To add the fractions [tex]\(\frac{2}{5}\)[/tex] and [tex]\(\frac{7}{13}\)[/tex], we need to follow these steps:
1. Find a common denominator:
- To add fractions, both need the same denominator. The common denominator can be found by multiplying the denominators of the two fractions.
- For [tex]\(\frac{2}{5}\)[/tex] and [tex]\(\frac{7}{13}\)[/tex], we multiply [tex]\(5\)[/tex] and [tex]\(13\)[/tex]:
[tex]\[
5 \times 13 = 65
\][/tex]
- Thus, [tex]\(65\)[/tex] is the common denominator.
2. Adjust the numerators to match the common denominator:
- For the fraction [tex]\(\frac{2}{5}\)[/tex]:
[tex]\[
\frac{2}{5} = \frac{2 \times 13}{5 \times 13} = \frac{26}{65}
\][/tex]
- For the fraction [tex]\(\frac{7}{13}\)[/tex]:
[tex]\[
\frac{7}{13} = \frac{7 \times 5}{13 \times 5} = \frac{35}{65}
\][/tex]
3. Add the adjusted numerators:
- Now that both fractions have the same denominator, we can add the numerators:
[tex]\[
\frac{26}{65} + \frac{35}{65} = \frac{26 + 35}{65} = \frac{61}{65}
\][/tex]
Thus, the sum of [tex]\(\frac{2}{5}\)[/tex] and [tex]\(\frac{7}{13}\)[/tex] is:
[tex]\[
\frac{61}{65}
\][/tex]
So, [tex]\(\frac{2}{5} + \frac{7}{13} = \frac{61}{65}\)[/tex].
