Question

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

Answer 1

Hint: This question contains a mixed fraction term. Any mixed fraction $a{\displaystyle \frac{b}{c}}$ can be simplified and written in the form $${\displaystyle \frac{ac+b}{c}}$$. 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 $a{\displaystyle \frac{b}{c}}$ can be simplified and written in the form $${\displaystyle \frac{ac+b}{c}}$$ where a, b and c can be any real number.
In this question, we have to solve the question by multiplying the fraction ${\displaystyle \frac{2}{5}}\times 5{\displaystyle \frac{1}{4}}$. This fraction is containing a mixed fraction i.e. $5{\displaystyle \frac{1}{4}}$. Using the above formula by substituting a = 5, b = 1 and c = 4 in it, we can say that,
 $\begin{array}{rl}& 5{\displaystyle \frac{1}{4}}={\displaystyle \frac{5.4+1}{4}}\\ & \Rightarrow 5{\displaystyle \frac{1}{4}}={\displaystyle \frac{21}{4}}\end{array}$
Substituting $5{\displaystyle \frac{1}{4}}={\displaystyle \frac{21}{4}}$ in the question i.e. ${\displaystyle \frac{2}{5}}\times 5{\displaystyle \frac{1}{4}}$, we get,
${\displaystyle \frac{2}{5}}\times 5{\displaystyle \frac{1}{4}}={\displaystyle \frac{2}{5}}\times {\displaystyle \frac{21}{4}}$
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,
$\begin{array}{rl}& {\displaystyle \frac{2}{5}}\times {\displaystyle \frac{21}{4}}={\displaystyle \frac{42}{20}}\\ & \Rightarrow {\displaystyle \frac{21}{10}}\end{array}$
Hence the answer of the question is ${\displaystyle \frac{21}{10}}$.

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 $a{\displaystyle \frac{b}{c}}$ equal to ${\displaystyle \frac{ab}{c}}$. But since it is a mixed fraction, it has to be simplified using the formula $$a{\displaystyle \frac{b}{c}}={\displaystyle \frac{ac+b}{c}}$$. Writing $$a{\displaystyle \frac{b}{c}}$$ as $${\displaystyle \frac{ab}{c}}$$ will lead us to an incorrect answer.