Problem 68 - Introductory Algebra for College Students

Question

Simplify each series of additions and subtractions. $$-\frac{1}{2}-\frac{2}{3}-\left(-\frac{1}{3}\right)$$

Step-by-Step Solution

Answer

The simplified form of the series is \(-\frac{5}{6}\)

Step 1: Simplify parentheses

First, deal with the parentheses by multipying the negative sign on the outside with the fraction inside the parentheses, which yields: \(-\frac{1}{2}-\frac{2}{3}+\frac{1}{3}\)

Step 2: Identify common denominator

To add and subtract the fractions, a common denominator should be identified. The lowest common denominator (LCD) between 2 and 3 is 6.

Step 3: Transform fractions

Convert each fraction to an equivalent one with the common denominator of 6. They become: \(-\frac{3}{6}-\frac{4}{6}+\frac{2}{6}\)

Step 4: Perform the subtraction and addition

Perform the subtraction and addition of the fractions to simplify. It results in: \(-\frac{5}{6}\)