Fractions worksheet featuring multiplication exercises with whole numbers and fractions for math practice.

Fractions Worksheet Solution and Explanation

The worksheet involves multiplying fractions and whole numbers. Below is the step-by-step solution for each problem, along with explanations.

---

#### 1 a. \( 7 \times \frac{1}{3} \)

- Step 1: Write the whole number as a fraction: \( 7 = \frac{7}{1} \).
- Step 2: Multiply the numerators and the denominators:
\[
\frac{7}{1} \times \frac{1}{3} = \frac{7 \times 1}{1 \times 3} = \frac{7}{3}
\]
- Step 3: Simplify if possible (in this case, it is already in simplest form).

Answer: \( \frac{7}{3} \)

---

#### 1 b. \( \frac{6}{10} \times 6 \)

- Step 1: Write the whole number as a fraction: \( 6 = \frac{6}{1} \).
- Step 2: Multiply the numerators and the denominators:
\[
\frac{6}{10} \times \frac{6}{1} = \frac{6 \times 6}{10 \times 1} = \frac{36}{10}
\]
- Step 3: Simplify the fraction by dividing both numerator and denominator by their greatest common divisor (GCD), which is 2:
\[
\frac{36 \div 2}{10 \div 2} = \frac{18}{5}
\]

Answer: \( \frac{18}{5} \)

---

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

- Step 1: Write the whole number as a fraction: \( 6 = \frac{6}{1} \).
- Step 2: Multiply the numerators and the denominators:
\[
\frac{3}{5} \times \frac{6}{1} = \frac{3 \times 6}{5 \times 1} = \frac{18}{5}
\]
- Step 3: The fraction is already in simplest form.

Answer: \( \frac{18}{5} \)

---

#### 2 b. \( \frac{1}{5} \times 7 \)

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

Answer: \( \frac{7}{5} \)

---

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

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

Answer: \( 2 \)

---

#### 3 b. \( 2 \times \frac{2}{4} \)

- Step 1: Write the whole number as a fraction: \( 2 = \frac{2}{1} \).
- Step 2: Multiply the numerators and the denominators:
\[
\frac{2}{1} \times \frac{2}{4} = \frac{2 \times 2}{1 \times 4} = \frac{4}{4}
\]
- Step 3: Simplify the fraction:
\[
\frac{4}{4} = 1
\]

Answer: \( 1 \)

---

#### 4 a. \( \frac{3}{10} \times 8 \)

- Step 1: Write the whole number as a fraction: \( 8 = \frac{8}{1} \).
- Step 2: Multiply the numerators and the denominators:
\[
\frac{3}{10} \times \frac{8}{1} = \frac{3 \times 8}{10 \times 1} = \frac{24}{10}
\]
- Step 3: Simplify the fraction by dividing both numerator and denominator by their GCD, which is 2:
\[
\frac{24 \div 2}{10 \div 2} = \frac{12}{5}
\]

Answer: \( \frac{12}{5} \)

---

#### 4 b. \( 9 \times \frac{8}{9} \)

- Step 1: Write the whole number as a fraction: \( 9 = \frac{9}{1} \).
- Step 2: Multiply the numerators and the denominators:
\[
\frac{9}{1} \times \frac{8}{9} = \frac{9 \times 8}{1 \times 9} = \frac{72}{9}
\]
- Step 3: Simplify the fraction by dividing both numerator and denominator by their GCD, which is 9:
\[
\frac{72 \div 9}{9 \div 9} = \frac{8}{1} = 8
\]

Answer: \( 8 \)

---

#### 5 a. \( 3 \times \frac{1}{9} \)

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

Answer: \( \frac{1}{3} \)

---

#### 5 b. \( 8 \times \frac{1}{10} \)

- Step 1: Write the whole number as a fraction: \( 8 = \frac{8}{1} \).
- Step 2: Multiply the numerators and the denominators:
\[
\frac{8}{1} \times \frac{1}{10} = \frac{8 \times 1}{1 \times 10} = \frac{8}{10}
\]
- Step 3: Simplify the fraction by dividing both numerator and denominator by their GCD, which is 2:
\[
\frac{8 \div 2}{10 \div 2} = \frac{4}{5}
\]

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

---

#### 6 a. \( \frac{6}{10} \times 2 \)

- Step 1: Write the whole number as a fraction: \( 2 = \frac{2}{1} \).
- Step 2: Multiply the numerators and the denominators:
\[
\frac{6}{10} \times \frac{2}{1} = \frac{6 \times 2}{10 \times 1} = \frac{12}{10}
\]
- Step 3: Simplify the fraction by dividing both numerator and denominator by their GCD, which is 2:
\[
\frac{12 \div 2}{10 \div 2} = \frac{6}{5}
\]

Answer: \( \frac{6}{5} \)

---

#### 6 b. \( 10 \times \frac{3}{5} \)

- Step 1: Write the whole number as a fraction: \( 10 = \frac{10}{1} \).
- Step 2: Multiply the numerators and the denominators:
\[
\frac{10}{1} \times \frac{3}{5} = \frac{10 \times 3}{1 \times 5} = \frac{30}{5}
\]
- Step 3: Simplify the fraction:
\[
\frac{30}{5} = 6
\]

Answer: \( 6 \)

---

#### 7 a. \( \frac{1}{9} \times 3 \)

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

Answer: \( \frac{1}{3} \)

---

#### 7 b. \( \frac{7}{8} \times 7 \)

- Step 1: Write the whole number as a fraction: \( 7 = \frac{7}{1} \).
- Step 2: Multiply the numerators and the denominators:
\[
\frac{7}{8} \times \frac{7}{1} = \frac{7 \times 7}{8 \times 1} = \frac{49}{8}
\]
- Step 3: The fraction is already in simplest form.

Answer: \( \frac{49}{8} \)

---

#### 8 a. \( \frac{4}{9} \times 3 \)

- Step 1: Write the whole number as a fraction: \( 3 = \frac{3}{1} \).
- Step 2: Multiply the numerators and the denominators:
\[
\frac{4}{9} \times \frac{3}{1} = \frac{4 \times 3}{9 \times 1} = \frac{12}{9}
\]
- Step 3: Simplify the fraction by dividing both numerator and denominator by their GCD, which is 3:
\[
\frac{12 \div 3}{9 \div 3} = \frac{4}{3}
\]

Answer: \( \frac{4}{3} \)

---

#### 8 b. \( \frac{5}{7} \times 5 \)

- Step 1: Write the whole number as a fraction: \( 5 = \frac{5}{1} \).
- Step 2: Multiply the numerators and the denominators:
\[
\frac{5}{7} \times \frac{5}{1} = \frac{5 \times 5}{7 \times 1} = \frac{25}{7}
\]
- Step 3: The fraction is already in simplest form.

Answer: \( \frac{25}{7} \)

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
1 \text{ a. } \frac{7}{3} & 1 \text{ b. } \frac{18}{5} \\
2 \text{ a. } \frac{18}{5} & 2 \text{ b. } \frac{7}{5} \\
3 \text{ a. } 2 & 3 \text{ b. } 1 \\
4 \text{ a. } \frac{12}{5} & 4 \text{ b. } 8 \\
5 \text{ a. } \frac{1}{3} & 5 \text{ b. } \frac{4}{5} \\
6 \text{ a. } \frac{6}{5} & 6 \text{ b. } 6 \\
7 \text{ a. } \frac{1}{3} & 7 \text{ b. } \frac{49}{8} \\
8 \text{ a. } \frac{4}{3} & 8 \text{ b. } \frac{25}{7}
\end{array}
}
\]