CHAPTER

1Introduction to Real Numbers and Algebraic Expressions

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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.