Question

How do you simplify \[\dfrac{4}{18}+\dfrac{2}{9}\]?

Answer 1

Hint: We have to reduce the given expression in the simplest possible form. We know that for a fraction to add up or get subtracted we must have the denominators same. We will carry out the LCM (Least Common Multiple) first and then having the denominators same, we can carry out the addition of the two fractions given and hence we get the simplified form.

Complete step by step solution:
According to the given question, we have been given an expression which we have to simplify. To simplify this expression, we will be using multiplication operation and LCM as well.
LCM refers to Least Common Multiple, that is, it is the least number that is divisible by the numbers whose LCM is to be taken.
We will begin by writing the expression given first, we have,
\[\dfrac{4}{18}+\dfrac{2}{9}\]
We can see in the above expression that the denominators are different, so we will take the LCM of the denominators and we have, 9 and 18.
So, \[LCM(18,9)=18\]
We got the LCM as 18, so we will multiply and divide the fraction by a factor such that the denominator is 18 in both the fractions in the given expression. We have,
\[\Rightarrow \dfrac{4}{18}\times \dfrac{1}{1}+\dfrac{2}{9}\times \dfrac{2}{2}\]
Solving it further, we get,
\[\Rightarrow \dfrac{4}{18}+\dfrac{4}{18}\]
\[\Rightarrow \dfrac{4+4}{18}\]
\[\Rightarrow \dfrac{8}{18}\]
Reducing the terms, we get,
\[\Rightarrow \dfrac{4}{9}\]
Therefore, we have the simplified form of the expression, which is, \[\dfrac{4}{9}\].

Note:
LCM should not be confused with HCF. Both are two different concepts. LCM refers to the least number which is divisible by the numbers involved in LCM whereas HCF refers to the highest factors that are common between the numbers and which can divide the numbers involved in HCF.
For example-
\[LCM(9,18)=18\]
\[HCF(9,18)=9\]