Question

What is $\dfrac{1}{4}+\dfrac{1}{6}$?

Answer 1

Hint: To obtain the solution of the equation given we will LCM method. Firstly we will find the LCM of the denominator terms and then we will multiply each fraction with a term so that the denominators become equal to the LCM. Then finally add the numerator and simplify it to get the desired answer.

Complete step-by-step answer:
The value is given as:
$\dfrac{1}{4}+\dfrac{1}{6}$……$\left( 1 \right)$
Now firstly we will find LCM of the denominator value by using common division method as:
$\begin{align}
  & 2\left| \!{\underline {\,
  4,6 \,}} \right. \\
 & 2\left| \!{\underline {\,
  2,3 \,}} \right. \\
 & 3\left| \!{\underline {\,
  1,3 \,}} \right. \\
 & 1,1 \\
\end{align}$
The factors obtained are:
$\left\{ 2,2,3 \right\}$
So the LCM is:
$\begin{align}
  & = 2\times 2\times 3 \\
 & = 12 \\
\end{align}$
We got the LCM as 12.
Next, we will multiply and divide 3 and 2 in the first and second term of the left side of equation (1) respectively as:
$\begin{align}
  & = \dfrac{1}{4}\times \dfrac{3}{3}+\dfrac{1}{6}\times \dfrac{2}{2} \\
 & = \dfrac{3}{12}+\dfrac{2}{12} \\
\end{align}$


Now as the denominator of both the fraction is equal we can add the numerator as:
$\begin{align}
  & = \dfrac{3+2}{12} \\
 & = \dfrac{5}{12} \\
\end{align}$
So we got the value as $\dfrac{5}{12}$
Hence $\dfrac{1}{4}+\dfrac{1}{6}$ is equal to $\dfrac{5}{12}$

Note: Fraction values are used to represent a part of a whole or number of equal parts of a whole is known as fraction. Fraction has two parts numerator and denominator where numerator is the value above the line and denominator is the value below the line. For example- $\dfrac{3}{5}$ we can say that by numerator the fraction has 3 equal parts and by denominator we can say that 5 parts make up a whole. The denominator can never be 0 as 0 part can never make up a whole. Ratio is very common example of fraction which tells the relation between two numbers expressed as a fraction.