1 3 Adding and Subtracting Whole Numbers and

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, 3 ed 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, 3 ed 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, 3 ed 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, 3 ed 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, 3 ed 6

Perimeter The perimeter of a polygon is the distance around the polygon Copyright ©

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 of 6 and 5 6+5 increased by 16 increased by 7 16 + 7 sum of 50 and 11 50 + 11 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra & Introductory Algebra, 3 ed 8

Subtraction Problems Descriptions of problems solved by subtraction may include any of these key words or phrases: Key Words Examples Symbols subtract 3 from 9 9– 3 difference of 8 and 2 8– 2 less 12 less 8 12 – 8 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, 3 ed 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, 3 ed 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, 3 ed 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 The Hall. Top 10 of Everything, Russell Ash. . Copyright © 2011 Pearson Education, Inc. Publishing. Source: as Prentice Martin-Gay, Prealgebra & Introductory Algebra, 3 ed 12