Learning Objectives
- Define rational numbers and represent them on a number line
- Compare and order rational numbers
- Perform operations on rational numbers
- Find rational numbers between two given rational numbers
Key Concepts
What are Rational Numbers?
A rational number is a number that can be written as p/q where p and q are integers and q ≠ 0.
Examples: 3/4, -5/7, 0, 2 (= 2/1), -3 (= -3/1)
Standard Form
A rational number is in standard form when the denominator is positive and the numerator and denominator have no common factor other than 1.
Operations on Rational Numbers
Addition/Subtraction: Make denominators equal (LCM), then add/subtract numerators.
Multiplication: (a/b) × (c/d) = (ac)/(bd)
Division: (a/b) ÷ (c/d) = (a/b) × (d/c)
Rational Numbers on the Number Line
Positive rational numbers lie to the right of 0, negative rational numbers lie to the left. Between any two rational numbers, there are infinitely many rational numbers.
Summary
Rational numbers include all integers, fractions, and their negatives. They can be represented on a number line and compared by making denominators equal. All four arithmetic operations can be performed on rational numbers. There are infinitely many rational numbers between any two rational numbers.
Important Terms
- Rational Number
- A number expressible as p/q where p, q are integers and q ≠ 0
- Equivalent Rational Numbers
- Different fractions that represent the same value (e.g., 1/2 = 2/4)
- Standard Form
- A fraction with positive denominator and no common factors between numerator and denominator
Quick Revision
- Every integer is a rational number (n = n/1)
- Every fraction is a rational number
- 0 is a rational number (0 = 0/1)
- To compare rational numbers, convert to the same denominator
- Between any two rational numbers, there are infinitely many rational numbers
Practice Tips
- Plot rational numbers on a number line for better understanding
- Practice finding rational numbers between two given numbers
- Simplify rational numbers to standard form regularly