Problem 82 - Introductory Algebra for College Students

Question

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{3}{10}+\frac{2}{15}$$

Step-by-Step Solution

Answer

The simplified answer is \( \frac{13}{30} \).

Step 1: Find a common denominator

A common denominator for the fractions \( \frac{3}{10} \) and \( \frac{2}{15} \) is achieved by determining the least common multiple between 10 and 15, which is 30.

Step 2: Rewrite the fractions with the common denominator and perform addition

The fractions \( \frac{3}{10} \) and \( \frac{2}{15} \) can be rewritten as \( \frac{9}{30} \) and \( \frac{4}{30} \) respectively. By adding the two fractions, we obtain \( \frac{9}{30} + \frac{4}{30} = \frac{13}{30} \)

Step 3: Reduce the answer to lowest terms

The fraction \( \frac{13}{30} \) is already in its simplest form, as no common factor other than 1 exists between the numerator and the denominator.