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Chapter 2 Integers and Introduction to Solving Equations Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 2.1 Introduction to Integers Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Positive and Negative Numbers Numbers greater than 0 are called positive numbers. Numbers less than 0 are called negative numbers. zero negative numbers -6 -5 -4 -3 -2 -1 positive numbers 0 1 2 3 4 5 6 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra & Introductory Algebra, 3ed 3 Integers Some signed numbers are integers. The integers are { …, –6, –5, –4, –3, –2, –1, 0, 1, 2, 3, 4, 5, 6, …} negative numbers –6 –5 –4 –3 –2 –1 zero 0 positive numbers 1 2 3 4 5 6 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra & Introductory Algebra, 3ed 4 Negative and Positive Numbers –3 indicates “negative three.” 3 and +3 both indicate “positive three.” The number 0 is neither positive nor negative. zero negative numbers –6 –5 –4 –3 –2 –1 positive numbers 0 1 2 3 4 5 6 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra & Introductory Algebra, 3ed 5 Comparing Integers We compare integers just as we compare whole numbers. For any two numbers graphed on a number line, the number to the right is the greater number and the number to the left is the smaller number. < means “is less than” > means “is greater than” Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra & Introductory Algebra, 3ed 6 Graphs of Integers The graph of –5 is to the left of –3, so –5 is less than –3, written as –5 < –3 . We can also write –3 > –5. Since –3 is to the right of –5, –3 is greater than –5. –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra & Introductory Algebra, 3ed 7 Absolute Value The absolute value of a number is the number’s distance from 0 on the number line. The symbol for absolute value is | |. 2 is 2 because 2 is 2 units from 0. –6 –5 –4 –3 –2 –1 0 1 2 3 4 2 is 2 because –2 is 2 units from 0. 5 6 –6 –5 –4 –3 –2 –1 5 6 0 1 2 3 4 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra & Introductory Algebra, 3ed 8 Helpful Hint Since the absolute value of a number is that number’s distance from 0, the absolute value of a number is always 0 or positive. It is never negative. 6 =6 0 =0 zero a positive number Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra & Introductory Algebra, 3ed 9 Opposite Numbers Two numbers that are the same distance from 0 on the number line but are on the opposite sides of 0 are called opposites. 5 units –6 –5 –4 –3 –2 –1 5 units 0 1 2 3 4 5 6 5 and –5 are opposites. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra & Introductory Algebra, 3ed 10 Opposite Numbers 5 is the opposite of –5 and –5 is the opposite of 5. The opposite of 4 is –4 is written as –(4) = –4 The opposite of –4 is 4 is written as –(–4) = 4 –(–4) = 4 If a is a number, then –(–a) = a. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra & Introductory Algebra, 3ed 11 Helpful Hint Remember that 0 is neither positive nor negative. Therefore, the opposite of 0 is 0. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra & Introductory Algebra, 3ed 12