Question

How do you add \[\dfrac{2}{3} + \dfrac{3}{4}\]?

Answer 1

Hint: In the given question, we have been given two fractions. The denominators of the two fractions are different. So, to add them, we are going to have to apply the concept of the LCM.

Complete step-by-step answer:
We need to evaluate the following expression – \[\dfrac{2}{3} + \dfrac{3}{4}\].
Here, the denominators of the two fractions are different. So, we are going to need to apply the concept of LCM.
The LCM of the denominators is \[3 \times 4 = 12\].
Now, \[\dfrac{2}{3} \times \dfrac{4}{4} = \dfrac{8}{{12}}\]
And \[\dfrac{3}{4} \times \dfrac{3}{3} = \dfrac{9}{{12}}\]
Now, we add them as their denominators are now equal,
\[\dfrac{2}{3} + \dfrac{3}{4} = \dfrac{8}{{12}} + \dfrac{9}{{12}} = \dfrac{{17}}{{12}} = 1\dfrac{5}{{12}}\]

Note: In solving the fractions which have different denominators, we need to add them by making their denominators equal using the concept of LCM. If the denominators are equal, we just simply add the numerators and the denominators remain unchanged.