Commutative and Associative Properties

Commutative and Associative Properties Commutative Property means changing the order in which you add or subtract numbers does not change the sum or product. Associative Property means changing the grouping of numbers when adding or multiplying does not change their sum or product. Grouping symbols are typically parentheses (),but can include brackets [] or Braces {}.

Commutative Properties Commutative Property of addition - (Order) For any numbers a and b , a + b = b + a. 45 + 5 = 5 + 45 50 = 50 Commutative Property of multiplication - (order) For any numbers a and b , a  b = b  a. 6  8 = 8  6 48 = 48

Commute What does the word commute mean? It means to go from one place to another. Pick a partner. When I say commute, you will quickly change seats with your partner. When I say commute the 2nd time, you will return to you seat. Ready….commute. Commute! Commute! Commute! What does the commutative property mean to you?

Associative Properties Associative Property of addition - (grouping symbols) For any numbers a, b, and c, (a + b) + c = a + (b + c). (2 + 4) + 5 = 2 + (4 + 5) (6) + 5 = 2 + (9) 11 = 11 Associative Property of multiplication - (grouping symbols) For any numbers a, b, and c, (ab) c = a (bc). (2  3)  5 = 2  (3  5) (6)  5 = 2  (15) 30 = 30

Associate To associate with someone means that you are with them. To demonstrate associating, I want 3 people to come to the front of the room. You will use your arms as parentheses. The person in the middle will associate with the person on the right (put your arm around them). Now associate with the person on your left? Did the number or placement of the people change? What does the associative property mean to you?

Commutative and Associative Properties Commutative and Associative properties are very helpful to solve problems using mental math strategies. Rewrite the problem by grouping numbers that can be formed easily. (Associative property) This process may change the order in which the original problem was introduced. (Commutative property) Evaluate: 18 + 13 + 16 + 27 + 22 + 24 (18 + 22) + (16 + 24) + (13 + 27) (40) + (40) + (40) = 120

Commutative and Associative Properties Commutative and Associative properties are very helpful to solve problems using mental math strategies. Rewrite the problem by changing the order in which the original problem was introduced. (Commutative property) Group numbers that can be formed easily. (Associative property) Evaluate: 4  7  25 4  25  7 (4  25)  7 (100)  7 = 700

Additive Identity What does identity mean to you? (Your name?) What can I add to a number and it will keep its name and value? What can I multiply to a number and it will keep its name and value? O is the additive identity property and 1 is the mulitiplicative identity property. What does the identity property mean to you?

Identity Property 5 + 0 = 5 (5 retains its identity) 17 x 1 = 17 (17 retains its identity)

Multiplicative Property of Zero What can you multiply any number by to get zero??? This is the multiplication property of 0! 124 x 0 = 0 0 x 1,890 = 0

Multiplicative Identity What number can you multiply any number by so that it keeps its identity? 134 x = 134? The number is the multiplicative identity for all numbers!

Additive Inverse What is the inverse (opposite) of adding? What can I add to any number to make zero?? 7 + = 0 You can add the inverse of opposite to any number to get 0. 15 + -15 = 0 -173 + 173 = 0

Multiplicative Inverse What can I multiply to a number to make 1?? 1/3 x = 1 Multiply the reciprocal or the inverse of the number to make 1. -4 x = 1 (You have to multiply -4 by -1/4 to get 0.)

Distributive Property Remember to distribute the number on the outside of the parenthesis to everything inside of the parenthesis! 5(x + 3) + 12 = 5x + 15 + 12 = 5x + 27

Properties If you don’t know the properties… you can’t simplify or solve expressions or equations!! Which property do you understand well enough to explain to someone else? Explain it now and provide an example!

Algebraic Expressions What is the difference between an English phrase and a sentence? What is the difference between a mathematical expression and an equation? Since the root word of equation is equal, the equations have equal signs and the expressions don’t!

Algebraic Expressions Use the properties to solve these expressions: Explain the steps 3(w + 5) + 5w + 2 w + 4(y + 8) 7( x + y) + 3x – 5y 2(x + 19) + 3(x – 10)