Problem 64 - Introductory Algebra for College Students

Question

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{1}{8} \div \frac{1}{4}$$

Step-by-Step Solution

Answer

\(\frac {1}{2}\)

Step 1: Reciprocal of the Divisor

Firstly, find the reciprocal of the fraction \(\frac {1}{4}\). This is done by swapping the numerator and the denominator. So, the reciprocal will be \(\frac {4}{1}\) or simply \(4\)

Step 2: Multiplication

Next step is to carry out the multiplication operation. Replace the division sign with multiplication and multiply \(\frac {1}{8}\) by the reciprocal of \(\frac {1}{4}\) which is \(4\). This gives \(\frac {1}{8} * 4 = \frac {4}{8}\)

Step 3: Reduction to Lowest Terms

Finally, reduce the fraction to its lowest terms by dividing both the numerator and the denominator by their greatest common divisor, which is \(4\). This gives \(\frac {4}{8} = \frac {1}{2}\)