Answer :

To add the fractions [tex]\(\frac{2}{5}\)[/tex] and [tex]\(\frac{13}{15}\)[/tex], follow these steps:

1. Find a Common Denominator:
The numbers [tex]\(5\)[/tex] and [tex]\(15\)[/tex] are the denominators of the fractions. To add them, we need to find a common denominator. The least common multiple (LCM) of [tex]\(5\)[/tex] and [tex]\(15\)[/tex] is [tex]\(15\)[/tex].

2. Convert the Fractions:
- For [tex]\(\frac{2}{5}\)[/tex], convert it to have a denominator of [tex]\(15\)[/tex]:
[tex]\[
\frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15}
\][/tex]
- [tex]\(\frac{13}{15}\)[/tex] already has the denominator [tex]\(15\)[/tex], so it remains the same:
[tex]\[
\frac{13}{15}
\][/tex]

3. Add the Fractions:
Now that both fractions have the same denominator, you can add them by adding the numerators:
[tex]\[
\frac{6}{15} + \frac{13}{15} = \frac{6 + 13}{15} = \frac{19}{15}
\][/tex]

4. Convert to a Decimal:
[tex]\(\frac{19}{15}\)[/tex] as a decimal is approximately [tex]\(1.2667\)[/tex].

So, the result of [tex]\(\frac{2}{5} + \frac{13}{15}\)[/tex] is approximately [tex]\(1.2667\)[/tex] when expressed as a decimal.

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