Dividing Fractions Worksheet with Answers - Example Problems and Solutions.

Problem: Dividing Fractions Worksheet

The worksheet involves solving division problems with fractions. The general rule for dividing fractions is:

\[
\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}
\]

This means you multiply the first fraction by the reciprocal of the second fraction.

Let's solve each problem step by step.

---

#### a) \( \frac{2}{3} \div \frac{4}{5} \)

1. Rewrite the division as multiplication by the reciprocal:
\[
\frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4}
\]

2. Multiply the numerators and the denominators:
\[
\frac{2}{3} \times \frac{5}{4} = \frac{2 \times 5}{3 \times 4} = \frac{10}{12}
\]

3. Simplify the fraction:
\[
\frac{10}{12} = \frac{5}{6} \quad \text{(divide numerator and denominator by their greatest common divisor, which is 2)}
\]

Final Answer for a):
\[
\boxed{\frac{5}{6}}
\]

---

#### b) \( \frac{3}{5} \div \frac{5}{6} \)

1. Rewrite the division as multiplication by the reciprocal:
\[
\frac{3}{5} \div \frac{5}{6} = \frac{3}{5} \times \frac{6}{5}
\]

2. Multiply the numerators and the denominators:
\[
\frac{3}{5} \times \frac{6}{5} = \frac{3 \times 6}{5 \times 5} = \frac{18}{25}
\]

3. The fraction is already in simplest form:
\[
\frac{18}{25}
\]

Final Answer for b):
\[
\boxed{\frac{18}{25}}
\]

---

#### c) \( \frac{1}{4} \div \frac{1}{3} \)

1. Rewrite the division as multiplication by the reciprocal:
\[
\frac{1}{4} \div \frac{1}{3} = \frac{1}{4} \times \frac{3}{1}
\]

2. Multiply the numerators and the denominators:
\[
\frac{1}{4} \times \frac{3}{1} = \frac{1 \times 3}{4 \times 1} = \frac{3}{4}
\]

3. The fraction is already in simplest form:
\[
\frac{3}{4}
\]

Final Answer for c):
\[
\boxed{\frac{3}{4}}
\]

---

#### d) \( \frac{8}{10} \div \frac{7}{8} \)

1. Rewrite the division as multiplication by the reciprocal:
\[
\frac{8}{10} \div \frac{7}{8} = \frac{8}{10} \times \frac{8}{7}
\]

2. Multiply the numerators and the denominators:
\[
\frac{8}{10} \times \frac{8}{7} = \frac{8 \times 8}{10 \times 7} = \frac{64}{70}
\]

3. Simplify the fraction:
\[
\frac{64}{70} = \frac{32}{35} \quad \text{(divide numerator and denominator by their greatest common divisor, which is 2)}
\]

Final Answer for d):
\[
\boxed{\frac{32}{35}}
\]

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Summary of Answers:

\[
\boxed{\frac{5}{6}, \frac{18}{25}, \frac{3}{4}, \frac{32}{35}}
\]