Class 8 Chapter 1: Rational Numbers

# Class 8 Chapter 1: Rational Numbers

Important Concepts and Formulas on Rational Numbers

1.      A number of the form p/q, where p, q Z and q 0, is called a rational number.

2.      A rational number p/q is said to be in standard form if q is positive and the integers p and q are co-prime numbers.

3.      The absolute value of a rational number is the distance of the rational number from 0 on the number line. For any rational number x, |x| = x if x ≥ 0 and |x| = –x if x < 0.

4.      When two rational numbers are added, subtracted or multiplied, then the result is also a rational number. Hence, rational numbers are closed under addition, subtraction and multiplication.

5.      Rational numbers are not closed under division. If zero is excluded then we can say rational numbers are closed under division.

6.      Addition and multiplication of rational numbers are commutative.

7.      Subtraction and division of rational numbers are not commutative.

8.      Addition and multiplication are associative for rational numbers.

9.      Subtraction and division are not associative for rational numbers.

10. For any set of rational numbers a, b and c, the distributive property of multiplication over addition and subtraction states that a(b + c) = ab + ac, and a(b – c) = ab – ac.

11. ‘0’ is the additive identity for rational numbers.

12. 1 is the multiplicative identity for rational numbers.

13. There are infinitely many rational numbers between any two given rational numbers.