# Every rational number is a fraction ?

In this math chapter, we will try to answer the question if every rational number is fraction or not ?

To understand the explanation you should have basic understanding of the concept of fraction and rational numbers.

Let us revise the both the concept of fractions.

## What are fractions ?

The number which contain numerator and denominator are called fractions.

The fractions can also be a negative number.

Numbers like \mathtt{\frac{2}{3} ,\ \frac{4}{5} ,\ \frac{11}{13}} are examples of fractions.

Note that fractions can only be positive.

If you want to understand fractions in detail, click the red link.

## What are rational numbers ?

The numbers which can be arranged in the form of P / Q are called rational numbers.

Where P & Q are integers.

Numbers like \mathtt{\frac{1}{3} ,\ \frac{2}{7} ,\ 2.15,\ 3.97} are all examples of rational number.

Note that both the fractions and decimals can be the part of rational numbers.

If you want to understand the concept of rational number in detail, click the red link.

## Is every rational number a fraction ?

Given below are parts of rational number;

(a) Both positive & negative integers are part of rational numbers.

Numbers like -3, 0, 7, 22 are rational numbers but are not fractions.

(b) Numbers with negative numerators or denominators.

Numbers like \mathtt{\frac{-5}{11} ,\ \frac{6}{-25} ,\ \frac{-23}{3}} are all rational numbers but not fraction since fractions can’t be negative.

(c) Rational numbers as fraction

Numbers like \mathtt{\frac{1}{15} ,\ \frac{2}{17} ,\ \frac{3}{5}} are part of rational numbers and fraction.

Out of the above three part of rational numbers, only the part (c) are fractions.

Hence, all rational numbers are not fraction.

I hope you understood the concept, let us now solve some practice questions.

## Rational Numbers are fractions or not – Solved example

(i) Rational number \mathtt{\frac{6}{19}} is fraction or not.

Solution
The above rational number contain positive numerator and denominator.

Hence, the given rational number is a fraction.

(ii) Rational number \mathtt{\frac{-7}{29}} is fraction or not.

Solution
Since the number contain negative numerator, it is not a fraction.

(iii) Is the rational number 35, a fraction ?

The number 35 is not represented in form of numerator and denominator, hence it is not a fraction.

But if you want you can convert it into fraction by inserting denominator 1 without affecting the value of given number.

\mathtt{35\ \Longrightarrow \ \frac{35}{1}}

Now the number \mathtt{\frac{35}{1}} is a fraction.