Question

Simplify: $4\dfrac{5}{2} - 2\dfrac{3}{8} + 3\dfrac{7}{8}$ ?

Answer 1

Hint: For solving this question we will first check whether we can make the mixed fraction simpler or not and then convert the mixed fraction into the fraction. And then by taking the LCM we will solve this type of question.

Complete step by step answer:
So here we have the equation as $4\dfrac{5}{2} - 2\dfrac{3}{8} + 3\dfrac{7}{8}$
Now we will first convert it into the simplest form, so we get
$ \Rightarrow \not{4}\dfrac{5}{{\not{2}}} - \not{2}\dfrac{3}{{\not{8}}} + 3\dfrac{7}{8}$
So we get
$ \Rightarrow 2\dfrac{5}{1} - 1\dfrac{3}{4} + 3\dfrac{7}{8}$
Now converting the mixed fraction into the fraction, we get
$ \Rightarrow 10 - \dfrac{7}{4} + \dfrac{{31}}{8}$
Now on taking the LCM of the denominator and solving it we get
$ \Rightarrow \dfrac{{80 - 14 + 31}}{8}$
So on solving it, we get
$ \Rightarrow \dfrac{{97}}{8}$
And it can also be written as
$ \Rightarrow 12\dfrac{1}{8}$

Therefore, on simplifying $4\dfrac{5}{2} - 2\dfrac{3}{8} + 3\dfrac{7}{8}$, we get $12\dfrac{1}{8}$.

Note:
Here in this question we had come up with the concept of mixed fraction. A mixed fraction is numbers added with a proper fraction. For example, $2\dfrac{1}{4}$, it is the sum of $2units$ and an ${\dfrac{1}{4}^{th}}$ of a unit. Therefore, to convert the value of the mixed fraction into a proper fraction we have to add them.