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Chapter 1: Problem 77

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

Short Answer

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

Step by step solution

01

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.
02

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 \(\frac{2}{10}\).
03

Add the Fractions

Now, add the two fractions. This can be easily done by adding the numerators and keeping the common denominator: \(\frac{5}{10}+\frac{2}{10} = \frac{7}{10}\).
04

Simplify the Fraction

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

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