Rational Numbers
Work with fractions, decimals and percentages
Rational Numbers
A rational number is any number that can be written as a fraction a/b where a and b are integers and b ≠ 0. This includes integers, common fractions, decimal fractions (terminating and recurring) and percentages.
Example
Identifying Rational Numbers
Rational: 3/4, −2, 0.75, 0.333..., 150%, −7/2
Not rational: √2, π (these are irrational — non-terminating, non-repeating decimals)
Converting: −3 = −3/1, 0.8 = 4/5, 2.5 = 5/2
Operations with Rational Numbers
Apply the same rules for fractions and integers:
• Multiplication/Division: same signs → positive, different signs → negative
• Addition/Subtraction: find common denominators
Example
Calculations
−3/4 + 1/2 = −3/4 + 2/4 = −1/4
(−2/3) × (−6/5) = 12/15 = 4/5
−1.5 + 2.8 = 1.3
(−4) ÷ (−2/3) = (−4) × (−3/2) = 6
Note
Remember
All integers, fractions and terminating/recurring decimals are rational. Irrational numbers cannot be expressed as a simple fraction. The set of rational and irrational numbers together form the real numbers.
Key Vocabulary
Rational numberA number that can be written as a fraction a/b (b≠0)
IntegerA whole number (positive, negative or zero)
Recurring decimalA decimal with a pattern that repeats forever
Terminating decimalA decimal that ends (has a finite number of digits)
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Rational number
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