Answer
Verified
425.7k+ views
Hint: In this question use the concept that whenever the fraction $\dfrac{p}{q}$ is in lowest form then the fraction has no common factors except 1, so first apply this then convert into mixed fraction.
Whenever the numerator is greater than the denominator, the fraction is called an improper fraction. For example $\dfrac{5}{4}$.
As we know that whenever the fraction $\dfrac{p}{q}$ is in lowest form then the fraction has no common factors except 1. And when a whole number and a fraction combined into one mixed number for example $2\dfrac{1}{2}$ (two and a half) then the fraction is called as a mixed fraction.
Now as we know mixed fraction $ = $ quotient \[\dfrac{{{\text{remainder}}}}{{{\text{divisor}}}}\]
So, using this property of fraction first convert into lowest form fraction then convert into mixed fraction.
$\left( i \right) = 4 \times 6\dfrac{1}{5} = 4 \times \dfrac{{31}}{5} = \dfrac{{124}}{5}$ So, this is in lowest form as $\dfrac{{124 \times 1}}{{5 \times 1}} = \dfrac{{124}}{5}$ has no common factors except 1.
And this is an improper fraction according to the above condition.
Now, convert it into mixed fraction, so as we know that when 124 is divided by 5 it is not completely divisible so this is written as
\[ \Rightarrow \dfrac{{124}}{5} = 24\dfrac{4}{5}\], because\[\left( {\left( {\left( {5 \times 24} \right) + 4} \right) = 124} \right)\]
(Where 5 is divisor, 4 is quotient and 1 is remainder)
Note: In such types of questions the key concept is that while converting the fraction into lowest form fraction i.e. in $\dfrac{p}{q}$ form where $q \ne 0$, then p and q must have no common factors except 1. So, if a fraction has some common factors simply cancel out, it will be converted into the lowest form fraction, then apply a mixed fraction formula to convert the fraction into mixed fraction, we will get the required answer.
Whenever the numerator is greater than the denominator, the fraction is called an improper fraction. For example $\dfrac{5}{4}$.
As we know that whenever the fraction $\dfrac{p}{q}$ is in lowest form then the fraction has no common factors except 1. And when a whole number and a fraction combined into one mixed number for example $2\dfrac{1}{2}$ (two and a half) then the fraction is called as a mixed fraction.
Now as we know mixed fraction $ = $ quotient \[\dfrac{{{\text{remainder}}}}{{{\text{divisor}}}}\]
So, using this property of fraction first convert into lowest form fraction then convert into mixed fraction.
$\left( i \right) = 4 \times 6\dfrac{1}{5} = 4 \times \dfrac{{31}}{5} = \dfrac{{124}}{5}$ So, this is in lowest form as $\dfrac{{124 \times 1}}{{5 \times 1}} = \dfrac{{124}}{5}$ has no common factors except 1.
And this is an improper fraction according to the above condition.
Now, convert it into mixed fraction, so as we know that when 124 is divided by 5 it is not completely divisible so this is written as
\[ \Rightarrow \dfrac{{124}}{5} = 24\dfrac{4}{5}\], because\[\left( {\left( {\left( {5 \times 24} \right) + 4} \right) = 124} \right)\]
(Where 5 is divisor, 4 is quotient and 1 is remainder)
Note: In such types of questions the key concept is that while converting the fraction into lowest form fraction i.e. in $\dfrac{p}{q}$ form where $q \ne 0$, then p and q must have no common factors except 1. So, if a fraction has some common factors simply cancel out, it will be converted into the lowest form fraction, then apply a mixed fraction formula to convert the fraction into mixed fraction, we will get the required answer.
Recently Updated Pages
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Find the values of other five trigonometric functions class 10 maths CBSE
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Write an application to the principal requesting five class 10 english CBSE
Difference Between Plant Cell and Animal Cell
a Tabulate the differences in the characteristics of class 12 chemistry CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
Discuss what these phrases mean to you A a yellow wood class 9 english CBSE
List some examples of Rabi and Kharif crops class 8 biology CBSE