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This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr. Operations with algebraic expressions and numerical evaluations are introduced in this chapter. Coefficients are described rather than merely defined. Special binomial products have both literal and symbolic explanations and since they occur so frequently in mathematics, we have been careful to help the student remember them. In each example problem, the student is "talked" through the symbolic form.Objectives of this module: understand the meaning of an equation, be able to perform numerical evaluations.

Overview

  • Equations
  • Numerical Evaluation

Equations

Equation

An equation is a statement that two algebraic expressions are equal.

An equation is composed of three parts.

     =     

Each of the boxes represents an algebraic expression. An equation consists of two expressions separated by an equal sign. The equal sign makes the statement that the two expressions are equivalent, that is, they represent the same value. For example:

f = 32 a .
The equation expresses the relationship between the variables f and a . It states that the value of f is always 32 times that of a .

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y = 6 x + 8 .
The equation expresses the relationship between the variables x and y . It states that the value of y is always 8 more than 6 times the value of x .

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Numerical evaluation

Numerical evaluation

Numerical evaluation is the process of determining a value by substituting numbers for letters.

Formulas

In various areas (business, statistics, physics, chemistry, astronomy, sociology, psychology, etc.), particular equations occur quite frequently. Such equations are called formulas . Numerical evaluation is used frequently with formulas.

Sample set a

f = 32 a . Determine the value of f if a = 2. f = 32 ( 2 ) Replace a by 2. = 64

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p = 10 , 000 v .

This chemistry equation expresses the relationship between the pressure p of a gas and the volume v of the gas. Determine the value of p if v = 500 .

p = 10 , 000 500 Replace v by 500. = 20

On the Calculator
Type 10000 Press ÷ Type 500 Press = Display reads: 20

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z = x u s .

This statistics equation expresses the relationship between the variables z , x , u and s . Determine the value of z if x = 41 , u = 45 , and s = 1.3 . Round to two decimal places.

z = 41 45 1.3 = 4 1.3 = 3.08

On the Calculator
Type 41 Press Type 45 Press = Press ÷ Type 1.3 Press = Display reads: 3.076923 We'll round to 3.08

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p = 5 w 3 + w 2 w 1 .

This equation expresses the relationship between p and w . Determine the value of p if w = 5 .

p = 5 ( 5 ) 3 + ( 5 ) 2 ( 5 ) 1 = 5 ( 125 ) + 25 ( 5 ) 1 = 625 + 25 5 1 = 644

On the Calculator
Type 5 Press y x Type 3 Press = Press × Type 5 Press = Press + Type 5 Press x 2 Press Type 5 Press Type 1 Press = Display reads: 644

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Practice set a

f = 32 a . Determine the value of f if a = 6.

192

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p = 10 , 000 v . Determine the value of p if v = 250.

40

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F = 9 5 C + 32. Determine the value of F if C = 10.

50

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y = 9 x 14. Determine the value of y if x = 3.

13

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m = 5 p 3 2 p + 7. Determine the value of m if p = 2.

29

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Exercises

For the following problems, observe the equations and state the relationship being expressed.

x = 6 y

The value of x is equal to six times the value of  y .

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e = g 9

e  is equal to 9 less then the value of  g .

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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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