Question

How do you add \[\dfrac{{7\pi }}{6} + 2\pi \] ?

Answer 1

Hint: Here we are given two terms and asked to add it, we will combine the two terms by taking the LCM (least common multiple) considering the denominators and then simplify for the resultant required value.

Complete step-by-step answer:
Take the given expression: \[\dfrac{{7\pi }}{6} + 2\pi \]
The above expression can be re-written as –
 \[ = \dfrac{{7\pi }}{6} + \dfrac{{2\pi }}{1}\]
Take LCM ( Least common multiple) in the above expression. Multiply the second term within the numerator and the denominator so the resultant value remains the same.
 \[ = \dfrac{{7\pi }}{6} + \dfrac{{2\pi }}{1} \times \dfrac{6}{6}\]
Simplify the above expression –
 \[ = \dfrac{{7\pi }}{6} + \dfrac{{12\pi }}{6}\]
Simplify the above expression, when denominators are the same, we can combine the numerators.
 \[ = \dfrac{{7\pi + 12\pi }}{6}\]
Simplify the above terms finding the sum of terms in the numerator –
 \[ = \dfrac{{19\pi }}{6}\]
This is the required solution.
So, the correct answer is “ \[ \dfrac{{19\pi }}{6}\] ”.

Note: Always remember that when we have two terms to add, the denominator of both the terms should be the same then and then only we can add the numerator. Here we were given a fraction and so we converted the other given term in the form of an equivalent fraction. Fraction is the term expressed in the form of numerator upon the denominator.