User:Chandhini K Nair/sandbox

RATIONAL NUMBERS AND FRACTIONS

It is quite often that we will be confused with rational numbers and fractions. Is there any difference between rational numbers and fractions?

Are they same?Let us have a discussion on that.This article gives an idea about rational numbers and fractions and helps to clarify some misconceptions.

What is a rational number? A number which is in the form p/q, where p and q are integers and q is not equal to zero.

Examples: 1/2, 3/5, -4/5, 7, 0.23, 6/-7...

What is a fraction? Generally, in simple words we can say that fraction is part of a whole. It is in the form p/q, where p and q are natural numbers and q not equal to zero.

Examples: 3/5, 3/8, 5/2...

By looking into these definitions we can identify the similarity and difference between a rational number and a fraction. Let us make clarifications in our observations.

Both rational number and fraction can be written in the form p/q where q is not equal to zero.The difference is in the case of rational numbers, p and q are integers and in the case of fraction, p and q are natural numbers (i.e. positive integers)

For example, 2/-5 is a rational number but not a fraction. WHY? Here 2 and -5 are integers, so 2/-5 is a rational number. Since -5 is not a positive integer 2/-5 is not a fraction.

3/2 both a rational number and a fraction, since 3 and 2 are positive integers.

IS EVERY FRACTION A RATIONAL NUMBER?

Yes, the reason is quite simple.The set natural numbers is a subset of integers. A number which is in the form p/q where p and q are natural numbers and q is not equal to zero is both rational and fraction. We represent all the fractions in this form and so every fraction is a rational number. In other words we can say that set of fractions is a subset of rational numbers.

IS EVERY RATIONAL NUMBER A FRACTION?

No. we had already seen the example of 2/-5. It is a rational number but not a fraction. A rational number p/q where q s not equal to zero become a fraction only when p and q are positive integers.

IS EVERY INTEGER IS A RATIONAL NUMBER?

Yes. 2 is not in the form p/q, then how can it be a rational number? Every integer a can be written in the form a/1 where 1 is an integer and not equal to zero, so every integer is a rational number. Is 0 a rational number? Yes 0 can be written as 0/1 where 1 is not equal to zero. But the converse is not true. We can say that so integers is a subset of rational numbers.

IS EVERY NATURAL NUMBER A FRACTION?

Every natural number n can be represented as n/1 where 1 is a natural number an not equal to zero.

Is 0 a fraction? NO. 0 can be written as 0/1 but here 0 is not a natural number.