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

Last updated date: 17th Sep 2024
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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.

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