Problem 67 - Introductory Algebra for College Students

Question

Simplify each series of additions and subtractions. $$-\frac{3}{4}-\frac{1}{4}-\left(-\frac{5}{8}\right)$$

Step-by-Step Solution

Answer

The simplified form of the given series of addition and subtraction is \(-\frac{3}{8}\)

Step 1: Identify and Separate Subtractions and Additions

The given expression is \(-\frac{3}{4}-\frac{1}{4}-\left(-\frac{5}{8}\right)\). The subtraction sign before \(\frac{5}{8}\) becomes an addition because of the negative sign within its brackets.

Step 2: Simplify

The expression now changes to \(-\frac{3}{4}-\frac{1}{4}+\frac{5}{8}\). Now, compute the subtraction and addition operations. The Least Common Multiple (LCM) of 8 and 4 is 8. The expressions \(-\frac{3}{4}\) and \(-\frac{1}{4}\) are made to have the same denominator as \(\frac{5}{8}\) to simplify the calculation.

Step 3: Resolve Fractions to have same denominator

Multiplying each of the fractions -3/4 and -1/4 by 2/2 to make the denominator 8, they therefore become \(-\frac{6}{8}\) and \(-\frac{2}{8}\) respectively. The expression will now be \(-\frac{6}{8} -\frac{2}{8} + \frac{5}{8}\)

Step 4: Perform Arithmetic Operations

Next, add and subtract as described, from left to right: \(-\frac{6}{8} - \frac{2}{8} = -\frac{8}{8}\) and then \(-\frac{8}{8} + \frac{5}{8} = -\frac{3}{8}\)

Step 5: Write the Final Answer

The simplified form of the given expression is \(-\frac{3}{8}\)