Properties 6.19 Identify properties for addition and multiplication Multiplicative property of zero Inverse property for multiplication

COMMUTATIVE PROPERTY

C o mmutative Property a + b = b + a (a)(b) = (b)(a) O rder doesn’t matter

C o mmutative Property O rder doesn’t matter = = (4) = 4(2) 2 x 27 = 27 x 2

Does the Commutative Property work with Subtraction? 5 – 3 – 1 2 – – 1 – 5 2 – ≠

Does the Commutative Property work with Division? 4 ÷ 2 ÷ 2 2 ÷ ÷ 2 ÷ 4 1 ÷ 4 1/4 ≠

Check for understanding…. Name the property: a = C o mmutative Property of Addition Name the property: b. 3(2)(5) = 5(3)(2) C o mmutative Property of Multiplication

ASSOCIATIVE PROPERTY

Try: (1 + 3) Now Try: 1 + (3 + 14) =

When you are multiplying, change the grouping. See what happens. You will get the same answer. Try: (2 x 3) x 4 6 x 4 24 Now Try: 2 x( 3 x 4) 2 x =

Does the Associative Property work with Subtraction? (14 – 3) – – (3 – 2) ≠

Does the Associative Property work with Division? ≠

Check for understanding… (5 + 19) = (3+ 5) + 19 Associative Property of Addition (2 x 4) x 16 = 2 x (4 x 16) Associative Property of Multiplication = Commutative Property of Addition 20 x 14 x 8 = 14 x 8 x 20 Commutative Property of Multiplication

ADDITIVE IDENTITY PROPERTY

5 + 0 = = = = ____ 0.5 If you add zero to any number, the number keeps its identity – It stays the same!

MULTIPLICATIVE IDENTITY PROPERTY

15 x 1 = x 1 = 34 9 x 1 = x 1 = 101 If you multiply a number by 1, the number keeps its identity --- It stays the SAME!

Check for understanding…. What integer is the multiplicative identity? 1 What integer is the additive identity? 0

MULTIPLICATIVE INVERSE PROPERTY

Zero does NOT have a multiplicative inverse because you can NEVER have zero in the denominator of a fraction!

Do all real numbers have a multiplicative inverse? NO, Zero does NOT have a multiplicative inverse because you can NEVER have zero in the denominator of a fraction!

MULTIPLICATIVE PROPERTY OF ZERO

The product of any number and zero is zero! a x 0 = 0 5 x 0 = 0