Question

How do you add and simplify \[\dfrac{5}{7} + \dfrac{3}{4}\]?

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 – \[\dfrac{5}{7} + \dfrac{3}{4}\].
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 \[4 \times 7 = 28\].
Now, \[\dfrac{5}{7} \times \dfrac{4}{4} = \dfrac{{20}}{{28}}\]
And \[\dfrac{3}{4} \times \dfrac{7}{7} = \dfrac{{21}}{{28}}\]
Now, we add them as their denominators are now equal,

\[\dfrac{5}{7} + \dfrac{3}{4} = \dfrac{{20}}{{28}} + \dfrac{{21}}{{28}} = \dfrac{{41}}{{28}} = 1\dfrac{{13}}{{28}}\]

Note: In this question, we had to add two fractions. The most common mistake the students make is to simply add the numerators. Fractions are not whole numbers, so they cannot be simply added by just adding their numerators. First, we need to make their denominators equal, and then only we can add them. One other thing where the mistake occurs is when the fractions are added, and they are not converted to the lowest term. Converting the calculated fraction to the lowest term is very important.