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This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr. The symbols, notations, and properties of numbers that form the basis of algebra, as well as exponents and the rules of exponents, are introduced in this chapter. Each property of real numbers and the rules of exponents are expressed both symbolically and literally. Literal explanations are included because symbolic explanations alone may be difficult for a student to interpret.Topics covered in this module: understand the difference between variables and constants, be familiar with the symbols of operation, equality, and inequality, be familiar with grouping symbols, be able to correctly use the order of operations.

Overview

  • Variables and Constants
  • Symbols of Operation, Equality, and Inequality
  • Grouping Symbols
  • The Order of Operations

Variables and constants

A basic characteristic of algebra is the use of symbols (usually letters) to represent numbers.

Variable

A letter or symbol that represents any member of a collection of two or more numbers is called a variable .

Constant

A letter or symbol that represents a specific number, known or unknown is called a constant .

In the following examples, the letter x is a variable since it can be any member of the collection of numbers { 35 , 25 , 10 } . The letter h is a constant since it can assume only the value 5890.

Suppose that the streets on your way from home to school have speed limits of 35 mph, 25 mph, and 10 mph. In algebra we can let the letter x represent our speed as we travel from home to school. The maximum value of x depends on what section of street we are on. The letter x can assume any one of the various values 35,25,10.

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Suppose that in writing a term paper for a geography class we need to specify the height of Mount Kilimanjaro. If we do not happen to know the height of the mountain, we can represent it (at least temporarily) on our paper with the letter h . Later, we look up the height in a reference book and find it to be 5890 meters. The letter h can assume only the one value, 5890, and no others. The value of h is constant .

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Symbols of operation, equality, and inequality

Binary operation

A binary operation on a collection of numbers is a process that assigns a number to two given numbers in the collection. The binary operations used in algebra are addition, subtraction, multiplication, and division.

Symbols of operation

If we let x and y each represent a number, we have the following notations:
Addition x + y Subtraction x - y Multiplication x y ( x )( y ) x ( y ) x y Division x y x / y x ÷ y y x

Sample set a

a + b represents the sum of a and b .

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4 + y represents the sum of 4 and y .

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8 x represents the difference of 8 and x .

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6 x represents the product of 6 and x .

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a b represents the product of a and b .

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h 3 represents the product of h and 3.

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( 14.2 ) a represents the product of 14.2 and a .

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( 8 ) ( 24 ) represents the product of 8 and 24.

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5 6 ( b ) represents the product of 5,6, and b .

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6 x represents the quotient of 6 and x .

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Practice set a

Represent the product of 29 and x five different ways.

29 x , 29 x , ( 29 ) ( x ) , 29 ( x ) , ( 29 ) x

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If we let a and b represent two numbers, then a and b are related in exactly one of three ways:

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Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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