Full solution

Q. Reduce to simplest form.

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-\frac{1}{3}-\left(-\frac{3}{5}\right)=

Identify Numbers and Signs: Identify the numbers and their signs. $\newline$ We have two fractions, $-\frac{1}{3}$ and $-(-\frac{3}{5})$ . The second fraction has a double negative, which means it will become positive.
Simplify Double Negative: Simplify the double negative. $\newline$ The double negative in $-(-\frac{3}{5})$ becomes positive, so the expression now reads $-\frac{1}{3} + \frac{3}{5}$ .
Find Common Denominator: Find a common denominator for the fractions. $\newline$ The common denominator for $3$ and $5$ is $15$ . We will convert both fractions to have this common denominator.
Convert to Common Denominator: Convert each fraction to have the common denominator of $15$ . For $-\frac{1}{3}$ , we multiply the numerator and denominator by $5$ to get $-\frac{5}{15}$ . For $\frac{3}{5}$ , we multiply the numerator and denominator by $3$ to get $\frac{9}{15}$ .
Perform Subtraction: Perform the subtraction with the new fractions. $\newline$ Now we have $-\frac{5}{15} + \frac{9}{15}$ . Adding these together gives us $\frac{4}{15}$ .
Check for Simplification: Check if the result can be simplified further. $\newline$ The fraction $\frac{4}{15}$ cannot be simplified further as $4$ and $15$ have no common factors other than $1$ .