Find Common Denominator: To add the fractions (-25/9) and (2/5), we need to find a common denominator. The least common multiple of 9 and 5 is 45.Convert to Equivalent Fractions: We convert each fraction to an equivalent fraction with a denominator of 45. For (-25/9), we multiply the numerator and denominator by 5. For (2/5), we multiply the numerator and denominator by 9. (-25/9) * (5/5) = -125/45 (2/5) * (9/9) = 18/45Add Fractions: Now we can add the two fractions with the common denominator of 45. (-125/45) + (18/45) = (-125 + 18)/45Perform Addition: We perform the addition in the numerator. -125 + 18 = -107Simplify Fraction: The sum of the two fractions is now a single fraction with the numerator -107 and the denominator 45. (-107)/45 is the simplified form of the sum, as the numerator and denominator have no common factors other than 1.

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$\frac{-25}{9}+\frac{2}{5}$

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\frac{-25}{9}+\frac{2}{5}

Find Common Denominator: To add the fractions $(-\frac{25}{9})$ and $(\frac{2}{5})$ , we need to find a common denominator. The least common multiple of $9$ and $5$ is $45$ .
Convert to Equivalent Fractions: We convert each fraction to an equivalent fraction with a denominator of $45$ . For $(-\frac{25}{9})$ , we multiply the numerator and denominator by $5$ . For $(\frac{2}{5})$ , we multiply the numerator and denominator by $9$ . $\newline$ $(-\frac{25}{9}) \times (\frac{5}{5}) = -\frac{125}{45}$ $\newline$ $(\frac{2}{5}) \times (\frac{9}{9}) = \frac{18}{45}$
Add Fractions: Now we can add the two fractions with the common denominator of $45$ . $\$\frac{-125}{45}$ + $\frac{18}{45}$ = $\frac{-125 + 18}{45}$ \)
Perform Addition: We perform the addition in the numerator. $\newline$ $-125 + 18 = -107$
Simplify Fraction: The sum of the two fractions is now a single fraction with the numerator $-107$ and the denominator $45$ . $(-107)/45$ is the simplified form of the sum, as the numerator and denominator have no common factors other than $1$ .