To add the fractions [tex]\(\frac{2}{5}\)[/tex] and [tex]\(\frac{1}{10}\)[/tex], follow these steps:
1. Find a Common Denominator:
The denominators here are 5 and 10. The least common denominator (LCD) for 5 and 10 is 10.
2. Convert Each Fraction to the Common Denominator:
- For [tex]\(\frac{2}{5}\)[/tex]:
[tex]\[
\frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}
\][/tex]
- For [tex]\(\frac{1}{10}\)[/tex]:
[tex]\[
\frac{1}{10} \text{ (already has the common denominator)}
\][/tex]
3. Add the Fractions:
- Now that both fractions have the same denominator, we can add the numerators:
[tex]\[
\frac{4}{10} + \frac{1}{10} = \frac{4 + 1}{10} = \frac{5}{10}
\][/tex]
4. Simplify the Result:
- [tex]\(\frac{5}{10}\)[/tex] can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 5:
[tex]\[
\frac{5}{10} = \frac{5 \div 5}{10 \div 5} = \frac{1}{2}
\][/tex]
So, the result of adding [tex]\(\frac{2}{5}\)[/tex] and [tex]\(\frac{1}{10}\)[/tex] is [tex]\(\frac{1}{2}\)[/tex].
Therefore, the sum of [tex]\(\frac{2}{5} + \frac{1}{10} = \frac{1}{2}\)[/tex].
