Question

Convert the following mixed fraction $6\dfrac{5}{6}$ into a proper fraction?

Answer 1

Hint:This is a very basic question and only an elementary knowledge of fractions would be sufficient, here we will convert a mixed fraction into a proper fraction.If a fraction is improper or mixed from and given as $a\dfrac{b}{c}$ then the approach to convert it to a proper fraction by multiplying $c$ with $a$ and add it to $b$ to get the numerator and the denominator will remain the same.

Complete step-by-step answer:
Proper fraction : A fraction in which the numerator is less or of lower degree than the denominator.
Mixed fraction: A mixed number is a combination of a whole number and a fraction
The number needed to be converted to a proper fraction is $\left( {6\dfrac{5}{6}} \right)$.
Now we will simply implement the method of solving it as given in the hint i.e.If a fraction is improper or mixed from and given as $a\dfrac{b}{c}$ then the approach to convert it to a proper fraction by multiplying $c$ with $a$ and add it to $b$ to get the numerator and the denominator will remain the same.
So if we will compare the terms from the hint section then our answer will become and we get $ \Rightarrow a = 6,{\text{ }}b = 5{\text{ }}and{\text{ }}c = 6$.
Now finally we will apply the solving approach. On solving we will get
 $ \Rightarrow $Numerator$ = a \times c + b$ ...… $(1)$
$ \Rightarrow $Denominator $ = $ Remain Same … $(2)$
 Use equation$(1)$ and$(2)$ to solve,
$ \Rightarrow $Numerator$ = 6 \times 6 + 5$
$ \Rightarrow $Numerator$ = 36 + 5$
$ \Rightarrow $Numerator$ = 41$ … $(3)$
$ \Rightarrow $Denominator$ = 6$ … $(4)$
Write the equation $(3)$ and $(4)$ infraction format which could also be considered
as a proper fraction.
$ \Rightarrow $ Proper fraction$ = \dfrac{{\;Numerator}}{{\;Denominator}}$
$\therefore $ Proper fraction$ = \dfrac{{41}}{6}$
The answer to the question where conversion of mixed fraction into a proper fraction is asked can be found out as equal to $\dfrac{{41}}{6}$.

Note:The questions of these patterns are easy and can be solved very easily. Keep in mind, just the method of conversion from improper fraction to proper fraction. The only mistake students might commit is in solving the numerator part of the mixed fraction.