Question

Add or Subtract Fraction.

$-\frac{3}{4}-\left(-\frac{4}{5}\right)$

Short answer

The value of the given fraction is $\frac{1}{20}$.

Step-by-step solution

Step 1. Given information

Consider the expression$-\frac{3}{4}-\left(-\frac{4}{5}\right)$

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

$-\frac{3}{4}-\left(-\frac{4}{5}\right)=-\frac{3}{4}+\frac{4}{5}$

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 $4$and $5$.

$\begin{array}{rcl}4& =& 4·1\\ 5& =& 5·1\\ & \Rightarrow & LCM=4·5\\ & \Rightarrow & LCM=20\end{array}$

Step 4. Multiply the numerator and denominator of each fraction by a factor to get the denominator 20.

$\begin{array}{rcl}-\frac{3}{4}-\left(-\frac{4}{5}\right)& =& -\frac{3·5}{4·5}+\frac{4·4}{5·4}\\ & =& -\frac{15}{20}+\frac{16}{20}\end{array}$

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

$\begin{array}{rcl}-\frac{3}{4}-\left(-\frac{4}{5}\right)& =& \frac{-15+16}{20}\\ & =& \frac{1}{20}\end{array}$

Hence, the value is $\frac{1}{20}$.