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CHAPTER
1Introduction to Real Numbers and Algebraic Expressions
Slide 2Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
1.1 Introduction to Algebra
1.2 The Real Numbers
1.3 Addition of Real Numbers
1.4 Subtraction of Real Numbers
1.5 Multiplication of Real Numbers
1.6 Division of Real Numbers
1.7 Properties of Real Numbers
1.8 Simplifying Expressions; Order of Operations
OBJECTIVES
1.1 Introduction to Algebra
Slide 3Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
a Evaluate algebraic expressions by substitution.b Translate phrases to algebraic expressions.
A traditional math expression consists of numerals and operation signs.
23 + 38 19 – 14
1.1 Introduction to Algebra
a Evaluate algebraic expressions by substitution.
Slide 4Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
7X5 73
An algebraic expression consists of variables, numerals, and operation signs.
x + 38 19 – y
When we replace a variable with a number, we say that we are substituting for the variable.
This process is called evaluating the expression.
5a x
y
1.1 Introduction to Algebra
a Evaluate algebraic expressions by substitution.
Slide 5Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
EXAMPLE
SolutionWe substitute 38 for x and 62 for y.
1.1 Introduction to Algebra
a Evaluate algebraic expressions by substitution.
A Evaluate x + y for x = 38 and y = 62.
Slide 6Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
38 +100
62
Also can be written on one line putting = signs between expressions. x + y = 38 + 62 = 100
Write the original expression x + y
EXAMPLE
SolutionWe substitute 72 for x and 8 for y:
x
y
x
y
1.1 Introduction to Algebra
a Evaluate algebraic expressions by substitution.
B Evaluate and for x = 72 and y = 8.
Slide 7Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
y
x
y
x
EXAMPLE
SolutionThis expression can be used to find the Fahrenheit temperature that corresponds to 30 degrees Celsius.
932
5
C
932
5
C 30932
5
270
325
54 32 86.
1.1 Introduction to Algebra
a Evaluate algebraic expressions by substitution.
C Evaluate for C = 30.
Slide 8Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
perofdecreased by increased by
ratio oftwiceless than more than
divided intotimesminusplus
quotient of product ofdifference ofsum of
divided bymultiplied bysubtracted from
added toDivisionMultiplicationSubtractionAddition
1.1 Introduction to Algebra
b Translate phrases to algebraic expressions.
Slide 9Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
EXAMPLE
Phrase Algebraic Expressiona) 9 more than yb) 7 less than xc) the product of 3 and twice w
1.1 Introduction to Algebra
b Translate phrases to algebraic expressions.
D Translate each phrase to an algebraic expression.
Slide 10Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
3•2w or 2w • 3x – 7
y + 9 or 9 + y
EXAMPLE
Phrase Algebraic Expression
Eight more than some number
One-fourth of a number
Two more than four times some number
Eight less than some number
Five less than the product of two numbers
x + 8, or 8 + x
4x + 2, or 2 + 4x
1, , or / 4
4 4
xx x
n – 8ab – 5
1.1 Introduction to Algebra
b Translate phrases to algebraic expressions.
E Translate each phrase to an algebraic expression.
(continued)
Slide 11Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
EXAMPLE
Phrase Algebraic Expression
Twenty-five percent of some number
Seven less than three times some number
0.25n 3w – 7
1.1 Introduction to Algebra
b Translate phrases to algebraic expressions.
E Translate each phrase to an algebraic expression.
Slide 12Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.