8-1 - mathppt.com 49 1) 1, 36 2, 18-4, -9-1-2-5 2) −10x y2 10x y2 5x y2 2x y2 10 2 −2xy, 5x 10...
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Objective- To find factors of numerical and variable expressions. Factor - A whole number or variable expression that divides evenly into a given whole number or variable expression. List all the positive factors of the following. 18 24 5xy 1 18 2 9 3 6 1 24 2 12 3 8 4 6 1 5xy 5 xy 5x y 5y x Factor Tower Find three factorizations for each monomial. 36 1 36 2 18 3 12 4 9 1) 1, 36 2, 18 -4, -9 -1 -2 -5 2) 2 10x y − 2 10x y 2 5x y 2 2x y 10 2 2xy, 5x − 2 10 2 2, 5x y − 6 6 -1 -36 -2 -18 -3 -12 -4 -9 -6 -6 -10 2 xy -1x -2x -5x 10xy 5xy 2xy -10x xy . . . . . . 2 10y, x − Composite - “Made up of distinct parts”- Webster’s Composite Number - Numbers that are made up of a product of primes. Prime Factorization - The unique set of prime numbers whose product equals a given number. W it th i f t i ti f th f ll i Write the prime factorization for the following. 18 24 5xy Factor Tree 2 9 3 3 4 6 2 3 2 2 5 xy x y 2 • 3 2 2 3 • 3 5 • x • y Find the prime factorization of the given number. Factor Tree Upside-Down Division 840 840 2 420 2 210 2 420 2 210 2 105 5 2 3 7 105 5 21 21 7 3 3 2 3 5 7 • • • 3 2 3 5 7 • • • Largest number that divides evenly into a given set of numbers. GCF - Greatest Common Factor - Greatest Common Factor Two ways to find the GCF 1) Make a list of factors. 2) Select common factors from the prime factorizations. Find the GCF using the technique described. Make a List Prime Factorization 60 1 60 2 30 3 20 84 1 84 2 42 3 28 60 2 30 2 15 84 2 42 2 21 3 20 4 15 5 12 6 10 3 28 4 21 6 14 7 12 GCF = 12 2 15 3 5 2 21 3 7 2 2 3 5 • • • 2 2 3 7 • • • GCF 2 2 3 = • • GCF = 12 Lesson 8-1 Algebra Slide Show: Teaching Made Easy As Pi, by James Wenk © 2010
Transcript of 8-1 - mathppt.com 49 1) 1, 36 2, 18-4, -9-1-2-5 2) −10x y2 10x y2 5x y2 2x y2 10 2 −2xy, 5x 10...
Objective- To find factors of numerical and variable 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.
18 24 5xy1 182 93 6
1 242 123 84 6
1 5xy5 xy5x y5y x
FactorTower
Find three factorizations for each monomial.
361 362 183 124 9
1) 1, 362, 18
-4, -9
-1-2-5
2) 210x y−210x y
25x y22x y
10 2
2xy, 5x−210
22, 5x y−
6 6-1 -36-2 -18-3 -12-4 -9-6 -6
-10 2x y-1x-2x-5x
10xy5xy2xy
-10x xy......
210y, x−
Composite - “Made up of distinct parts”- Webster’sComposite Number - Numbers that are made up
of a product of primes.Prime Factorization - The unique set of prime
numbers whose productequals a given number.
W it th i f t i ti f th f ll iWrite the prime factorization for the following.18 24 5xy
FactorTree 2 9
3 3
4 6
2 32 2
5 xy
x y
2 • 32 23 • 3 5 • x• y
Find the prime factorization of the given number.Factor Tree Upside-Down Division
840 840
2 420
2 210
2420221021055
2
3 7
105
5 21
2173
32 3 5 7• • •
32 3 5 7• • •
Largestnumber that divides evenly into a given setof numbers.
GCF - Greatest Common Factor -
Greatest Common Factor
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 List Prime Factorization60
1 602 303 20
841 842 423 28
60
2 30
2 15
84
2 42
2 213 204 155 126 10
3 284 216 147 12
GCF = 12
2 15
3 5
2 21
3 7
2 2 3 5• • • 2 2 3 7• • •GCF 2 2 3= • •
GCF = 12
Lesson 8-1
Algebra Slide Show: Teaching Made Easy As Pi, by James Wenk © 2010
GCF - Greatest Common Factor
Find the GCF of the following.
20 24
2 10 2 12
2 5
2 •2 •5
2 6
2 32 •2 •2 • 3
GCF = 2 •2 = 4
GCF - Greatest Common Factor
Find the GCF of the following.
9mn
6 9 mn6m2
m2
2 • 3•m•m 3• 3•m•n
GCF = 3•m = 3m
m m2 3 m n3 3
Finding the GCF Using Upside-Down Division
200 1802100 90250 45510 925
33
Common Factors
5 3
GCF 2 2 5= • •
GCF = 20
Find the GCF using the technique described.Factor Trees Upside-Down Division
96
2 48
6 8
240
2 120
4 30
2 3 2 4 2 2 2 15
96 240248 120224 60212 3026 153
2 2 2 2 2 3• • • • •2 2 2 2 3 5• • • • •
GCF 2 2 2 2 3= • • • •GCF = 48
2 3 2 4
2 2
2 2 2 15
3 5GCF 2 2 2 2 3= • • • •
GCF = 48
6 1532 5
GCF - Greatest Common Factor
Find the GCF of the following mentally.
1) 15x2y 12xy3 3x y
2)
3)
30a2b 42a3b2
14m4n3 21m5n2
6 2a b
7 4m 2n
Find the missing factor.
1)
2)
3)
x10 = (x4 )( )
8a4 = (2a)( )
2x2y = (x)( )
6x
34a
2xy
4)
5)
6)
36a3b4 = (9ab)( )
7x4 y3 = (−xy2)( )
−6h2k3 = (3hk)( )
2 34a b37x y−
22hk−
Lesson 8-1 (cont.)
Algebra Slide Show: Teaching Made Easy As Pi, by James Wenk © 2010
GCF Word ProblemsA baker has 16 loaves of white bread and 40 loaves of 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 greatest possible number of loaves on each shelf, how many shelves will he need?
White = 16 loaves Wheat = 40 loavesGCF = 8
Shelves Needed for White =Shelves Needed for Wheat =
Total Shelves Needed =
16 8÷ 2 shelves=40 8÷ 5 shelves=
7 shelves
Lesson 8-1 (cont.)
Algebra Slide Show: Teaching Made Easy As Pi, by James Wenk © 2010
