Question

How do you simplify $\dfrac{1}{3} + \dfrac{1}{4}$?

Answer 1

Hint:
In order to solve this problem, we need to add two fractional numbers. To add two fractional terms, they must be represented with common denominators. In the given case the Lowest Common Denominator (LCD) for $3$ and $4$ will be $12$.

Complete step by step:
According to the given information, we have to simplify $\dfrac{1}{3} + \dfrac{1}{4}$.
We should be aware of the fact that to add two fractions it is a must to have them represented with common denominators.
In this case, the lowest common denominator is $12$.
Hence we will multiply each fraction by the necessary form of 1 to ensure the denominator is 12.
$\therefore \dfrac{1}{3} \times \dfrac{4}{4} = \dfrac{4}{{12}}$ and, $\dfrac{1}{4} \times \dfrac{3}{3} = \dfrac{3}{{12}}$
Now, we have obtained two fractional terms with the same denominator and thus, we can add two such terms.
Therefore,
$\dfrac{1}{3} + \dfrac{1}{4} = \dfrac{4}{{12}} + \dfrac{3}{{12}}$
$ \Rightarrow \dfrac{1}{3} + \dfrac{1}{4} = \dfrac{{4 + 3}}{{12}} = \dfrac{7}{{12}}$

We get that, addition of two fractions $\dfrac{1}{3}$and $\dfrac{1}{4}$gives us $\dfrac{7}{{12}}$.

Note:
Fractions represent equal parts of a whole or a collection. A fraction has two parts numerator and denominator. The number on the top of the line is called the numerator which tells how many equal parts of the whole or collection are taken. The number below the line is called the denominator which shows the total divisible number of equal parts the whole into or the total number of equal parts that are there in a collection.