## Pre-Requisires

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**Rational Numbers | Speed Notes**

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Rational numbers are closed under the operations of addition, subtraction and multiplication, But not in division. **(Scroll down to continue …)**

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The operations addition and multiplication are

(i) **commutative** for rational numbers.

(ii) **associative** for rational numbers.

The rational number 0 is the additive identity for rational numbers.

The additive inverse of the rational number **a/b** is **-a/b** and vice- versa.

The reciprocal or multiplicative inverse of the rational number

is if a/b is c/d if (a/b)(c/d) =1

**Distributive property of rational numbers:**

For all rational numbers a, b and c, a(b + c) = ab + ac

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.

The idea of mean helps us to find rational numbers between two rational numbers.

**Positive Rationals:** Numerator and Denominator both are either positive or negative.

**Example:** 2/3, -4/-5

**Positive Rationals:** Numerator and Denominator both are either positive or negative.

**Example:** -2/3, 4/-5

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