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# Rational Numbers

• Rational numbers are the numbers that can be expressed in p/q form, where p and q are both integers and q ≠0.
• It comes from the word ‘ratio‘. Every rational number can be written as ratio of two integers.
• All fractions are rational numbers, but all rational numbers are not fractions.
• Positive Rationals: Numerator and Denominator both are either positive or negative. Example: 4/7,(-3/4)
• Negative Rationals: Numerator and Denominator both are of opposite signs. Example: (-2/11), (3/-4)
• Rational numbers are closed under the operations of addition, subtraction and multiplication.
• The operations addition and multiplication are
(i) commutative for rational numbers.
(ii) associative for rational numbers.
• The additive identity of rational numbers is 0.
• The multiplicative identity of rational numbers is 1.
• The additive inverse of the rational number a/b is -a/b and vice-versa.
• The reciprocal or multiplicative inverse of the rational number a/b is b/a.
• Distributivity of rational numbers: For all rational numbers a, b and c,
a(b + c) = ab + ac and and  a(b – c) = ab – ac
• Rational numbers can be represented on a number line.
• Between any two given rational numbers there are countless rational numbers.
• Reciprocal of 1 is 1 and that of -1 is also 1.
• Reciprocal of 0 is Not Defined.