# 6th Grade - Order and Compare Rational Numbers

## Introduction

• Rational Number =
• 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:

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

$\frac{3}{7}⤡\frac{14}{3}$,  and $-\frac{3}{7}⤢-\frac{14}{3}$

The number that is closer to 0 is greater.

So, , hence

## 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.