Problem 68 - Introductory Algebra for College Students

Question

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{5}{13}+\frac{2}{13}$$

Step-by-Step Solution

Answer

The result of this operation is \(\frac{7}{13}\).

Step 1: Identify the Denominator

In this step, we identify the denominators of the fractions. Both fractions, \(\frac{5}{13}\) and \(\frac{2}{13}\), share the same denominator, which is 13. This will simplify the addition process.

Step 2: Addition of Fractions

As the fractions have the same denominator, the addition becomes a straightforward process. We add the numerators and put the result over the common denominator: \(\frac{5+2}{13} = \frac{7}{13}\).

Step 3: Simplify to the Lowest Term

Examine if the resulting fraction can be reduced to its lowest term. In this case, \(\frac{7}{13}\) cannot be simplified further, as 7 and 13 have no common factors apart from 1. Hence, \(\frac{7}{13}\) is the simplest form of the fraction.