Question

How do you simplify \[\dfrac{4}{15}+\dfrac{2}{4}\]?

Answer 1

Hint: We have been provided with an expression with two fractions which we have to add. We will first take the LCM of the denominators. Then we will multiply and divide the fractions by factors so that both become the same (equal to LCM). Now, the denominators are equal, we will now add the two fractions and reduce or simplify as much as possible.

Complete step by step solution:
According to the given question, we have two fractions whom we have to add and then simplify it. We will take the LCM first to equalize the denominator so that we can add them and proceed with further calculation.
We have the given expression as,
\[\dfrac{4}{15}+\dfrac{2}{4}\]
We can see the denominators are different so we cannot carry out any addition or subtraction.
So we will take the LCM of the denominators, that is, 15 and 4.
\[LCM(15,4)=60\]
We have the LCM of the denominators as 60. So, now we will multiply and divide the fractions with a suitable factor so that each of their denominators are equal to LCM. We get,
\[\Rightarrow \dfrac{4}{15}\times \dfrac{4}{4}+\dfrac{2}{4}\times \dfrac{15}{15}\]
We now proceed with the calculation and we get,
\[\Rightarrow \dfrac{4\times 4}{15\times 4}+\dfrac{2\times 15}{4\times 15}\]
\[\Rightarrow \dfrac{16}{60}+\dfrac{30}{60}\]
\[\Rightarrow \dfrac{16+30}{60}\]
\[\Rightarrow \dfrac{46}{60}\]
We will now reduce the obtained the fraction into its simplest form and we will get,
\[\Rightarrow \dfrac{23}{30}\]
Therefore, the simplest form of the expression is \[\dfrac{23}{30}\].

Note:
While taking the LCM, the numbers under consideration should be dealt carefully. And also, the question given to us was in fraction, so we need not simplify it too much so as to get it the form of decimal numbers, so we should give the answers in fraction form and in the reduced form.