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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:

Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
what is titration
John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
hello friend how are you
Muhammad Reply
fine, how about you?
Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir Reply
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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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