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.
Is 0 rational?
- 2.
Is 2/3 + 1/4 rational?
- 3.
Write 0.6 as a fraction.
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Is 0.75 a rational number? Explain.
- 2.
Show that 2.333... is rational by writing it as a fraction.