Problem 80 - Introductory Algebra for College Students

Question

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{2}{5}+\frac{2}{15}$$

Step-by-Step Solution

Answer

So, the simplified answer to the problem \(\frac{2}{5} + \frac{2}{15}\) is \(\frac{8}{15}\)

Step 1: Find a Common Denominator

To add fractions, they must have a common denominator. In this case, the denominators are 5 and 15. A common denominator is a number that both 5 and 15 can divide into. The smallest such number is called the least common denominator. In this case, the least common denominator is 15.

Step 2: Convert the Fractions

Now that the common denominator is identified (15), the fractions can be converted so that they share this denominator. The first fraction \(\frac{2}{5}\) becomes \(\frac{2 \times 3}{5 \times 3} = \frac{6}{15}\) because to keep the value of fraction same, what is done in the denominator must be done in the numerator. The second fraction is already over the common denominator of 15.

Step 3: Perform the Addition

Adding the two fractions gives \(\frac{6}{15} + \frac{2}{15} = \frac{8}{15}\)

Step 4: Simplify the Fraction

It is always important to check if a fraction can be simplified to lower terms, however in this case \(\frac{8}{15}\) is already in its simplest form as 8 and 15 has no common factors than 1.