To add the fractions [tex]\(\frac{2}{5}\)[/tex] and [tex]\(\frac{1}{10}\)[/tex], follow these steps:
1. Identify the denominators: The denominators of the fractions are 5 and 10.
2. Find the least common denominator (LCD): The LCD of 5 and 10 is 10. The least common denominator is the smallest number that both denominators divide into evenly.
3. Convert the fractions to have the same denominator:
- Convert [tex]\(\frac{2}{5}\)[/tex] to a fraction with a denominator of 10. Multiply the numerator and the denominator by 2 to get [tex]\(\frac{4}{10}\)[/tex].
[tex]\[
\frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}
\][/tex]
- [tex]\(\frac{1}{10}\)[/tex] already has a denominator of 10, so it remains the same.
4. Add the fractions:
- Now that the fractions have the same denominator, add the numerators together while keeping the denominator the same.
[tex]\[
\frac{4}{10} + \frac{1}{10} = \frac{4 + 1}{10} = \frac{5}{10}
\][/tex]
6. Simplify the fraction (if needed):
- In this case, [tex]\(\frac{5}{10}\)[/tex] can be simplified to [tex]\(\frac{1}{2}\)[/tex] by dividing the numerator and the denominator by their greatest common divisor, which is 5.
[tex]\[
\frac{5}{10} = \frac{5 \div 5}{10 \div 5} = \frac{1}{2}
\][/tex]
The final result of adding [tex]\(\frac{2}{5}\)[/tex] and [tex]\(\frac{1}{10}\)[/tex] is [tex]\(\frac{5}{10}\)[/tex], which simplifies to [tex]\(\frac{1}{2}\)[/tex].
