Question

What is \[3\dfrac{1}{3}+4+\dfrac{2}{5}\]?

Answer 1

Hint: For solving this question you should know about the improper fraction of the fractions and about the least common denominator or lowest common denominator of a fraction. The least common denominator is the value of the denominator which can be divided by all denominators of the fractions and this denominator is also known as lowest common denominator because we take smallest value in it as a denominator.

Complete step by step answer:
According to our question we have to calculate the least common denominator to make sure the addition of \[3\dfrac{1}{3}\], 4 and \[\dfrac{2}{5}\] fractions.
Let us consider. If we multiply numerator and denominator by the same number then the fraction remains the same. Similarly, if we multiply numerators and denominators in another fraction too it will be the same number as before.
If we notice then it is clear that we add, subtract or compare these three functions, only if their denominators are the same. Hence only the proper way to find the least common denominator or lowest common denominator is to identify a common denominator to which all the denominators can be raised.
According to our question we have to add the \[3\dfrac{1}{3}+4+\dfrac{2}{5}\].
For solving these we will make their improper fraction or we will make the same denominator for all.
So, for this: \[3\dfrac{1}{3}=\dfrac{3\times 3+1}{3}=\dfrac{9+1}{3}=\dfrac{10}{3}\]
We can write \[\Rightarrow \dfrac{10}{3}+\dfrac{4}{1}+\dfrac{2}{5}\]
If we make all numerators same, then:
\[\begin{align}
  & \Rightarrow \dfrac{10}{3}\times \dfrac{5}{5}+\dfrac{4}{1}\times \dfrac{15}{15}+\dfrac{2}{5}\times \dfrac{3}{3} \\
 & \Rightarrow \dfrac{50}{15}+\dfrac{60}{15}+\dfrac{6}{15}=\dfrac{116}{15} \\
\end{align}\]

So, the \[3\dfrac{1}{3}+4+\dfrac{2}{5}\] is equal to \[\dfrac{116}{15}\].

Note: During calculating the least common denominator and lowest common denominator it is important to make the denominator as a number which is divided by all denominators of fraction. And it will be the lowest number for that operation which will be divided by all denominators. And then we can add or subtract these.