Problem 63 - Introductory Algebra for College Students

Question

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{1}{14} \div \frac{1}{7}$$

Step-by-Step Solution

Answer

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

Step 1: Identify the reciprocal of the second fraction

The reciprocal of a fraction is found by swapping its numerator and denominator. For the fraction \(\frac{1}{7}\), its reciprocal is \(\frac{7}{1}\) or simply 7.

Step 2: Multiply first fraction by the reciprocal of the second

Now, replace the division operation with multiplication and use the reciprocal of the second fraction to perform the operation. This gives \(\frac{1}{14} * 7\).

Step 3: Perform the multiplication

When multiplying fractions, simply multiply the numerators and the denominators. This gives \(\frac{1*7}{14*1} = \frac{7}{14}\).

Step 4: Reduce to lowest terms

The fraction \(\frac{7}{14}\) can be simplified by dividing both the numerator and denominator by 7, their greatest common divisor. The simplified fraction is \(\frac{1}{2}\).