Question

What is: $\dfrac{2}{3} + \dfrac{{10}}{{15}}$ ?

Answer 1

Hint:Here in this question, we have \[ + \] symbol which represents the addition and we have to add the two numbers. The numbers are in the form of a fraction. We are going to simplify the sum of two fractions by taking the LCM of the denominators of the fractions such that the value of both the fractions remains unchanged and then add them up.

Complete step by step answer:
Here in this question, we have to add the numbers. As we know \[ + \] sign indicates the addition. The numbers are in the form of a fraction. In fraction we have 3 types: proper fraction, improper fraction and mixed fraction.

In the fraction the numerator is less than the denominator then it is the proper fraction. The numerator is greater than denominator then it is improper fraction. The fraction is a combination of whole number and fraction then it is a mixed fraction.Here in this question, both numbers are proper fractions.

Now consider, $\dfrac{2}{3} + \dfrac{{10}}{{15}}$. The values of the denominator are not the same so we take LCM for the denominator.Taking L.C.M. of denominators and multiplying the numerator and denominator of $\dfrac{2}{3}$ with $5$, we get,
$\dfrac{2}{3} + \dfrac{{10}}{{15}} = \dfrac{2}{3} \times \dfrac{5}{5} + \dfrac{{10}}{{15}}$
$ \Rightarrow \dfrac{2}{3} + \dfrac{{10}}{{15}} = \dfrac{{10}}{{15}} + \dfrac{{10}}{{15}}$
$ \Rightarrow \dfrac{2}{3} + \dfrac{{10}}{{15}} = \dfrac{{20}}{{15}}$
Cancelling the common factors in numerator and denominator, we get,
$ \therefore \dfrac{2}{3} + \dfrac{{10}}{{15}} = \dfrac{4}{3}$

Hence, we have $\dfrac{2}{3} + \dfrac{{10}}{{15}} = \dfrac{4}{3}$.

Note:While adding the two fractions we need to check the values of the denominator, if both denominators are having the same value then we can add the numerators. Suppose if the fractions have different denominators, we have to take LCM for the denominators and we simplify for further. Note that the resultant fraction is an improper fraction and can be simplified into a mixed fraction as $\dfrac{4}{3} = 1\dfrac{1}{3}$.