Rational Numbers

11-1Properties of Rational Numbers

Overview

A rational number is any number that can be written as a/b with integers a, b and b ≠ 0.

Key ideas

  • All integers are rational.
  • Rationals are closed under +, −, ×, ÷ (b ≠ 0).
  • Density: between any two rationals lies another rational.

Worked examples

Example 1

Problem. Is 0.5 rational?

Solution. Yes, 1/2.

Example 2

Problem. Is −7 rational?

Solution. Yes, −7/1.

Practice

Try each one. Click Show answer when ready.

  1. 1.

    Is 0 rational?

  2. 2.

    Is 2/3 + 1/4 rational?

  3. 3.

    Write 0.6 as a fraction.

Challenge problems

A little tougher — great for test prep. Click Show answer when ready.

  1. 1.

    Is 0.75 a rational number? Explain.

  2. 2.

    Show that 2.333... is rational by writing it as a fraction.