Question

Add or Subtract Fraction.

$\frac{x}{5}-\frac{1}{4}$

Short answer

The value of the given fraction is $\frac{4x-5}{20}$.

Step-by-step solution

Step 1. Given information

Consider the expression.

$\frac{x}{5}-\frac{1}{4}$

Step 2. 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 $5$and $4$.

$\begin{array}{rcl}5& =& 5·1\\ 4& =& 2·2\\ & \Rightarrow & LCM=5·2·2\\ & \Rightarrow & LCM=20\end{array}$

Step 3. Multiply the numerator and denominator of each fraction by a factor to get the denominator 20.

$\begin{array}{rcl}\frac{x}{5}-\frac{1}{4}& =& \frac{x·4}{5·4}-\frac{1·5}{4·5}\\ & =& \frac{4x}{20}-\frac{5}{20}\end{array}$

Step 4. Apply the Fraction Addition rule:ac+bc=a+bc, where c≠0.

$\frac{x}{5}-\frac{1}{4}=\frac{4x-5}{20}$

Hence, the value is $\frac{4x-5}{20}$.