Problem 79 - Introductory Algebra for College Students

Question

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{3}{4}+\frac{3}{20}$$

Step-by-Step Solution

Answer

\(\frac{9}{10}\)

Step 1: Finding the Common Denominator

First, we have to find a common denominator for \(\frac{3}{4}\) and \(\frac{3}{20}\). A common practice is to multiply the denominators together, but it is better to use the lowest common multiple of the denominators to simplify the process. The lowest common multiple of 4 and 20 is 20.

Step 2: Converting to the Common Denominator

Next, convert both fractions to have this common denominator. Manipulate \(\frac{3}{4}\) to have 20 as a denominator, which can be done by multiplying both the numerator and denominator by 5. Our fractions then become \(\frac{15}{20}\) and \(\frac{3}{20}\).

Step 3: Performing the Operation

Now, add together the two fractions: \(\frac{15}{20} + \(\frac{3}{20}\) = \(\frac{18}{20}\). This result should be simplified to the lowest possible terms.

Step 4: Reducing to the Lowest Terms

Lastly, \(\frac{18}{20}\) can be simplified. Both 18 and 20 are divisible by 2, so divide both the numerator and denominator by 2 to reduce the fraction to its lowest terms. After doing so, the final answer is \(\frac{9}{10}\).