Question

How do you simplify $\dfrac{2}{3} + \dfrac{1}{6}$.

Answer 1

Hint: In this question, we have to add two numbers which are actually fractional numbers having different denominators. Use the common denominator or least common multiple, in order to make the denominators equal which will help us to add the numbers successfully. Finally we get the required answer.

Complete step-by-step solution:
It is given that the question stated as $\dfrac{2}{3} + \dfrac{1}{6}$
Here we have to simplify the denominator first
So we can write it as $3 \times 2 = 6$, which means that if we multiply $\dfrac{2}{3}$ by $6$ in both numerator and denominators, we will have a denominator that matches with the other number.
This is one of the most important steps while performing a fractional addition or subtraction.
Therefore, the common denominator will be 6, since we have a number that can be multiplied with 3 in order to have a common denominator like the other fractional number.
So, multiplying both the numerator and denominator by 2,
$ \Rightarrow \dfrac{{2 \times 2}}{{3 \times 2}} = \dfrac{4}{6}$
Now, we have both the fractional numbers with a common denominator. So, we can add them now.
Adding both fractional numbers,
$ \Rightarrow \dfrac{4}{6} + \dfrac{1}{6}$
Taking the numerators of both the fractions and adding them together, keeping the denominator common,
$ \Rightarrow \dfrac{{4 + 1}}{6}$
Adding the numerators,
$ \Rightarrow \dfrac{5}{6}$
We know that the above number cannot be divided, unless and until we want decimal numbers as an answer, so we can stop here.

Hence, the value of $\dfrac{2}{3} + \dfrac{1}{6} = \dfrac{5}{6}$

Note: When we have two fractional numbers, they can only be added when and if and only if they have a common denominator.
This happens because then both the numbers have equal numbers dividing them.
When a number is to be added or subtracted, it should have equal number of pieces like the number it is being added to or getting subtracted from each other
At such times, it is necessary to equalize the denominators.