Rational Numbers

Rational Numbers

Concept

Rational numbers are one very common type of number that we usually study after integers in math. These numbers are in the form of $\fn_phv \frac{p}{q}$ , where p and q can be any integer and q ≠ 0. Most often people find it confusing to differentiate between fractions and rational numbers because of the basic structure of numbers, that is $\fn_phv \frac{p}{q}$ form. Fractions are made up of whole numbers while rational numbers are made up of integers as their numerator and denominator. The word “Rational” originated from the word “ratio”. So, rational numbers are very well related to the ratio concept of ratio.

Rules

Use the diagram, go through the number classifications, working from the outside in.

Example

Which category does this number belong to?
$\fn_phv 7.2%$

Solution

Rational numbers can all be written as fractions.

$\fn_phv 7.2% = \frac{72}{100}$

Thus, 7.2 is a rational number.

Practice Rational Numbers

Practice Problem 1

Select all of the rational numbers.

Practice Problem 2

Select all of the categories that this number belongs to.
$\fn_phv -5$

Practice Problem 3

Select all of the categories that this number belongs to.
$\fn_phv \sqrt{20}$

Real Numbers: The set of rational numbers together with the set of irrational numbers.

Rational Number – is a real number that can be written as a ratio of two integers (i.e. a simple fraction).

Irrational Number – is a real number that cannot be written as a simple fraction.

Pre-requisite Skill
Compare and Order Rational Numbers

Related Skills
Terminating and Repeating Decimals
Compare and Order Rational Numbers
Add and Subtract Like Fractions
Add and Subtract Unlike Fractions
Add and Subtract Mixed Numbers
Multiply Rational Numbers
Divide Rational Numbers
Convert Units