Aim #6: What are the properties of real numbers?Homework: pg 18-19 #1-20Do Now: Simplify the following:

a) 3(x + 4) b) (x - 4)(2x - 1) c) (3x - 5y) 2

The order of the numbers

does NOT affect the sum.

The order of the numbers

does NOT affect the product.

The way the numbers are

paired does NOT affect the 

sum.

The way the numbers are

paired does NOT affect the 

product.

When zero is added to any 

number, the number remains

unchanged.

Any number multiplied by 1

remains unchanged.

The sum of a number and its 

additive inverse (also called 

its opposite) is zero.

The product of any number 

and its multiplicative inverse

(its reciprocal) is 1. 

The product of zero and any 

number is zero. 

Multiplication can be 

distributed over addition

or subtraction.

9-15-16

State the property illustrated in each example.

11. (3 + 5) - 3 = (5 + 3) - 3 12.

17. Fill in the circles with the correct property:

14. ab + cd = ab + dc 15. 1a = a 16. 0.5(2) = 1

13. π(0) = 0

Use these abbreviations for the properties of real numbers and complete the flow diagram.C+ for the commutative property of additionC× for the commutative property of multiplicationA+ for the associative property of additionA× for the associative property of multiplicationD for distributive property

Now, show a mathematical proof of the statement that (x + y) + z = (z + y) + x are equivalent expressions:

(x + y) + z Givenz + (x + y) _____________________________z + (y + x) ________________________

(z + y) + x ________________________

Is it true for all real numbers x, y, and z that (x + y) + z should equal (z + y) + x? Lets prove that (x + y) + z = (z + y) + x using a flow diagram and the commutative and associative properties.

(x + y) + z

The Distributive, Associative and Commutative Properties can be applied to algebraic expressions using variables that represent real numbers.

Two algebraic expressions are equivalent if we can convert one expression into the other by repeatedly applying the Commutative, Associative, and Distributive Properties and the properties of rational exponents to components of the first expression.

Sum It Up!