Answer :

To solve the expression

[tex]$$
\frac{2}{5} + \left(-\frac{13}{15}\right),
$$[/tex]

we first note that the two fractions have different denominators. The denominators are 5 and 15, and a common denominator for these is 15.

1. Convert [tex]$\frac{2}{5}$[/tex] to an equivalent fraction with denominator 15. Multiply the numerator and denominator by 3:

[tex]$$
\frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15}.
$$[/tex]

2. Now, rewrite the original expression using the common denominator:

[tex]$$
\frac{6}{15} + \left(-\frac{13}{15}\right).
$$[/tex]

3. Since the fractions have a common denominator, combine the numerators:

[tex]$$
\frac{6}{15} + \left(-\frac{13}{15}\right) = \frac{6 - 13}{15} = \frac{-7}{15}.
$$[/tex]

Thus, the final result of the calculation is:

[tex]$$
-\frac{7}{15}.
$$[/tex]

In decimal form, this is approximately [tex]$-0.4666666666666667$[/tex].

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Rewritten by : Barada