Question

Write a fraction less than $1$ , with denominator $5.$

Answer 1

Hint: A fraction whose value is less than $1$ is known as a proper fraction, while the fraction whose value is one or more than one is an improper fraction. A proper fraction is the fraction where the numerator is lower than the denominator.

Complete step-by-step answer:
We have to write a fraction whose denominator is $5$ and the value is less than $1$, so firstly let’s understand the types of fractions.
A proper fraction is the one whose numerator or top value is smaller than the denominator. For example, the fraction ${\displaystyle \frac{5}{8}}$ is a proper fraction as the numerator is smaller than the denominator.
An improper fraction is the one whose numerator is the same or larger than the denominator. For example, the fraction ${\displaystyle \frac{8}{5}}$ is an improper fraction as the numerator is larger than the denominator.
Here we have to write a fraction whose value is less than $1$ , so we have to write a proper fraction with denominator as $5$
So, all the positive numbers less than $5$ can be the numerator of the fraction

So we have the fractions as ${\displaystyle \frac{1}{5}},{\displaystyle \frac{2}{5}},{\displaystyle \frac{3}{5}},$ and ${\displaystyle \frac{4}{5}}$ all these are proper fractions with value less than $1$ and denominator $5$ .

Additional Information: A third type of fraction is known as a mixed fraction which is a combination of a number and a fraction. For example $2{\displaystyle \frac{1}{3}}$ is a mixed fraction with a number as $2$ and fraction as ${\displaystyle \frac{1}{3}}$.
Mixed fractions when converted into fractions always form an improper fraction and they are converted by multiplying the number with the denominator and then adding the numerator to the resultant which then becomes the new numerator and the denominator remains the same as previous .
For example converting the mixed fraction $2{\displaystyle \frac{1}{3}}$ as $2\times 3=6$ and adding the numerator $1$ to the result we get new numerator as $6+1=7$ and the denominator is same as $3$.
So our improper fraction becomes ${\displaystyle \frac{7}{3}}$ which is greater than $1$ .

Note: Do not take zero as a numerator of the fraction as ${\displaystyle \frac{0}{5}}=0$ which is not a fraction. Take the positive numbers from $1$ to denominator $-1$ as we are asked to write the fractions less than $1$ . If asked to write the fraction equal to $1$ , then we can write the numerator same as the denominator, which is equal to $1$