## RATIONAL NUMBERS - ESSENTIAL POINTS

• Rational Number: A number that can be expressed in the form p/q, where p and q are integers and q ≠ 0, is called a rational number. The numbers etc. are rational numbers.
• Any operation addition, multiplication, division or subtraction can be done with rational numbers.
• The operations addition and multiplication are
1. Commutative for rational numbers.
2. Associative for rational numbers.
• The rational number 0 is the additive identity for rational numbers.
• The rational number 1 is the multiplicative identity for rational numbers.
• The additive inverse of the rational number p/q is –p/q because p/q – p/q = 0.
• The reciprocal or multiplicative inverse of the rational number p/q is a/b if p/q x a/b = 1.
• Distributive property of rational numbers state that p(q + r) = pq + pr and p(q - r) = pq – qr where p, q, r are any three rational numbers.
• Rational numbers can be represented on a number line.
• Rational numbers are classified as Positive and Negative rational numbers. A positive rational number has both numerator and denominator positive. Negative rational number has either denominator or numerator negative. For example, 2/7 is a positive rational number whereas -3/7 is a negative rational number
• Positive rational numbers are greater than negative rational numbers.
• The number 0 is neither a positive nor a negative rational number.
• Between any two given rational numbers there are countless rational numbers. The idea of mean helps us to find rational numbers between two rational numbers.
• Reciprocal of 0 does not exist.
• Every rational number is not a fraction.