Adding and Subtracting Adding and Subtracting Whole Numbers and PerimeterWhole Numbers and Perimeter

3 + 4 = 73 + 4 = 7

addend addend sumaddend addend sum

Section 1.3

Addition Property of 0Addition Property of 0

The sum of 0 and any number is that number.The sum of 0 and any number is that number.

8 + 0 = 8 8 + 0 = 8 andand 0 + 8 = 8 0 + 8 = 8

2Martin-Gay, Prealgebra, 5ed

Commutative Property of Addition

Changing theChanging the order order of two addends of two addends does not change their sum.does not change their sum.

4 + 2 = 6 4 + 2 = 6 andand 2 + 4 = 6 2 + 4 = 6

3Martin-Gay, Prealgebra, 5ed

Associative Property of Addition

Changing theChanging the groupinggrouping of addends of addends does not change their sum.does not change their sum.

3 + (4 + 2) = 3 + 6 = 93 + (4 + 2) = 3 + 6 = 9

andand

(3 + 4) + 2 = 7 + 2 = 9(3 + 4) + 2 = 7 + 2 = 9

4Martin-Gay, Prealgebra, 5ed

Subtraction Properties of 0Subtraction Properties of 0

The difference of any number and that The difference of any number and that same number is 0.same number is 0.

9 - 9 = 09 - 9 = 0

The difference of any number and 0 is The difference of any number and 0 is the same number.the same number.

7 - 0 = 77 - 0 = 7

5Martin-Gay, Prealgebra, 5ed

A A polygonpolygon is a flat figure formed by line is a flat figure formed by line segments connected at their ends. segments connected at their ends.

Geometric figures such as triangles, Geometric figures such as triangles, squares, and rectangles are called squares, and rectangles are called polygons.polygons.

rectanglerectanglesquaresquare

triangletriangle

6Martin-Gay, Prealgebra, 5ed

Finding theFinding the PerimeterPerimeter of a of a PolygonPolygon

The perimeter of a polygon is the The perimeter of a polygon is the distance arounddistance around the polygonthe polygon.

7Martin-Gay, Prealgebra, 5ed

Descriptions of problems solved through addition Descriptions of problems solved through addition may include any of these key words or phrases:may include any of these key words or phrases:

Key WordsKey Words ExamplesExamples SymbolsSymbols

added toadded to 3 added to 93 added to 9 3 + 93 + 9

plusplus 5 plus 225 plus 22 5 + 225 + 22

more thanmore than 7 more than 87 more than 8 7 + 87 + 8

totaltotal total of 6 and 5total of 6 and 5 6 + 56 + 5

increased byincreased by 16 increased by 716 increased by 7 16 + 716 + 7

sumsum sum of 50 and 11sum of 50 and 11 50 + 1150 + 118

Martin-Gay, Prealgebra, 5ed

Descriptions of problems solved by subtraction Descriptions of problems solved by subtraction may include any of these key words or phrases:may include any of these key words or phrases:

Key WordsKey Words ExamplesExamples SymbolsSymbols

subtractsubtract subtract 3 from 9subtract 3 from 9 9 - 39 - 3

differencedifference difference of 8 and 2difference of 8 and 2 8 - 28 - 2

lessless 12 less 812 less 8 12 - 812 - 8

take awaytake away 14 take away 914 take away 9 14 - 914 - 9

decreased bydecreased by 16 decreased by 716 decreased by 7 16 - 716 - 7

subtracted fromsubtracted from 5 subtracted from 95 subtracted from 9 9 - 59 - 5

9Martin-Gay, Prealgebra, 5ed

Be careful when solving applications Be careful when solving applications that suggest subtraction. Although that suggest subtraction. Although order order does not matterdoes not matter when adding, when adding, order does matter when subtracting. order does matter when subtracting. For example, 10 – 3 and 3 – 10 do For example, 10 – 3 and 3 – 10 do notnot simplify to the same number.simplify to the same number.

Helpful HintHelpful Hint

10Martin-Gay, Prealgebra, 5ed

Since subtraction and addition are Since subtraction and addition are reverse operations, don’t forget that a reverse operations, don’t forget that a subtraction problem can be checked subtraction problem can be checked by adding.by adding.

Helpful HintHelpful Hint

11Martin-Gay, Prealgebra, 5ed

Reading a Bar GraphReading a Bar Graph

The graph shows the ratings of Best Picture The graph shows the ratings of Best Picture nominees since 1984.nominees since 1984.

Source: The internet Movie Database and Cuadra Associates Movie Star Database, 2003.Source: The internet Movie Database and Cuadra Associates Movie Star Database, 2003.

Nu

mb

er o

f B

est

Nu

mb

er o

f B

est

Pic

ture

No

min

ees

Pic

ture

No

min

ees

0

10

20

30

40

50

60

G PG PG-13 R NC-17/X

0022

1616

2525

5252

RatingsRatings

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