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# Multiply the following fraction.$\dfrac{2}{5}\times 5\dfrac{1}{4}$ Verified
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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.

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.
Last updated date: 24th Sep 2023
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