 # Rational Numbers

## A rational number can be expressed in the form of p/q, where p and q are integers and q≠0. Rational numbers include natural numbers, whole numbers, integers, fractions, decimals (recurring and non-recurring) and negative fractional quantity. Rational numbers are closed under the operations of addition, subtraction and multiplication but not under division. Rational numbers are commutative under the operations of addition and multiplication but not under subtraction and division. Rational numbers are associative under the operations of addition and multiplication but not under subtraction and division. The number ‘0’ is the additive identity for rational numbers. The number ‘1’ is the multiplicative identity for rational numbers. The additive inverse of a rational number p/q is –p/q and vice-versa. The multiplicative inverse or reciprocal of the rational number p/q is r/s if p/q × r/s = 1. Distributive property for rational numbers p, q and r is p (q + r) = pq + pr and p (q – r) = pq – pr. There are unlimited or infinite numbers between any two rational numbers. To find rational numbers between two rational numbers, make the denominators equal and then find the mean of two rational numbers. If ‘a’ and ‘b’ are two rational numbers, then (a+b)/2 is the mean of the rational numbers, such that a < (a + b)/2 < b. Rational numbers can be represented on a number line.

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