Problem 77 - Introductory Algebra for College Students

Question

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{1}{2}+\frac{1}{5}$$

Step-by-Step Solution

Answer

The result of the fraction addition is \(\frac{7}{10}\).

Step 1: Find a Common Denominator

First, a common denominator must be identified. This value is the least common multiple of the denominators of the given fractions, in this case 2 and 5. The least common multiple of 2 and 5 is 10.

Step 2: Convert the Fractions

Next, convert each fraction to an equivalent fraction with a denominator of 10. The fraction \(\frac{1}{2}\) is equivalent to \(\frac{5}{10}\) and the fraction \(\frac{1}{5}\) is equivalent to \(\frac{2}{10}\).

Step 3: Add the Fractions

Now, add the two fractions. This can be easily done by adding the numerators and keeping the common denominator: \(\frac{5}{10}+\frac{2}{10} = \frac{7}{10}\).

Step 4: Simplify the Fraction

Lastly, the obtained fraction is already in its simplest form so no further simplification is needed.