Question

Add or Subtract Fraction.

$-\frac{2}{3}-\left(-\frac{3}{4}\right)$

Short answer

The value of the given fraction is $\frac{1}{12}$.

Step-by-step solution

Step 1. Given information

Consider the expression.

$-\frac{2}{3}-\left(-\frac{3}{4}\right)$

Apply the rule:a-(-b)=a+b, where a and b are any real numbers.

$-\frac{2}{3}-\left(-\frac{3}{4}\right)=-\frac{2}{3}+\frac{3}{4}$

Step 3. Determine the whether the given fraction has the same denominator.

The given fraction does not have the same denominator.

So, find the least common denominator of $3$and role="math" localid="1644387616775" $4$.

$\begin{array}{rcl}3& =& 3·1\\ 4& =& 4·1\\ & \Rightarrow & LCM=3·4\\ & \Rightarrow & LCM=12\end{array}$

Step 4. Multiply the numerator and denominator of each fraction by a factor to get the denominator 12.

$\begin{array}{rcl}-\frac{2}{3}-\left(-\frac{3}{4}\right)& =& -\frac{2·4}{3·4}+\frac{3·3}{4·3}\\ & =& -\frac{8}{12}+\frac{9}{12}\end{array}$

Step 5. Apply the Fraction Addition rule:ac+bc=a+bc, where c≠0.

$\begin{array}{rcl}-\frac{2}{3}-\left(-\frac{3}{4}\right)& =& \frac{-8+9}{12}\\ & =& \frac{1}{12}\end{array}$

Hence, the value is $\frac{1}{12}$.