Question

9
Express the result in fraction form.



−
2
4
5
+
(
−
2
5
)
=
−2
5
4
​
+(−
5
2
​
)

Answer 1

To solve the expression

\[
-\frac{24}{5} + \left(-\frac{25}{2}\right),
\]

we first need a common denominator to combine the fractions.

The denominators here are 5 and 2. The least common denominator (LCD) of 5 and 2 is 10.

Now, we will convert each fraction to have the denominator of 10:

1. Convert \(-\frac{24}{5}\):

\[
-\frac{24}{5} = -\frac{24 \times 2}{5 \times 2} = -\frac{48}{10}.
\]

2. Convert \(-\frac{25}{2}\):

\[
-\frac{25}{2} = -\frac{25 \times 5}{2 \times 5} = -\frac{125}{10}.
\]

Now, we can add the two fractions together:

\[
-\frac{48}{10} + \left(-\frac{125}{10}\right) = -\frac{48 + 125}{10} = -\frac{173}{10}.
\]

Thus, the result of the operation is

\[
-\frac{173}{10}.
\]