Rational Numbers

Understand the definition, explore algebraic properties, and place ratios on dynamic number lines and grids.

What is a Rational Number?

A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.

Formal Rule:
ℚ = { p/q : p, q ∈ ℤ and q ≠ 0 }

Core Examples:

Simple Fractions

Direct ratios: 1/2, -3/4, or 7/5.

All Integers

Any integer can have a denominator of 1: e.g. 5 = 5/1, -8 = -8/1.

Terminating Decimals

Decimals that end: e.g. 0.75 = 3/4, -1.25 = -5/4.

Repeating Decimals

Infinite repeating patterns: e.g. 0.333... = 1/3, 0.142857... = 1/7.

Did You Know?

The word Rational originates from the term ratio. The symbol used to denote rational numbers stands for Quotient.

Irrational numbers like π or √2 cannot be written as simple fractions because their decimal representations go on forever without repeating.

Math Teacher Platform Lesson series.