Chapter 1 Section 8 Properties of Numbers

Commutative Properties of Addition and Multiplication You can add two numbers in any order and get the same result. 7 + 12 = 12 + 7 or a + b = b + a You can multiply two numbers in any order and get the same result 7 * 12 = 12 * 7 or a * b = b * a

Associative Properties of Addition and Multiplication You can change the grouping of numbers before you add them. So you can add them in any order and get the same result. (4 + 7) + 3 = 4 + (7 + 3) You can change the grouping of numbers before you multiply them. So you can multiply them in any order and get the same result. (2 * 3) * 10 = 2 * (3 * 10)

Identity Property of Addition Adding zero does not change the value of a number 3 + 0 = 3 97 + 0 = 97

Identity Property of Multiplication Multiplying by one does not change the value of a number. 3 * 1 = 3 67 * 1 = 67

Distributive Property How would you explain the Distributive Property?

Distributive Property The distributive property is telling us how to deal with those parenthesis when we just have letters inside.  We're going to need this a lot in Algebra!  Remember that you always do what's in the parenthesis first...  But, in Algebra, you may not be able to add the b and the c...   So, this property tells you what to do... 

Distributive Property You distribute the a to the b and, then you distribute the a to the c.

Is the Commutative Property true for subtraction and division? Prove why or why not

Is the Commutative Property true for subtraction and division?

Is the Commutative Property true for subtraction and division? NO 6 - 2 ≠ 2 - 6 because 6 -2 = 4 and 2 - 6 = -4 6÷2 ≠ 2 ÷ 6 because 6 ÷ 2 = 3 and 2 ÷ 6 = 1/3

Is the Associative Property true for subtraction and division? Prove why or why not

Is the Associative Property true for subtraction and division?

Is the Associative Property true for subtraction and division? NO (12 - 6) – 2 ≠ 12- (6 - 2) because (12 - 6) – 2 = 6 – 2 =4 and 12- (6 - 2) = 12- 4 = 8

Is the Associative Property true for subtraction and division? NOI (12÷ 6) ÷2 ≠ 12 ÷ (6 ÷2) because (12÷ 6) ÷2 = 2 ÷2= 1 and 12 ÷ (6 ÷2) = 12 ÷ 3 = 4

Dividing by Zero The quotient of any number a and zero is not defined a ÷ 0 = undefined but 0 ÷ a = 0 9 ÷ 0 = undefined but 0 ÷ 9 = 0

Zero product property If ab = 0 then either a or b is = 0 or both are = 0

Inverse Property For any real number a, there is a single real number 1/a that makes the following true a * 1/a = 1 3 * 1/3 =1