# Multiply the following fraction.

$\dfrac{2}{5}\times 5\dfrac{1}{4}$

Last updated date: 19th Mar 2023

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Answer

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Hint: This question contains a mixed fraction term. Any mixed fraction $a\dfrac{b}{c}$ can be simplified and written in the form \[\dfrac{ac+b}{c}\]. In this formula, a, b and c are any real numbers. Convert the mixed fraction to simple fraction using this formula and then apply rules for simple multiplication and division.

Complete step-by-step answer:

Before proceeding with the question, we must know the formula that will be required to solve this question.

Any mixed fraction in the form of $a\dfrac{b}{c}$ can be simplified and written in the form \[\dfrac{ac+b}{c}\] where a, b and c can be any real number.

In this question, we have to solve the question by multiplying the fraction $\dfrac{2}{5}\times 5\dfrac{1}{4}$. This fraction is containing a mixed fraction i.e. $5\dfrac{1}{4}$. Using the above formula by substituting a = 5, b = 1 and c = 4 in it, we can say that,

$\begin{align}

& 5\dfrac{1}{4}=\dfrac{5.4+1}{4} \\

& \Rightarrow 5\dfrac{1}{4}=\dfrac{21}{4} \\

\end{align}$

Substituting $5\dfrac{1}{4}=\dfrac{21}{4}$ in the question i.e. $\dfrac{2}{5}\times 5\dfrac{1}{4}$, we get,

$\dfrac{2}{5}\times 5\dfrac{1}{4}=\dfrac{2}{5}\times \dfrac{21}{4}$

None, this question has been converted into a question of simple multiplication and division which can be easily solved. Since none of the factors in numerator and denomination are cancelling, we can say,

$\begin{align}

& \dfrac{2}{5}\times \dfrac{21}{4}=\dfrac{42}{20} \\

& \Rightarrow \dfrac{21}{10} \\

\end{align}$

Hence the answer of the question is $\dfrac{21}{10}$.

Note: There is a possibility that one may commit a mistake while simplifying the mixed fraction term. It is a very common mistake to write a mixed fraction term $a\dfrac{b}{c}$ equal to $\dfrac{ab}{c}$. But since it is a mixed fraction, it has to be simplified using the formula \[a\dfrac{b}{c}=\dfrac{ac+b}{c}\]. Writing \[a\dfrac{b}{c}\] as \[\dfrac{ab}{c}\] will lead us to an incorrect answer.

Complete step-by-step answer:

Before proceeding with the question, we must know the formula that will be required to solve this question.

Any mixed fraction in the form of $a\dfrac{b}{c}$ can be simplified and written in the form \[\dfrac{ac+b}{c}\] where a, b and c can be any real number.

In this question, we have to solve the question by multiplying the fraction $\dfrac{2}{5}\times 5\dfrac{1}{4}$. This fraction is containing a mixed fraction i.e. $5\dfrac{1}{4}$. Using the above formula by substituting a = 5, b = 1 and c = 4 in it, we can say that,

$\begin{align}

& 5\dfrac{1}{4}=\dfrac{5.4+1}{4} \\

& \Rightarrow 5\dfrac{1}{4}=\dfrac{21}{4} \\

\end{align}$

Substituting $5\dfrac{1}{4}=\dfrac{21}{4}$ in the question i.e. $\dfrac{2}{5}\times 5\dfrac{1}{4}$, we get,

$\dfrac{2}{5}\times 5\dfrac{1}{4}=\dfrac{2}{5}\times \dfrac{21}{4}$

None, this question has been converted into a question of simple multiplication and division which can be easily solved. Since none of the factors in numerator and denomination are cancelling, we can say,

$\begin{align}

& \dfrac{2}{5}\times \dfrac{21}{4}=\dfrac{42}{20} \\

& \Rightarrow \dfrac{21}{10} \\

\end{align}$

Hence the answer of the question is $\dfrac{21}{10}$.

Note: There is a possibility that one may commit a mistake while simplifying the mixed fraction term. It is a very common mistake to write a mixed fraction term $a\dfrac{b}{c}$ equal to $\dfrac{ab}{c}$. But since it is a mixed fraction, it has to be simplified using the formula \[a\dfrac{b}{c}=\dfrac{ac+b}{c}\]. Writing \[a\dfrac{b}{c}\] as \[\dfrac{ab}{c}\] will lead us to an incorrect answer.

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