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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.

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