Problem 139 - Introductory Algebra for College Students

Question

Describe how to add or subtract fractions with identical denominators. Provide an example with your description.

Step-by-Step Solution

Answer

To add or subtract fractions with identical denominators, ensure that the denominators are the same, then add or subtract the numerators while keeping the common denominator the same. Simplify the resulting fraction if possible. For example, \(\frac{3}{8} + \frac{5}{8} = 1\) and \(\frac{7}{4} - \frac{5}{4} = \frac{1}{2}\).

Step 1: Understand the concept of common denominators

Before you begin the operation, ensure that the fractions involved have the same denominator. For example, if we are to solve an equation like \(\frac{3}{8} + \frac{5}{8}\) or \(\frac{7}{4} - \frac{5}{4}\), notice that the denominators (8 and 4, respectively) are the same for all fractions involved.

Step 2: Add or subtract the numerators

Once you confirm that the fractions have common denominators, add or subtract the numerators while keeping the common denominator the same. For our examples, \(\frac{3}{8} + \frac{5}{8} = \frac{3+5}{8} = \frac{8}{8}\) and \(\frac{7}{4} - \frac{5}{4} = \frac{7-5}{4} = \frac{2}{4}\).

Step 3: Simplify if possible

If possible, simplify the resulting fraction to its simplest form. The fraction \(\frac{8}{8}\) simplifies to 1 because any number divided by itself equals 1. The fraction \(\frac{2}{4}\) simplifies to \(\frac{1}{2}\) because both the numerator and the denominator can be divided by 2.