Question

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

Answer 1

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.