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Property Of Numbers
 

Property Of Numbers

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Chapter 2, Section1: Property of Numbers: Associative/Commutative/Identity

Chapter 2, Section1: Property of Numbers: Associative/Commutative/Identity

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    Property Of Numbers Property Of Numbers Presentation Transcript

    • Chapter 2, Section 1: Properties of Numbers Ms. Dewey-Hoffman, 2009
    • Commutative Properties (addition/multiplication)
      • When JUST adding or multiplying (not at the same time), you can move the numbers around and the answer will be the same.
      • Addition
      • 7 + 17 + 23 = 47
      • 23 + 7 + 17 = 47
      • 7 + 17 + 23 = 23 + 7 + 17
      • A + B + C = B + A + C
      • Multiplication
      • 5 • 3 • 11 = 165
      • 11 • 5 • 3 = 165
      • 11 • 5 • 3 = 5 • 3 • 11
      • A • B • C = B • A • C
    • Associative Properties (addition/multiplication)
      • When JUST adding or multiplying (not at the same time), you can change the grouping symbol locations and get the same answer.
      • Addition
      • (3 + 4) + 7 = 14
      • 3 + (4 + 7) = 14
      • (3 + 4) + 7 = 3 + (4 + 7)
      • A + (B + C) = (A + B) + C
      • Multiplication
      • (3 + 4) + 7 = 14
      • 3 + (4 + 7) = 14
      • (3 + 4) + 7 = 3 + (4 + 7)
      • A + (B + C) = (A + B) + C
    • Identity Properties of Addition and Multiplication
      • The identity for ADDITION is ZERO.
      • When you ADD ZERO to a number, the sum is that number.
      • Addition likes ZERO.
      • 5 + 0 = 5
      • The identity for MULTIPLICATION is ONE.
      • When you MULTIPLY ONE by a number, the product is that number.
      • Multiplication likes ONE.
      • 4 • 1 = 4
    • Identify the Property Shown
      • 3 + 6 = 6 + 3
      • 8 = 1 • 8
      • (3z)m = 3(xm)
      • 0 + b = b
      Commutative Property Multiplicative Identity Associative Property of Multiplication Additive Identity
    • Mental Math and the Properties
      • If it is easier to do Mental Math and all you’re doing is just Addition or just Multiplication, then move numbers to make it easier for you.
      • This works because of the Associative Property of Addition/Multiplication and the Commutative Property of Addition/Multiplication .
      • Example:
      • 19 + (-30) + 21 =
      • 19 + 21 + (-30)  easier to Add 19 and 21 first before adding (-30)
      • 40 + (-30)  it is simplified, drop down the (-30)
      • 40 + (-30) = 10
      • 10
    • More Examples
      • Hint: Look for things that add to 10. 9+1, 8+2, 7+3, etc.
      • 6 + 7 + 14 =
      • 8 + 0 + 2 + (-7) =
      • 5 + 12 + 18 + 5 =
      • 7 + 2 + 8 + 23 =
    • Moving Multiplication
      • (4 • 9) • 5 =
      • (9 • 4) • 5  Commutative Property of Multiplication.
      • 9 • (4 • 5)  Associative Property of Multiplication, because it is easier to multiply 4 and 5, instead of 4 and 9.
      • 9 • 20  Simplify, Multiply inside the Parentheses.
      • 180  Simplify, Multiply.
    • More Examples
      • 25 • (3 • 4) =
      • 3 • 1 • -5 • 8 =
      • 2(-8)(-15) =
      • 5 • 9 • 6 • (-2) • (-1) =
    • #9
      • Page 71-72: 1-33 odd. #35 is Extra Credit.
      • Remember to show your steps, even for the Mental Math Problems.
      • Tell me which numbers you added or multiplied first.