Question

How do you write in simplest form \[\dfrac{2}{5} + \dfrac{1}{5}\] ?

Answer 1

Hint: Here the fractions given have the same denominator. So we will directly add the numerator with the same denominator. Then after that if the fraction can be simplified further like if the numerator is divisible by the denominator or have a common multiple then we will check that and will proceed with the same.

Complete step by step solution:
Given that,
 \[\dfrac{2}{5} + \dfrac{1}{5}\]
Since the denominators are same we will directly add the numerators like,
\[ = \dfrac{{2 + 1}}{5}\]
On adding the numerators,
\[ = \dfrac{3}{5}\]
This is the final answer because we cannot divide any number and they both have only 1 a a common multiple. So it is already simplified.
So, the correct answer is “\[ \dfrac{3}{5}\]”.

Note: Note that combining is not like directly adding or subtracting the terms because if the denominators of the terms or fractions are different.
\[\dfrac{a}{b} + \dfrac{c}{d} = \dfrac{{a + c}}{{b + d}} \] this is not correct way. So we need to take the LCM.
Rather if the terms had same denominator we can proceed very simply like,
\[\dfrac{a}{b} + \dfrac{c}{b} = \dfrac{{a + c}}{b}\]
As in our case above.