Properties of Real Numbers

Properties of Addition & Multiplication:For all real #’s, a, b, c…

Closure: then a+b is a real number ab is a real number

Commutative: a + b = b + aab = ba

Associative: (a+b)+c = a+(b+c) (ab)c = a(bc)

Identity: a + 0 = 0 + a = aa*1 = 1*a = a

Inverse: a + (-a) = 0 11a

a

Distributive Property

For all real numbers a, b, and c:

a(b + c) = ab + ac and (b + c)a = ba + bc)

State a property to justify the following statements…

6 +(-3) = (-3) + 6

3(4a+5) = 12a + 15

(x+3) + 6 = 6 + (x+ 3)

-5 + 5 = 0

State a property to justify the following statements…

2(4 – 5) = (4- 5)2

-5 + (x + 2) = (-5 + x) + 2

4 ( 1) = 4

Using Properties for Mental Math

A movie ticket costs $7.75. A drink costs $2.40 and popcorn is $1.25. What is the total cost?

Using Properties for Mental Math

You buy a sandwich for $2.95, an apple for $.45, and a bottle of juice for $1.05. What is the total cost?

Simplify – using properties

Simplify – using properties

Simplify – using properties

Simplify – using properties

Simplify – using properties

Simplify – using properties

Homework

Worksheet