Question

What is the sum of \[2\dfrac{1}{3},3\dfrac{5}{6}\] and \[6\dfrac{2}{3}\] ?

Answer 1

Hint: We are given three mixed fractions in this question and we are asked to add them up and find the value of their sum. We will first write these mixed fractions into fractions and then we will write the mathematical expression to add these three fractions. We will have the expression as, \[\dfrac{7}{3}+\dfrac{23}{6}+\dfrac{20}{3}\]. We will then carry out the addition operation but before that we will make their denominators the same by taking their LCM first. We will then solve it further and reduce the expression as much as possible. Hence, we will have the sum of the expression.

Complete step-by-step solution:
According to the given question, we are given three mixed fractions in this question and we are asked to add them up and find the value of their sum.
The fractional form of the given respective mixed fractions with the addition operator is as follows,
\[\dfrac{7}{3}+\dfrac{23}{6}+\dfrac{20}{3}\]
We will now solve them. We will first have to make the denominators same by taking the LCM, so we have,
\[LCM(3,6)=6\]
So, we have the new expression as,
\[\Rightarrow \dfrac{7}{3}.\dfrac{2}{2}+\dfrac{23}{6}+\dfrac{20}{3}.\dfrac{2}{2}\]
We will now be solving the expression we have, we get,
\[\Rightarrow \dfrac{14}{6}+\dfrac{23}{6}+\dfrac{40}{6}\]
Adding up the terms, we get,
\[\Rightarrow \dfrac{14+23+40}{6}\]
So, we have the value of the asked expression as,
\[\Rightarrow \dfrac{77}{6}\]
Therefore, the sum of the given mixed fractions is \[\dfrac{77}{6}\].

Note: The mixed fraction cannot be directly used, so do not make the mistake of taking them directly without converting them either into a proper or an improper fraction. Also, while taking the LCM do not get confused with HCF, so be clear with LCM and HCF and also regarding where either of them are to be applied.