1. Properties of Real Numbers
Algebra
2014/2015

2. I can use the properties of real numbers correctly.
AIM
I can use the properties of real numbers correctly.
TOPIC: Properties of Numbers

3. DO NOW
How can we represent the distributive property as an algebraic formula?

4. Distributive Property
If a, b, and c are real numbers, then a(b+c)= ab + ac
Example: 7(m+4)

5. Distributive Property
Example: 6 – 2 (k + 3)
Example: (m - 4)(m + 2)

6. Commutative Property of Addition
Does = 4 + 3?

7. Commutative Property of Multiplication
Does 3 * 4 = 4 * 3?
Can we represent this geometrically?
Does 2 * 3 * 4 = 4 * 2 * 3?

8. Associative Property of Addition
Does 3 + (4 + 5) = (3 + 4) + 5?

9. Associative Property of Multiplication
Does 3 * (4 * 5) = (3 * 4) * 5?

10. If a, b, and c are real numbers…
Commutative Property of Addition:
a + b = b + a.
Commutative Property of Multiplication:
a × b = b × a.
Associative Property of Addition:
(a+b)+c = a + (b+c)
Associative Property of Multiplication:
(ab)c =a(bc).

11. Commutative Property Continued
Does it work with three numbers?
Can we re-arrange all three numbers?

12. Property of Equality
If two sides of an equation are balanced, we can preserve the balance by adding or multiplying number to both sides.
Example:
Addition Multiplication
k = b = 6
k + 3 = b • 4 = 6 • 4

13. Identity Property
How can we multiply or add to disguise the variable S, but not change its identity.
S = S +
S = S •

14. Inverse Properties Think of a synonym for inverse:
What would happen if we added or multiplied by the inverse of a variable?
J + (-J) = .

15. Homework: Properties WS
EXIT TICKET
Pick any property you learned in class today and describe it in your own words.
Homework: Properties WS