**Important Concepts and Formulas on Rational Numbers**

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.

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To study about rational numbers in detail -------- Click Here!