Reduce to simplest form. $\newline$ $-\frac{5}{12}-\left(-\frac{9}{3}\right)=$

Full solution

Q. Reduce to simplest form.

\newline

-\frac{5}{12}-\left(-\frac{9}{3}\right)=

Identify Numbers and Signs: Identify the numbers and their signs. $\newline$ We have two fractions, $-\frac{5}{12}$ and $-(-\frac{9}{3})$ . The second fraction has a double negative, which will become positive.
Simplify Double Negative: Simplify the double negative. $-(-\frac{9}{3})$ becomes $+\frac{9}{3}$ because the rule of signs states that a negative times a negative is a positive.
Simplify Fraction $\frac{9}{3}$ : Simplify the fraction $\frac{9}{3}$ . $\frac{9}{3}$ divided by $3$ equals $3$ . So, $-(-\frac{9}{3})$ simplifies to $+3$ .
Combine Numbers: Combine the two numbers. $\newline$ Now we have $-\frac{5}{12} + 3$ . To add these, we need a common denominator. Since $3$ is a whole number, we can write it as a fraction with a denominator of $12$ to get the common denominator. $3$ is the same as $\frac{36}{12}$ .
Rewrite Whole Number: Rewrite the whole number as a fraction. $3$ as a fraction with a denominator of $12$ is $\frac{36}{12}$ because $3 \times 12$ equals $36$ .
Add Fractions: Add the two fractions. $\newline$ Now we add $-\frac{5}{12}$ and $\frac{36}{12}$ . The common denominator is $12$ , so we add the numerators: $-5 + 36$ .
Perform Addition: Perform the addition. $\newline$ $-5 + 36 = 31$ . So, $-\frac{5}{12} + \frac{36}{12} = \frac{31}{12}$ .