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How do you simplify $\left( {\dfrac{2}{5}} \right) + \left( {\dfrac{1}{5}} \right)$?

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Last updated date: 13th Jun 2024
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Answer
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Hint: Whenever we need to add two fractions we need to make the denominator common by taking the LCM of the two denominators. But whenever we have the denominators as the same number then we need to take that number as the LCM itself and add all the numerators of all the fractions whose denominators are the same.

Complete step by step solution:
Here we are given to simplify the term which is given as $\left( {\dfrac{2}{5}} \right) + \left( {\dfrac{1}{5}} \right)$.
Here we need to add the two fractions but we need to notice that both the denominators are the same. We need to know that when we are given the two fractions and we need to add them, then we need to take the LCM of the two fractions. This means that we need to make the denominator common.
For example: If we have the fractions sum as $\left( {\dfrac{2}{5}} \right) + \left( {\dfrac{1}{{10}}} \right)$ then we need to take the LCM of two denominators. The LCM of the $5{\text{ and 10}}$ is $10$.
Hence the fraction will become $\left( {\dfrac{2}{5}} \right) + \left( {\dfrac{1}{{10}}} \right) = \left( {\dfrac{4}{{10}}} \right) + \left( {\dfrac{1}{{10}}} \right) = \left( {\dfrac{{4 + 1}}{{10}}} \right) = \left( {\dfrac{5}{{10}}} \right)$.
Similarly here we are given that we have the fraction $\left( {\dfrac{2}{5}} \right) + \left( {\dfrac{1}{5}} \right)$.
Here already the denominator is the same in both the fractions that are added. Therefore we can take the LCM as the same number which is the denominator.
$\left( {\dfrac{2}{5}} \right) + \left( {\dfrac{1}{5}} \right)$
Taking LCM as $5$ we get:
$\left( {\dfrac{2}{5}} \right) + \left( {\dfrac{1}{5}} \right) = \left( {\dfrac{{2 + 1}}{5}} \right) = \left( {\dfrac{3}{5}} \right)$.

Hence we get the simplified form of $\left( {\dfrac{2}{5}} \right) + \left( {\dfrac{1}{5}} \right)$ as $\left( {\dfrac{3}{5}} \right)$.

Note:
Here the student must know what the LCM of two numbers is. The LCM means to take the least common multiple of those two numbers. In simple words, the LCM of two numbers represents the least number that is divisible by both the numbers.