Commutative & Associative Property

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Warm-Ups

1.  5(2 + x) + 7x

2.  3(5 + 2p)

3.  3(a + 2b) - 3a

4.  7m + 6(n + m)

5.  (d + 5)f + 2f

Commutative Property

Words:  The order in which you add or multiply numbers does not change their sum or product.

Symbols:  For any numbers a and b, a + b = b + a and a*b = b*a

Ex:  5 + 6 = 6 + 5, 3*2 = 2*3

Associative Property

Words:  The way you group three or more numbers when adding or multiplying does not change their sum or product. Symbols:  For any numbers a,b, and a(bc)

Ex:  (2 + 4) + 6 = 2 + (4 + 6), (3*5) *4 = 3*(5*4)

Multiplication Properties

Evaluate:  8 * 2 * 3 * 5

You can rearrange and group the factors to make mental calculations easier.

Evaluate:  2 * 8 * 5 * 7

Use the expression three times the sum of 3x and 2y added to five times the sum of x and 4y.  

a.  Write an algebraic expression for the verbal                    expression.

b.  Simplify the expression.