CHAPTER 1 Introduction to Real Numbers and Algebraic Expressions Slide 2Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. 1.1Introduction to Algebra 1.2The Real Numbers 1.3Addition of Real Numbers 1.4Subtraction of Real Numbers 1.5Multiplication of Real Numbers 1.6Division of Real Numbers 1.7Properties of Real Numbers 1.8Simplifying Expressions; Order of Operations

OBJECTIVES 1.1 Introduction to Algebra Slide 3Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. aEvaluate algebraic expressions by substitution. bTranslate phrases to algebraic expressions.

A traditional math expression consists of numerals and operation signs – Introduction to Algebra a Evaluate algebraic expressions by substitution. Slide 4Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

An algebraic expression consists of variables, numerals, and operation signs. x – 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. 1.1 Introduction to Algebra a Evaluate algebraic expressions by substitution. Slide 5Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

EXAMPLE Solution We substitute 38 for x and 62 for y. 1.1 Introduction to Algebra a Evaluate algebraic expressions by substitution. AEvaluate x + y for x = 38 and y = 62. Slide 6Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc Also can be written on one line putting = signs between expressions. x + y = = 100 Write the original expression x + y

EXAMPLE Solution We substitute 72 for x and 8 for 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.

EXAMPLE Solution This expression can be used to find the Fahrenheit temperature that corresponds to 30 degrees Celsius. 1.1 Introduction to Algebra a Evaluate algebraic expressions by substitution. CEvaluate for C = 30. Slide 8Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

perofdecreased byincreased by ratio oftwiceless thanmore than divided intotimesminusplus quotient ofproduct ofdifference ofsum of divided bymultiplied bysubtracted from added to DivisionMultiplicationSubtractionAddition 1.1 Introduction to Algebra b Translate phrases to algebraic expressions. Slide 9Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

EXAMPLE PhraseAlgebraic Expression a) 9 more than y b) 7 less than x c) the product of 3 and twice w 1.1 Introduction to Algebra b Translate phrases to algebraic expressions. DTranslate each phrase to an algebraic expression. Slide 10Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. 32w or 2w 3 x – 7 y + 9or 9 + y

EXAMPLE PhraseAlgebraic 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 n – 8 ab – Introduction to Algebra b Translate phrases to algebraic expressions. ETranslate each phrase to an algebraic expression. (continued) Slide 11Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

EXAMPLE PhraseAlgebraic Expression Twenty-five percent of some number Seven less than three times some number 0.25n 3w – Introduction to Algebra b Translate phrases to algebraic expressions. ETranslate each phrase to an algebraic expression. Slide 12Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.