## Introduction

- Rational Number =$\frac{\mathrm{numerator}}{\mathrm{denominator}}=\frac{\mathrm{x}}{\mathrm{y}},\mathrm{where}\mathrm{x}\mathrm{and}\mathrm{y}\mathrm{both}\mathrm{are}\mathrm{integers}\mathrm{and}\mathrm{y}\ne 0$
- A rational number is the ratio of two integers, meaning both the numerator and the denominator should be integers.
- Rational numbers can be represented on a number line.
- A rational number with a positive sign is greater than 0 and is to the
**right**of 0 on the number line. - A rational number with a negative sign is less than 0 and is to the
**left**of 0 on the number line. - Zero is a rational number.

## Comapre Rational Numbers

- To compare rational numbers, all the rational numbers should be in the same form, such as in decimals or ratios.
- To compare two rational numbers with the like/ same denominator, the rational number with the greater numerator is greater.
- To compare two rational numbers with unlike/ different denominators, cross-multiply the numerator of one rational number by the denominator of the other rational number.
- The denominator of the rational numbers must be positive when comparing two rational numbers.

For example, Compare the following: $-\frac{3}{7}\mathrm{and}-\frac{14}{3}$

Solution: Multiply the numerator of one rational number by the denominator of the other.

$\frac{3}{7}\u2921\frac{14}{3}$, and $-\frac{3}{7}\u2922-\frac{14}{3}$

$-3\times 3\mathrm{and}-14\times 7$

$-9\mathrm{and}-98$

The number that is closer to 0 is greater.

So, $-9-98$, hence $-\frac{3}{9}-\frac{14}{3}$

## Order Rational Numbers

- After comparing the rational number, order the rational numbers as required - least to greatest or greatest to least.

## Cheat sheet

- Rational numbers can be represented on the number line.
- The denominator of the rational numbers must be positive when comparing two rational numbers.

- Rishi Jethwa
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