Commutative Property: the order in which you add or multiply numbers does not change their sum or product
a = b = b + a and a*b = b*a
2 + 3 = 3 + 2 and 3*4 = 4*3
Associative Property: the way you group 3 or more numbers whenadding or multiplying does not change their sum or product.
(a + b) + c = a + (b + c) and (ab)c = a(bc)
(2 + 3) + 4 = 2 + (3 + 4) and (2*3)*4 = 2(3*4)
Example 1: Evaluate 2*8*5*7
| Summary: Properties of Numbers | ||
| Property | Addition | Multiplication |
| Commutative | a + b = b + a | (ab)c = a(bc) |
| Associative | (a + b) + c = a + (b + c) | (ab)c = a(bc) |
| Identity | 0 is the identity a + 0 = 0 + a = a |
1 is the identity a*1 = 1*a = a |
| Zero | - | a*0 = 0*a = 0 |
| Distributive | a(b + c) = ab + ac and (b + c)a = ba + ca | |
| Substitution | if a = b, then a may be substituted for b | |
Example 2: Simplify 3(3x + 2y) + 5(x + 4y) and indicate the properties used.
Homework: p34 #16-26 even, 28-31, 32-46 even, 58, 60