Problem 87 - Introductory Algebra for College Students

Question

Find the value of each expression. $$\frac{5}{8}-\left(\frac{1}{2}-\frac{3}{4}\right)$$

Step-by-Step Solution

Answer

The result of the expression \(\frac{5}{8}-\left(\frac{1}{2}-\frac{3}{4}\right)\) is \(\frac{7}{8}\)

Step 1: Subtract the fractions within the bracket

For fraction subtraction, make the denominators the same. The Least Common Multiple (LCM) of 2 and 4 is 4, so we keep 4 as a common denominator, and convert 1/2 to 2/4. So, the equation becomes \(5/8 - (2/4 - 3/4)\). Subtracting these gives \(5/8 - (-1/4)\)

Step 2: Simplifying the equation

The negative sign before the bracket changes the signs of all terms inside the bracket. The equation becomes \(5/8 +1/4\).

Step 3: Adding the fractions

First, change the fractions to a common denominator. The LCM of 8 and 4 is 8. So, we convert 1/4 to 2/8. Now, the equation becomes \(5/8 + 2/8\), which gives \(7/8\) as the final result.