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1.3 Adding and Subtracting Whole Numbers, and Perimeter Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Addition Property of 0 The sum of 0 and any number is that number. 8 + 0 = 8 and 0 + 8 = 8 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra & Introductory Algebra, 3ed 2 Commutative Property of Addition Changing the order of two addends does not change their sum. 4 + 2 = 6 and 2 + 4 = 6 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra & Introductory Algebra, 3ed 3 Associative Property of Addition Changing the grouping of addends does not change their sum. 3 + (4 + 2) = 3 + 6 = 9 and (3 + 4) + 2 = 7 + 2 = 9 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra & Introductory Algebra, 3ed 4 Subtraction Properties of 0 The difference of any number and that same number is 0. 9–9=0 The difference of any number and 0 is the same number. 7–0=7 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra & Introductory Algebra, 3ed 5 Polygons A polygon is a flat figure formed by line segments connected at their ends. Geometric figures such as triangles, squares, and rectangles are called polygons. triangle square rectangle Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra & Introductory Algebra, 3ed 6 Perimeter The perimeter of a polygon is the distance around the polygon. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra & Introductory Algebra, 3ed 7 Addition Problems Descriptions of problems solved through addition may include any of these key words or phrases: Key Words Examples Symbols added to 3 added to 9 3+9 plus 5 plus 22 5 + 22 more than 7 more than 8 7+8 total total of 6 and 5 6+5 increased by 16 increased by 7 16 + 7 sum sum of 50 and 11 50 + 11 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra & Introductory Algebra, 3ed 8 Subtraction Problems Descriptions of problems solved by subtraction may include any of these key words or phrases: Key Words Examples Symbols subtract subtract 3 from 9 9–3 difference difference of 8 and 2 8–2 less 12 less 8 12 – 8 less than 2 less than 20 20 – 2 take away 14 take away 9 14 – 9 decreased by subtracted from 16 decreased by 7 5 subtracted from 9 16 – 7 9–5 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra & Introductory Algebra, 3ed 9 Helpful Hint Be careful when solving applications that suggest subtraction. Although order does not matter when adding, order does matter when subtracting. For example, 10 – 3 and 3 – 10 do not simplify to the same number. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra & Introductory Algebra, 3ed 10 Helpful Hint Since subtraction and addition are reverse operations, don’t forget that a subtraction problem can be checked by adding. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra & Introductory Algebra, 3ed 11 Reading a Bar Graph Number of Endangered Species The graph shows the number of endangered species in each country. 146 89 83 73 72 64 Country Source: The Top 10 of Everything, Russell Ash. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra & Introductory Algebra, 3ed 12