Question

How do you simplify $\dfrac{2}{9} + \dfrac{1}{2}$?

Answer 1

Hint: Whenever we need to add two fractions we need to make the denominator common by taking the LCM of the two denominators. Then we just need to find the value of LCM which is actually the least number which is divisible by both $2{\text{ and 9}}$ completely. So we know that it is $18$.

Complete step by step solution:
Here we are given to simplify the term which is given as $\dfrac{2}{9} + \dfrac{1}{2}$
Here we need to add the two fractions but we need to notice that both the denominator are different and therefore we need to make the denominator common by making the denominator the LCM of the two denominators which are $2{\text{ and 9}}$ and we know that LCM is actually least number which is divisible by both $2{\text{ and 9}}$ completely. So we know that it is $18$.
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 $\dfrac{2}{9} + \dfrac{1}{2}$
So we know that we need to take its LCM which is $18$
Taking LCM as $18$ we get:
$\dfrac{2}{9} + \dfrac{1}{2}$$ = \left( {\dfrac{{4 + 9}}{{18}}} \right) = \left( {\dfrac{{13}}{{18}}} \right)$

Hence we get the simplified form of $\dfrac{2}{9} + \dfrac{1}{2}$ as $\left( {\dfrac{{13}}{{18}}} \right)$.

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.