2 5math Laws
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2 5math Laws

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2 5math Laws 2 5math Laws Presentation 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
    • Addition
  • Identity Properties
    • 208 = 208
    • What number can we add to 208 to get the same answer? (208)
    • 208+0 = 208
    • Identity Property of Addition
    • 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
    • Copyright D DAHLBERG
    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