INDEX
Complex Numbers
Exponentiation
Algebraic Transformations
Algebraic Equations and Inequalities
Functions
Discrete Algebra
Basic Formulas
Graphics of Basic Functions
Numbers and Sets
Balloon

Introduction

About Algebra

Arithmetic Operations

Addition and Subtraction

Multiplication and Division

Criterions for Divisibility

Real Number System

Types of Numbers

Geometric Interpretation of Real Numbers

Irrational Number

Properties of Real Numbers

Fractions
Proportions

Property of Equal Proportions
Absolute Values

Graphical Illustrations

Sets and Intervals

Sets

Subsets

Operations with Sets

Intervals



The Property of Equal Proportions
Key Topics Remaining: Absolute Values » Sets » Intervals

If at least one of the real numbers    is non-zero, then the equalities

imply

.

Proof. By the given conditions,

.

Therefore,

Hence, the property.


Examples
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