Property Of Numbers

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.

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Property Of Numbers

by Middle School on Sep 19, 2009

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Property Of Numbers — Presentation Transcript