Question

Add or Subtract Fraction.

$\frac{x}{3}+\frac{1}{4}$

Short answer

The value of the given fraction is $\frac{4x+3}{12}$.

Step-by-step solution

Step 1. Given information

Consider the expression.

$\frac{x}{3}+\frac{1}{4}$

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 $3$and $4$.

$\begin{array}{rcl}3& =& 3·1\\ 4& =& 2·2\\ & \Rightarrow & LCM=3·2·2\\ & \Rightarrow & LCM=12\end{array}$

Step 3. Multiply the numerator and denominator of each fraction by a factor to get the denominator 12.

$\begin{array}{rcl}\frac{x}{3}+\frac{1}{4}& =& \frac{x·4}{3·4}+\frac{1·3}{4·3}\\ & =& \frac{4x}{12}+\frac{3}{12}\end{array}$

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

$\frac{x}{3}+\frac{1}{4}=\frac{4x+3}{12}$

Hence, the value is $\frac{4x+3}{12}$.