Problem 81 - Introductory Algebra for College Students

Question

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{3}{8}+\frac{5}{12}$$

Step-by-Step Solution

Answer

The solution to \(\frac{3}{8} + \frac{5}{12}\) is \(\frac{19}{24}\). This cannot be further simplified so it is the final answer.

Step 1: Find a Common Denominator

First, need to find a common denominator for the two fractions \(\frac{3}{8}\) and \(\frac{5}{12}\). The least common denominator (LCD) for 8 and 12 is 24.

Step 2: Convert Fractions

Next, convert the original fractions into equivalent fractions that have the common denominator. Multiply the numerator and denominator of \(\frac{3}{8}\) by 3 to get \(\frac{9}{24}\) and multiply \(\frac{5}{12}\) by 2 to get \(\frac{10}{24}\). Now have two new fractions: \(\frac{9}{24}\) and \(\frac{10}{24}\).

Step 3: Add Fractions

Now can add the two fractions, since they have the same denominator. Simply add the numerators together and leave the denominator the same. So, \(\frac{9}{24} + \frac{10}{24} = \frac{19}{24}\).

Step 4: Simplify

Finally, see if the fraction can be reduced or simplified to the lowest terms. Since there is no number that can evenly divide both the numerator 19 and the denominator 24, the fraction is already in its simplest form.