Question

What is 4 divided by $\dfrac{2}{5}$?

Answer 1

Hint: We know very well that the division of two fractions is, nothing but, the multiplication of the first fraction with the reciprocal of the second fraction. Using this concept, we can find the result of division of 4 by $\dfrac{2}{5}$.

Complete step-by-step answer:
We know that when one fraction is divided by another fraction, then the process of division is exactly the same as the process of multiplication of the first fraction by the reciprocal of another fraction.
So, mathematically, we can write that when $\dfrac{a}{b}$ is divided by $\dfrac{c}{d}$, then the result is
$\dfrac{a}{b}\div \dfrac{c}{d}=\dfrac{a}{b}\times \dfrac{d}{c}$
We can also understand this concept using the fraction as division.
We know that a divided by b is written as $\dfrac{a}{b}$. Similarly, we can write that when $\dfrac{a}{b}$ is divided by $\dfrac{c}{d}$, the result is $\dfrac{\left( \dfrac{a}{b} \right)}{\left( \dfrac{c}{d} \right)}$.
We know by our knowledge of fractions, that this result is equivalent to $\dfrac{a}{b}\times \dfrac{d}{c}$, or $\dfrac{ad}{bc}$.
Here, in this question, we need to divide 4 by $\dfrac{2}{5}$.
Mathematically, we need to find $4\div \dfrac{2}{5}$.
We know very well that every integer can be expressed as a fraction, where that number is the numerator, and the denominator is 1. Hence, we can write the integer 4 as $\dfrac{4}{1}$.
And so, we now need to find, $\dfrac{4}{1}\div \dfrac{2}{5}$.
Now, using the concept explained above, we can write
$\dfrac{4}{1}\div \dfrac{2}{5}=\dfrac{4}{1}\times \dfrac{5}{2}$
We can cancel the common factor 2 from 2 and 4 on the right hand side. Thus, we now have
$\dfrac{4}{1}\div \dfrac{2}{5}=\dfrac{2}{1}\times \dfrac{5}{1}$
On evaluating the right hand side of this equation, we get
$\dfrac{4}{1}\div \dfrac{2}{5}=\dfrac{10}{1}$
Thus, when 4 is divided by $\dfrac{2}{5}$, the result is 10.

Note: We must remember that when this division process is changed to multiplication, the reciprocal of the second fraction is taken, and not the reciprocal of the first fraction. We must remember to cancel all the common factors from our final answer.