Let's add the fractions [tex]\(\frac{2}{5}\)[/tex] and [tex]\(\frac{1}{2}\)[/tex] step by step.
1. Find a common denominator:
The denominators are 5 and 2. The least common multiple (LCM) of 5 and 2 is 10. So, we will use 10 as the common denominator.
2. Convert each fraction to an equivalent fraction with the common denominator:
For [tex]\(\frac{2}{5}\)[/tex], we need to find an equivalent fraction with a denominator of 10:
[tex]\[
\frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}
\][/tex]
For [tex]\(\frac{1}{2}\)[/tex], we need to find an equivalent fraction with a denominator of 10:
[tex]\[
\frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}
\][/tex]
So, we have:
[tex]\[
\frac{2}{5} = \frac{4}{10} \quad \text{and} \quad \frac{1}{2} = \frac{5}{10}
\][/tex]
3. Add the fractions:
Now that both fractions have the same denominator, we can add them directly:
[tex]\[
\frac{4}{10} + \frac{5}{10} = \frac{4 + 5}{10} = \frac{9}{10}
\][/tex]
4. Simplify the fraction (if needed):
The fraction [tex]\(\frac{9}{10}\)[/tex] is already in its simplest form, as 9 and 10 have no common factors other than 1.
Thus, the sum of [tex]\(\frac{2}{5}\)[/tex] and [tex]\(\frac{1}{2}\)[/tex] is:
[tex]\[
\frac{4}{10} + \frac{5}{10} = \frac{9}{10}
\][/tex]
So the solution to the problem is:
[tex]\[
\boxed{
\begin{array}{r}
\frac{2}{5} = \frac{4}{10} \\
+\quad \frac{1}{2} = \frac{5}{10} \\
\hline
\frac{9}{10}
\end{array}
}
\][/tex]
