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# Property Of Numbers

## on Sep 20, 2009

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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 NumbersPresentation Transcript

• Chapter 2, Section 1: Properties of Numbers Ms. Dewey-Hoffman, 2009
• When JUST adding or multiplying (not at the same time), you can move the numbers around and the answer will be the same.
• 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
• When JUST adding or multiplying (not at the same time), you can change the grouping symbol locations and get the same answer.
• (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.
• 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.