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RATIONAL NUMBERS

Positive Rational Numbers ‘A number that can be expressed in the form of p , where p and
A rational number whose q
numerator and denominator q both are integers and q ≠ 0 is called a rational number.
are both either positive or
negative. Standard Form of a Rational Equivalent Rational Numbers
Number If p is a rational number and
A rational number whose q
Negative Rational Numbers denominator is a positive m is a non-zero integer, then
÷
×
A rational number in which integer and the numerator and pm or pm is a rational
×
÷
either the numerator or denominator have no common qm qm
denominator is negative. number equivalent to p .
factor other than 1.
q
Absolute Value of a Rational Comparision of Rational Numbers
Number • Firstly, convert each rational number into its standard form by
p making denominators positive, if required.
If is a rational number, then
q • Find the LCM of the denominators of the rational numbers if the
its absolute value is represented denominators are unequal.
p p • Express each rational number to an equivalent rational number
as or . with the denominators equal to the LCM.
q q
• The rational number having greater numerator will be greater.

Operations on Rational Numbers

Addition and Subtraction of Rational Multiplication and Division of Rational Numbers
Numbers
Multiplication of a rational number by a whole number:
Addition or subtraction of rational numbers Product of a rational number and a whole number
with the same denominator:
Sum or difference ofnumerators Numerator × Whole number
= =
Commondenominator Denominator
Addition or subtraction of rational numbers Multiplication of a rational number by another rational
with different denominators: number:
• Convert the given rational numbers into Product of two rational number = Product of numerators
their standard form, if required. Product of denominators
• Find the LCM of denominators of rational Division of a rational number by an integer:
numbers.
 a  a  a 1
• Write the equivalent rational numbers to   ÷ integer =   × reciprocal of an integer =   × integer

b
b


b
the given rational numbers with this LCM
a
b
of the denominator. or Integer ÷  a = Integer × reciprocal of    = Integer ×   
b

• Add or subtract them.    b  a
Division of rational number by another rational number:
a ÷ c = a × Reciprocal of c  = a × d

b d b   d  b c
71 Rational Numbers