6th Grade - Order and Compare Rational Numbers

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.

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

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

$-9 \mathrm{and} - 98$

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.