# Multiply and express as a mixed fraction:

$4 \times 6\dfrac{1}{5}$.

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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.

Last updated date: 22nd Sep 2023

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