Problem 33 - Introductory Algebra for College Students

Question

Find each sum without the use of a number line. $$-\frac{5}{8}+\frac{3}{4}$$

Step-by-Step Solution

Answer

The sum of \( -\frac{5}{8} \) and \( \frac{3}{4} \) is \( \frac{1}{8}. \)

Step 1: Identifying like denominators

Firstly, we need to find a common denominator that both fractions can share. This will be 8, since \( \frac{3}{4} \) can be converted to the fraction \( \frac{6}{8} \) without changing its value, and -\( \frac{5}{8} \) already has 8 as the denominator.

Step 2: Converting fractions

Next, we convert \( \frac{3}{4} \) to \( \frac{6}{8} \). Now we have -\( \frac{5}{8} \) and \( \frac{6}{8} \), which can be added together due to their common denominator.

Step 3: Performing the addition

Perform the addition operation. Adding the numerators of the two fractions gives -5+6=1. Thus, the sum is \( \frac{1}{8} \).