Add the following fractions. Be sure to find the common denominator:

[tex]\[
\begin{array}{l}
\frac{2}{5} + \frac{1}{10}
\end{array}
\][/tex]

[tex]\[ = \][/tex]



Answer :

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].