Question

find the quotient. $$ \frac{1}{8} \div \frac{1}{2} $$

Short answer

The quotient of \(\frac{1}{8}\) divided by \(\frac{1}{2}\) is \(\frac{1}{4}\).

Step-by-step solution

Reciprocal of the divisor

Transform the problem by finding the reciprocal of the divisor. The reciprocal of a fraction is obtained by switching the numerator and the denominator. Hence, the reciprocal of \(\frac{1}{2}\) is \(\frac{2}{1}\) or simply 2.

Transform Division into Multiplication

Replace the division operation with a multiplication operation using the reciprocal of the divisor from the previous step. This transforms the problem into \(\frac{1}{8} \times 2 = \frac{1 \times 2}{8 \times 1}\).

Solve the Multiplication

Multiplication of fractions is carried out by multiplying the numerators and the denominators separately. Hence, \(\frac{1 \times 2}{8 \times 1}\) equals \(\frac{2}{8}\).

Simplify the Fraction

2 and 8 have a common divisor, 2. Divide both the numerator and the denominator by this common divisor to simplify the fraction. Thus, \(\frac{2}{8}\) simplifies to \(\frac{1}{4}\).