Lesson 8-1 - Math Slide Show

Lesson 8-1Objective- To find factors of numerical andvariable expressions.Factor - A whole number or variable expressionthat divides evenly into a given wholenumber or variable expression.List all the positive factors of the following.FactorTower18 24 5xy1 18 1 24 1 5xy2 9 2 12 5 xy3 6 3 8 5x y4 6 5y xFind three factorizations for each monomial.21) 362) −10x y1 36 1, 362-1 10x y22 18 2, 182-2 5x y −2, 5x y3 12 -4, -92-5 2x y −2xy, 5x4 9226 6-10xy10y, −x-1 -36-1x 10xy-2 -18-2x 5xy-3 -12-5x 2xy-4 -9-6 -6-10x xy. .Composite - “Made up of distinct parts”- Webster’sComposite Number - Numbers that are made upof a product of primes.Prime Factorization - The unique set of primenumbers whose productequals a given number.Wit Write the prime factorization ti for the following.18 24 5xyFactor 2 9 4 6 5 xyTree3 3 2 2 2 3 x y2 • 3 2 2 3 • 3 5 • x• yFind the prime factorization of the given number.Factor TreeUpside-Down Division840 2 8402 4202 4202 2102 2105 1057 212 105335 21 2 • 3• 5•73 732 • 3• 5•7Greatest Common FactorGCF - Greatest Common Factor - Largestnumber that divides evenly into a given setof numbers.Two ways to find the GCF1) Make a list of factors.2) Select common factors from the primefactorizations.Find the GCF using the technique described.Make a List601 602 303 204 155 126 10GCF = 12841 842 423 284 216 147 12Prime Factorization60 842 302 153 52 422 213 72• 2• 3• 5 2• 2• 3•7GCF = 2• 2•3GCF = 12Algebra Slide Show: Teaching Made Easy As Pi, by James Wenk © 2010

Lesson 8-1 (cont.)GCF - Greatest Common FactorFind the GCF of the following.20 242 10 2 122 52 •2 •5GCF = 2 •2 = 42 62 32 •2 •2 • 3GCF - Greatest Common FactorFind the GCF of the following.6m 2 9mn6 m 29 mn2 3 m m 3 3 m n2 • 3•m •m 3• 3•m •nGCF = 3•m = 3mFinding the GCF Using Upside-Down DivisionCommonFactors2 200 1802 100 905 50 452 10 3 95 3GCF = 2• 2•5GCF = 20Find the GCF using the technique described.Factor Trees Upside-Down Division96 240 2 96 2402 48 2 1202 48 1202 24 606 8 4 30 2 12 302 3 2 42 2 2 1536 152 52 2 3 52• 2• 2• 2• 2•3 GCF= 2• 2• 2• 2•32• 2• 2• 2• 3•5 GCF = 48GCF = 2 • 2• 2• 2•3GCF = 48GCF - Greatest Common FactorFind the GCF of the following mentally.1) 15x 2 y 12xy 3 3x yFind the missing factor.1) x 10 = (x 4 6)( x )2) 8a 4 3= (2a)( 4a )2)3)30a 2 b 42a 3 b 26a 2b14m 4 n 3 21m 5 n 27m 4 n23) 2x 2 y = (x)( 2xy )4) 36a 3 b 4 2 3= (9ab)( 4a b )5) 7x 4 y 3 = (−xy 2 3)( −7x y )6) −6h 2 k 3 2= (3hk)( −2hk )Algebra Slide Show: Teaching Made Easy As Pi, by James Wenk © 2010

Lesson 8-1 (cont.)GCF Word ProblemsA baker has 16 loaves of white bread and 40 loavesof wheat. He wants to store the loaves with the samenumber of loaves on each shelf, while keeping whiteand wheat on separate shelves. If he puts the greatestpossible number of loaves on each shelf, how manyshelves will he need?White = 16 loaves Wheat = 40 loavesGCF = 8Shelves Needed for White = 16 ÷ 8 = 2 shelvesShelves Needed for Wheat = 40 ÷ 8 = 5 shelvesTotal Shelves Needed = 7 shelvesAlgebra Slide Show: Teaching Made Easy As Pi, by James Wenk © 2010