Question

Explain the steps you would take to find the quotient of

1
3
÷ 4
3
.

Answer 1

To find the quotient of the fractions \( \frac{1}{3} \) and \( \frac{4}{3} \), follow these steps:

1. **Understand Division of Fractions**: Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of a fraction is obtained by swapping its numerator and denominator.

2. **Write the Expression**: Start with the division of fractions:
\[
\frac{1}{3} \div \frac{4}{3}
\]

3. **Convert to Multiplication**: Change the division to multiplication by using the reciprocal of \( \frac{4}{3} \):
\[
\frac{1}{3} \div \frac{4}{3} = \frac{1}{3} \times \frac{3}{4}
\]

4. **Multiply the Numerators and the Denominators**: Multiply the numerators together and the denominators together:
\[
\frac{1 \times 3}{3 \times 4} = \frac{3}{12}
\]

5. **Simplify the Result**: Now, simplify \( \frac{3}{12} \). Both the numerator and the denominator can be divided by their greatest common divisor, which is 3:
\[
\frac{3 \div 3}{12 \div 3} = \frac{1}{4}
\]

Thus, the quotient of \( \frac{1}{3} \div \frac{4}{3} \) is \( \frac{1}{4} \).