Problem 78 - Introductory Algebra for College Students

Question

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{1}{3}+\frac{1}{5}$$

Step-by-Step Solution

Answer

The sum of \(\frac{1}{3}\) and \(\frac{1}{5}\) is \(\frac{8}{15}\).

Step 1: Find the least common denominator

In order to find the least common denominator of the fractions \(\frac{1}{3}\) and \(\frac{1}{5}\), identify the least common multiple (LCM) of 3 and 5. The least common multiple of 3 and 5 is 15, so the least common denominator is 15.

Step 2: Convert the fractions

Once the least common denominator has been found, convert both fractions to have this denominator. For \(\frac{1}{3}\), multiply both the numerator and the denominator by 5 to get \(\frac{5}{15}\). For \(\frac{1}{5}\), multiply both the numerator and the denominator by 3 to get \(\frac{3}{15}\).

Step 3: Add the fractions

Now that both fractions have the same denominator, they can be added together. Add the numerators and keep the common denominator the same. \(\frac{5}{15} + \(\frac{3}{15} = \frac{8}{15}\).

Step 4: Simplify the fraction

Finally, check if the result can be simplified. In this case, the fraction \(\frac{8}{15}\) is already in its simplest form as 8 and 15 have no common factors apart from 1.