COMMUTATIVE PROPERTY (Ordering) WordsNumbers You can add or multiply numbers in any order = 2 = 2 15
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)
The Commutative and Associative Properties do not apply to subtraction or division.
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) = = 84
Changing the Order Examples: Numbers: = 1910 x 7 = = 197 x 10 = 70 Letters: A + B = B + A Pictures: + = +
Changing the Grouping Examples: Numbers:(7 + 2) + 9 = 18 (12 x 2) x 4 = (2 + 9) = x (2 x 4) = 96 Letters: (A + B) + C = A + (B +C) Pictures: ( + ) + = + ( + )
Break It Down Examples: Numbers:6 x (10 +4) = 6 x 14 = 84 6 x (10 + 4) = (6 x 10) + (6 x 4) = 84
Letter: Picture: x ( + ) = ( x ) + ( x ) A x (B + C) = (A x B) + (A x C)
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
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)
Represent each property with numbers, letters, and pictures (symbols). Refer to textbook page 24 or your notes for the properties and their meaning.
Example Commutative Property: Letters: ▪ A + B = B + A Numbers ▪ = Pictures or Symbols ▪ + = +