Problem 71 - Introductory Algebra for College Students

Question

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{5}{8}+\frac{5}{8}$$

Step-by-Step Solution

Answer

The sum of the given fractions is \(1\frac{1}{4}\) or \(1.25\) in decimal form.

Step 1: Sum of Numerators

Since the denominators of the two fractions, \(\frac{5}{8}\) and \(\frac{5}{8}\), are identical, we can add their numerators together to get \(\frac{5+5}{8} = \frac{10}{8}\).

Step 2: Simplify the Fraction

Let's reduce the fraction to its lowest terms by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2. Therefore, we have \(\frac{10}{8} = \frac{10 ÷ 2}{8 ÷ 2} = \frac{5}{4}\).

Step 3: Representing as a Mixed Number

Since the numerator 5 is greater than the denominator 4, this fraction can be represented as a mixed number. We obtain this by performing the division operation: 5 divided by 4 gives 1 and leaves a remainder of 1. Thus, \(\frac{5}{4}=1\frac{1}{4}\).