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Boundless Algebra
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Chapter 1

Numbers and Operations

Book Version 13
By Boundless
Boundless Algebra
Algebra
by Boundless
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Section 1
Introduction to Arithmetic Operations
Basic Operations

The basic arithmetic operations for real numbers are addition, subtraction, multiplication, and division.

Negative Numbers

Arithmetic operations can be performed on negative numbers according to specific rules.

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Fractions

A fraction represents a part of a whole and consists of an integer numerator and a non-zero integer denominator.

Complex Fractions

A complex fraction is one in which the numerator, denominator, or both are fractions, which can contain variables, constants, or both.

Introduction to Exponents

Exponential form, written bnb^nb​n​​, represents multiplying the base bbb times itself nnn times.

The Order of Operations

The order of operations is an approach to evaluating expressions that involve multiple arithmetic operations.

Section 2
Properties of Real Numbers
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Interval Notation

Interval notation uses parentheses and brackets to describe sets of real numbers and their endpoints.

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Absolute Value

Absolute value can be thought of as the distance of a real number from zero.

Sets of Numbers

A set is a collection of unique numbers, often denoted with curly brackets: {}.

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Factors

Any whole number greater than one can be factored, which means it can be broken down into smaller integers.

Section 3
Basic Applications of Arithmetic Operations
Percents

Percentages are used to express how large or small one quantity is relative to another quantity.

Averages

The arithmetic mean, or average, of a set of numbers indicates the "middle" or "typical" value of a data set.

Section 4
Radicals
Introduction to Radicals

Radical expressions yield roots and are the inverse of exponential expressions.

Adding, Subtracting, and Multiplying Radical Expressions

Radicals and exponents have particular requirements for addition and subtraction while multiplication is carried out more freely.

Fractions Involving Radicals

Root rationalization is a process by which any roots in the denominator of an irrational fraction are eliminated.

Imaginary Numbers

There is no such value such that when squared it results in a negative value; we therefore classify roots of negative numbers as "imaginary."

Section 5
Further Exponents
Rules for Exponent Arithmetic

There are rules for operating on numbers with exponents that make it easy to simplify and solve problems.

Negative Exponents

Numbers with negative exponents are treated normally in arithmetic operations and can be rewritten as fractions.

Rational Exponents

Rational exponents are another method for writing radicals and can be used to simplify expressions involving both exponents and roots.

Scientific Notation

Scientific notation is used to express a very large or small number in the form m⋅10nm \cdot 10^nm⋅10​n​​, where mmm has only one digit left of the decimal point.

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Boundless Algebra by Boundless
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Chapter 1
Numbers and Operations
  • Introduction to Arithmetic Operations
  • Properties of Real Numbers
  • Basic Applications of Arithmetic Operations
  • Radicals
  • Further Exponents
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Chapter 2
Introduction to Equations, Inequalities, and Graphing
  • Variables and Expressions
  • Introduction to Equations
  • Inequalities
  • Graphing and Equations of Two Variables
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