Definition Of Rational Numbers Definition Of Rational Numbers In this unit we are going to learn about Definition of Rational Number. Rational numbers are the series of numbers which are infinite and endless. They can not be counted. They contain all the numbers which are either natural numbers, Whole numbers, Integers or even the fractions. All Rational numbers which can be grouped up under the set which defines as follows: The numbers which can be expressed in the form of p / q, where p and q both are integers and q is not equal to zero. Rational numbers can be all natural numbers which start from 1, 2, 3, 4 … …. And goes up to infinite. Rational numbers also have a set of Whole numbers 0, 1, 2, …….. up to infinite and the set of all integers which extend from negative infinite to positive infinite. It looks strange that these numbers are not in the form of p/q, but we must remember that all numbers n can be written as n / 1.
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Thus we observe that these numbers are written in form of p / q , so they are rational numbers. Moreover these numbers also consist of fractions. All mathematical operators can be performed on the rational numbers namely addition, subtraction, multiplication and division. Besides this logical operators can be performed on the set of rational numbers. It means that rational numbers can be compared and they can also be arranged in ascending or descending order. Lets see how the comparison of rational numbers can be done: If the two rational numbers are given such that one is positive and another negative, then a positive number is always greater than the negative number. Also we must remember that negative numbers are less than 0 and the positive numbers are always greater than zero. To compare the two positive or two negative rational numbers, we should first try to make the denominators same. Then the comparison of the numerators is done Similarly when we have to add or subtract the rational numbers we again proceed in the same pattern. We make the denominators of the rational numbers same and then perform the mathematical operation as directed. E.g.: Compare 2/3 and 5/2 Take the l.c.m of 3 and 2 as 6,, now we make the denominators of 2/3 and 5/2 as 6 We get 4/6 and 15/6 . Now in the two rational numbers we have 15 > 4 so 15/6 > 4/6 Solve 2/3 + 5/2
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Take the l.c.m of 3 and 2 as 6,, now we make the denominators of 2/3 and 5/2 as 6 We get 4/6 and 15/6 so above values can be written as = ( 4/6 ) + ( 15/6 ) = 19/6 Similarly subtraction operation can also be performed on the rational numbers. If we need to find the product of 2 rational numbers, then we simply multiply the numerators with the numerator and the denominator with the denominator. Eg: (2/5) * (3/7) = ( 2 * 3 ) / ( 5*7 ) = 6 / 35 Ans
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