Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 2 Integers and Introduction to Solving Equations

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 2.1 Introduction to Integers

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 33 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Numbers greater than 0 are called positive numbers. Numbers less than 0 are called negative numbers. negative numbers zero positive numbers Positive and Negative Numbers

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 44 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Some signed numbers are integers. negative numbers zero positive numbers –1–1–2–2–3–3–4–4–5–5–6–6 The integers are { …, –6, –5, –4, –3, –2, –1, 0, 1, 2, 3, 4, 5, 6, …} Integers

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 55 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. – 3 indicates “negative three.” 3 and + 3 both indicate “positive three.” The number 0 is neither positive nor negative. negative numbers zero positive numbers –1–1–2–2–3–3–4–4–5–5–6–6 Negative and Positive Numbers

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 66 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 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” Comparing Integers

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 77 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 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 – –1–1–2–2–3–3–4–4–5–5–6–6 Graphs of Integers

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 88 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. The absolute value of a number is the number’s distance from 0 on the number line. The symbol for absolute value is | |. is 2 because 2 is 2 units from –1–1–2–2–3–3–4–4–5–5–6–6 is 2 because –2 is 2 units from –1–1–2–2–3–3–4–4–5–5–6–6 Absolute Value

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 99 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 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. zero a positive number Helpful Hint

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 10 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 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 5 and –5 are opposites –1–1–2–2–3–3–4–4–5–5–6–6 Opposite Numbers

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 11 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 5 is the opposite of –5 and –5 is the opposite of 5. The opposite of 4 is – 4 written as –(4) = –4–4 The opposite of – 4 is 4 written as –(– –(– 4) = 4 –(–4) = 4 If a is a number, then –(– a) = a. Opposite Numbers

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 12 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Remember that 0 is neither positive nor negative. Therefore, the opposite of 0 is 0. Helpful Hint