Question

Is $\dfrac{5}{1}$ equal to $\dfrac{1}{5}?$

Answer 1

Hint: In this question we have been given two fractions. We will try to solve the values and see if they are equal or not. We will also check what type of factions they are on the basis of the numerator and denominator. There are mainly three types of such fractions: Proper fractions, Improper fractions and Mixed fractions.

Complete step by step answer:
Here we have two fractions; $\dfrac{5}{1}$ and $\dfrac{1}{5}$ .
Let us take the first fractions i.e.
$\dfrac{5}{1}$ .
It can also be written as
$\dfrac{5}{1} = 5$.
We can see that this is a whole number. So if we will place it on number line, it will come between $4$ and $6$ .
Now in the second fraction we have: $\dfrac{1}{5}$ .
The value of $\dfrac{1}{5}$is $0.2$ .
We can see that this number is different from the other number in the first fractions. Also if we place this value in the number line it will come between $0$ and $1$.
So we can say that both these fractions are not equal,
Or we can write this also as
 $\dfrac{5}{1} \ne \dfrac{1}{5}$
Also we know that a fraction in which the numerator is less than the denominator, it is called a proper fraction.
So we can say that $\dfrac{1}{5}$ is a proper fraction.
While the definition of improper fraction says that a fraction in which the numerator is equal to or larger than the denominator.
So the first fraction i.e.
 $\dfrac{5}{1}$ is an improper fraction.
Hence we can say that $\dfrac{5}{1}$ is not equal to $\dfrac{1}{5}$ .

Note:
 We should note that the other fraction is the reciprocal of the first fraction Or, we can say that $\dfrac{5}{1}$ and $\dfrac{1}{5}$ are reciprocals.
So their product has to be equal to one. i.e.
 $\dfrac{5}{1} \times \dfrac{1}{5} = 1$ .
We should also know that $\dfrac{1}{5}$ , in this proper fraction, means that a whole part is divided into five equal portions, each being $\dfrac{1}{5}$ .
A fraction that is represented with its quotient and remainder is called a mixed fraction. It is a combination of a whole number and a proper fraction.
As for example: $2\dfrac{1}{2}$ .