CHAPTER 2 Introduction to Integers and Algebraic Expressions Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 2.1Integers and the Number Line 2.2Addition of Integers 2.3Subtraction of Integers 2.4Multiplication of Integers 2.5Division of Integers and Order of Operations 2.6Introduction to Algebra and Expressions 2.7Like Terms and Perimeter 2.8Solving Equations

OBJECTIVES 2.1 Integers and the Number Line Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. aState the integer that corresponds to a real-world situation. bForm a true sentence using. cFind the absolute value of any integer. dFind the opposite of any integer.

2.1 Integers and the Number Line a State the integer that corresponds to a real-world situation. Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The integers to the left of zero on the number line are called negative integers and those to the right of zero are called positive integers. Zero is neither positive nor negative. We call –1 and 1 opposites of each other.

2.1 Integers and the Number Line INTEGERS Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 2.1 Integers and the Number Line a State the integer that corresponds to a real-world situation. 2Stock Price Change. Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Tell which integers correspond to this situation: Hal owns a stock whose price decreased from $27 per share to $11 per share over a recent time period. He owns another stock whose price increased from $20 per share to $22 per share over the same time period. The integer –16 corresponds to the decrease in the value of the first stock. The integer 2 represents the increase in the value of the second stock.

2.1 Integers and the Number Line b Form a true sentence using. Slide 7Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Numbers are written in order on the number line, increasing as we move to the right. For any two numbers on the line, the one to the left is less than the one to the right. The symbol means “is greater than.”

EXAMPLE 2.1 Integers and the Number Line b Form a true sentence using. Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

2.1 Integers and the Number Line c Find the absolute value of any integer. Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

The absolute value of a number is its distance from zero on the number line. We use the symbol to represent the absolute value of a number x. 2.1 Integers and the Number Line ABSOLUTE VALUE Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

Title 2.1 Integers and the Number Line Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To find the absolute value of a number: a) If a number is negative, its absolute value is its opposite. b) If a number is positive or zero, its absolute value is the same as the number.

EXAMPLE 2.1 Integers and the Number Line c Find the absolute value of any integer. Slide 12Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Find the absolute value of each number.

2.1 Integers and the Number Line d Find the opposite of any integer. Slide 13Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Given a number on one side of 0 on the number line, we can get a number on the other side by reflecting the number across zero.

2.1 Integers and the Number Line NOTATION FOR OPPOSITES Slide 14Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The opposite of a number x is written –x (read “the opposite of x”).

EXAMPLE 2.1 Integers and the Number Line d Find the opposite of any integer. 9 Slide 15Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

2.1 Integers and the Number Line d Find the opposite of any integer. Slide 16Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. When the variable is replaced with a number, we say that we are evaluating the expression.

EXAMPLE 2.1 Integers and the Number Line d Find the opposite of any integer. 11 Slide 17Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

2.1 Integers and the Number Line d Find the opposite of any integer. Slide 18Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. A negative number is sometimes said to have a negative sign. A positive number is said to have a positive sign, even though it rarely is written in.

EXAMPLE 2.1 Integers and the Number Line d Find the opposite of any integer. Slide 19Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Determine the sign of each number.

2.1 Integers and the Number Line d Find the opposite of any integer. Slide 20Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Replacing a number with its opposite, or additive inverse, is sometimes called changing the sign.

EXAMPLE 2.1 Integers and the Number Line d Find the opposite of any integer. Slide 21Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Change the sign (find the opposite, or additive inverse) of each number.

EXAMPLE 2.1 Integers and the Number Line d Find the opposite of any integer. 19 Slide 22Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

2.1 Integers and the Number Line d Find the opposite of any integer. Slide 23Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. When we change a number’s sign twice, we return to the original number.

EXAMPLE 2.1 Integers and the Number Line d Find the opposite of any integer. 20 Slide 24Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.