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 ?

The answer is **NO **!!!

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.