2. COMMUTATIVE PROPERTY (Ordering) WordsNumbers You can add or multiply numbers in any order. 18 + 9 = 9 + 18 15  2 = 2  15

3. ASSOCIATIVE PROPERTY (Grouping) WordsNumbers When you are only adding or only multiplying, you can group any of the numbers together. (17 + 2) + 9 = 17 + (2 + 9) (12  2)  4 = 12  (2  4)

4.  The Commutative and Associative Properties do not apply to subtraction or division.

5. DISTRIBUTIVE PROPERTY WordsNumbers To multiply a number by a sum, multiply by each number in the sum and then add. 6  (10 + 4) = (6  10) + (6  4) = 60 + 24 = 84

6. Changing the Order Examples: Numbers:13 + 6 = 1910 x 7 = 70 6 + 13 = 197 x 10 = 70 Letters: A + B = B + A Pictures: + = +

7. Changing the Grouping Examples: Numbers:(7 + 2) + 9 = 18 (12 x 2) x 4 = 96 7 + (2 + 9) = 18 12 x (2 x 4) = 96 Letters: (A + B) + C = A + (B +C) Pictures: ( + ) + = + ( + )

8. Break It Down Examples: Numbers:6 x (10 +4) = 6 x 14 = 84 6 x (10 + 4) = (6 x 10) + (6 x 4) 60 + 24 = 84

9. Letter: Picture: x ( + ) = ( x ) + ( x ) A x (B + C) = (A x B) + (A x C)

10. Name the property.  2 x 15 = 15 x 2  8 x 1 = 8  4 x (2 + 1) = (4 x 2) + (4 x 1)  (3 x 6) x 2 = 3 x (6 x 2)  7 x 0 = 0

11. Fill in the blank. Name the property.  __ x 1 = 6  8 + (5 + 3) = (8 + __) + 3  6 x 7 = __ x 6  4 X (7 x __) = (4 x __) x 9  8 x (2 + __) = (8 x __) + ( __ x 4)  __ x 15 = __ x 12  (4 x 7) + (4 x 13) = __ x (7 x 13)

12.  Represent each property with numbers, letters, and pictures (symbols). Refer to textbook page 24 or your notes for the properties and their meaning.

13.  Example Commutative Property:  Letters: ▪ A + B = B + A  Numbers ▪ 24 + 12 = 12 + 24  Pictures or Symbols ▪ + = +