5} \)

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#### 7. \( \frac{2}{7} \times 2 \)

- Step 1: Write the whole number as a fraction: \( 2 = \frac{2}{1} \).
- Step 2: Multiply the numerators and the denominators:
\[
\frac{2}{7} \times \frac{2}{1} = \frac{2 \times 2}{7 \times 1} = \frac{4}{7}
\]
- Step 3: The fraction \( \frac{4}{7} \) is already in its simplest form.

Answer: \( \frac{4}{7} \)

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#### 8. \( \frac{6}{8} \times 18 \)

- Step 1: Write the whole number as a fraction: \( 18 = \frac{18}{1} \).
- Step 2: Multiply the numerators and the denominators:
\[
\frac{6}{8} \times \frac{18}{1} = \frac{6 \times 18}{8 \times 1} = \frac{108}{8}
\]
- Step 3: Simplify the fraction by dividing both the numerator and the denominator by their GCD, which is 4:
\[
\frac{108 \div 4}{8 \div 4} = \frac{27}{2}
\]
- Step 4: Convert the improper fraction to a mixed number (optional):
\[
\frac{27}{2} = 13 \frac{1}{2}
\]

Answer: \( \frac{27}{2} \) or \( 13 \frac{1}{2} \)

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Final Answers:

\[
\boxed{
\begin{aligned}
1. & \ \frac{4}{5} \\
2. & \ 6 \\
3. & \ \frac{2}{3} \\
4. & \ \frac{15}{2} \text{ or } 7 \frac{1}{2} \\
5. & \ 4 \\
6. & \ \frac{39}{5} \text{ or } 7 \frac{4}{5} \\
7. & \ \frac{4}{7} \\
8. & \ \frac{27}{2} \text{ or } 13 \frac{1}{2}
\end{aligned}
}
\]