What are Rational numbers?

posted on: 12 Jan, 2012 | updated on: 11 Oct, 2012

Math is all about Numbers, and whenever we deal with mathematics we have to deal with different Types of Numbers. In the different categories of numbers, Rational numbers play an important and vital role. Now the query is What is a Rational Number?

The word 'Rational' is derived from the most popular Math term Ratio. Rational number can be defined as the number that is formed by dividing one Integer by the other. When a number is written as a simple fraction like $\frac{p}{q}$ where p and q are integers, then it is a Rational number. It is a Set of positive Fractions, negative fractions and zero. It is dented by I. where I is:

I = { 0, $\pm$ 1, $\pm$ 2, $\pm$ 3..................}.

Note:

Rational numbers can be both positive and negative. As we all know, there are two type real numbers exist in mathematics – rational number and irrational number. So, except irrational number all numbers like natural numbers(1,2,3…..), whole numbers(0,1,2,3..) and integers(….-2,-1,0,1,2….) are define in rational numbers and we all know that integers include all kind of numbers whether number is positive or negative. Now we discuss when rational numbers are positive and when rational numbers are negative: If a and b both are positive, then this kind of rational numbers (a/b) are called as a positive rational number. Like we have an integer ‘a’, which is equal to +5 and integer ‘b’, which is equal to +7 in rational number form (a/b), then this produces (5/7) which is a positive rational number. If one of integer between a and b are negative, then this kind of rational numbers (a/b) are called as a negative rational number. Like we have an integer a is equal to -7 and integer b is equal to +9 in rational number form (a/b), then this produces (-7/9), which is a negative rational number. If both integer a and b are negative, then this kind of rational numbers (a/b) are called as a positive rational number. For instance, we have an integer a, which is equal to -3 and integer b is equal to -4 in rational number form (a/b), then this produces (3/4) which is a positive rational number. Now, we can say that rational number can be positive and negative and it can be represented on number line.