Introduction to Rational Numbers
Understanding numbers that can be expressed in the form p by q where p and q are integers and q is not equal to zero.
Definition
A rational number is a number that can be expressed in the form p/q, where p and q are integers and q is not equal to zero. They include all integers, fractions, and terminating or repeating decimals. Understanding them helps extend our number system beyond whole numbers and fractions.
Key formula
r = p/q where p, q in Z and q != 0
Worked examples
3/4 is a rational number because both 3 and 4 are integers and the denominator is not zero.
-5 can be written as -5/1, making it a rational number.
0 is a rational number because it can be expressed as 0/1.
Common mistakes
- • Thinking that a fraction with a zero denominator like 5/0 is a rational number.
- • Assuming whole numbers are not rational numbers.
Properties of Rational Numbers
Rational Numbers
Representation on Number Line
Rational Numbers
Rational Numbers Between Two Rational Numbers
Rational Numbers
Algebraic Expressions and Equations
Linear Equations in One Variable
Solving Equations with Variables on Both Sides
Linear Equations in One Variable
Reducing Equations to Simpler Form
Linear Equations in One Variable