Problem 64 - Introductory Algebra for College Students

Question

Simplify each series of additions and subtractions. $$2-\frac{3}{4}-\left(-\frac{7}{8}\right)$$

Step-by-Step Solution

Answer

Simplifying the series of additions and subtractions gives a final answer of \(2\frac{1}{8}\).

Step 1: Remove Parentheses

The first step is to remove the parentheses. This can be done by changing the subtraction sign before the parentheses to addition, which changes the sign of the fraction inside the parentheses. We have \(2-\frac{3}{4}+\frac{7}{8}\).

Step 2: Convert to Common Denominator

Next, convert the fractions to have the same denominator. The least common denominator of \(4\) and \(8\) is \(8\). So, convert \(\frac{3}{4}\) to \(\frac{6}{8}\). Now, the series looks like this: \(2-\frac{6}{8}+\frac{7}{8}\).

Step 3: Add and Subtract Fractions

Now, complete the addition and subtraction of the fractions: \(2+(-\frac{6}{8})+\frac{7}{8}=\frac{2}{1}+(-\frac{6}{8})+\frac{7}{8}=\frac{16}{8}+(-\frac{6}{8})+\frac{7}{8}=\frac{17}{8}\). Convert this improper fraction back into a mixed number to get \(\frac{17}{8}=2\frac{1}{8}\).

Step 4: Final Answer

Once simplified, the expression becomes \(2\frac{1}{8}\).