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# 2 5math Laws

## on Sep 18, 2008

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## 2 5math LawsPresentation Transcript

• Math Laws Properties of Addition, Multiplication, and Equalities
• Warm-Up
• Warm-Up View slide
• What’s the Deal?
• In these lessons we will use the commutative, associative, and distributive properties of addition and multiplication.
• We will use the reflexive, symmetric, transitive, and substitution properties of equality.
• We will be reminded of the additive inverse and identity properties.
View slide
• Properties of Addition and Multiplication
• Commutative
• Associative
• Examples:
• 4+3=3+4
• 71*25 = 25*71
• (6+7)+9=6+(7+9)
• (8*10)*73=8*(10*73)
• Nicknames
• Commutative Property
• Associative Property
• Order Property
• Grouping Property
• Complete each step and name the property used
• 24+(27+56) =
• (27 +__) + 56 =
• 27 + (24 + __ ) =
• 27 + __ = ____
• Given
• Commutative Property
• Associative Property
• Identity Properties
• 208 = 208
• What number can we add to 208 to get the same answer? (208)
• 208+0 = 208
• 98 = 98
• What number can we multiply by 98 to get the same answer? (98)
• 98*1 = 98
• Identity Property of Multiplication
• What is the opposite?
• 15x – 8y + 7
• Two Ways:
• Change all signs or,
• Multiply all terms by -1
• One way:
• -1(15x-8y+7) =
• -15x + 8y – 7
• OR
• +15x – 8y +7
• -15x +8y -7
• I MUST GET PAID!
• Nora has two part-time jobs. She gets paid \$8 per hour at the retail store and \$12 per hour typing term papers for college students. How much will she be able to deposit into her piggy bank after working 7 hours at the store and 5 hours of typing?
(8*7)+(5*12) \$56+\$60=\$106
Woodard Bay WIldlife Sanctuary Olympia, Washington
• Pg. 86:
• 12; 15-21; 43, 44
Assignment
• Distributive Property & Properties of Equality
• Transitive Property of Equality
• a = a
• Looks pretty straightforward.
• Symmetric Property of Equality
• If b = a, then a = b
• If n = 99, then 99 = ____.
• Transitive Property of Equality
• If a = b, and a=c, then a = c
• If x = 42, and n=(42), then x = ____.
• Hint: any time you see trans- in part of a word, the meaning usually involves “across”.
• Substitution Property of Equality
• If b = a, then a = b
• If x = (44-2), and n=(40+2), then x = __.
42
• Distributive Property of Multiplication
• 35(20 + 9)
• means 35 x everything in the parentheses.
• 35*20 + 35 *9 =
• 700 + 315 =1015
• 755 * 45 = (700 + 50 + 5)•45
• (700•45)+ (50•45)+ (5•45)
• Try Some
• 9 (5+y)=
• 45 + 9y
• 14(x-5)=
• 14x - 70
• 3(n+2)=
• 3n + 6
• 3p(r+2)=
• 3pr+3p2
• Write these using the Distributive Property
• rs+rq
• 4bk + sk
• 9xy – 21xyz
• 10fg – 2kg
• Start by finding the factors that are common to both terms.
• The first one shows r is common to both.
• r(s+q)
• k(4b + s)
• 3xy(3 – 7z)
• 2g(5f – 2k)
• assignment
• Pg 86: 24-31; 33-37; 45, 47 all