DO NOW#11 – Thurs, 9/26 1) 3² - 4 x ) 4 x 3 + (9 + 2³) - 4

Homework Review & Dipstick Quiz

Chap 1.3 – 1.4 Quiz

Chapter 9 Lesson 1 Properties

Important Properties we NEED to know… Commutative Property Associative Property Distributive Property

Commutative Property We all know that…. ◦ 4 x 5 and 5 x 4 give us the same product ◦ and give us the same sum When adding or multiplying, ORDER DOES NOT MATTER!!

Commutative Property The commutative property tells us that the order in which numbers are added or multiplied does not change the sum or the product. This property is not true for subtraction or division because order DOES matter in these problems.  9 – 2 and 2 – 9 give you different differences!

Commutative Property ALGEBRA a + b = b + a c × d = d × c EXAMPLES = = 15 4 x 6 = 6 x 4 24 = 24

Associative Property The associative property involves the use of parentheses. We use parentheses to group numbers in expressions. The associative property tells us that the way numbers are grouped when added or multiplied does not change the sum or product.

Associative Property ALGEBRA (a + b) + c = a + (b + c) (d × e) × f = d × (e × f) EXAMPLES (6 + 7) + 8 = 6 + (7 + 8) = = 21 (2 × 3) × 4 = 2 × (3 × 4) 6 × 4 = 2 × = 24

Distributive Property We can use the distributive property to help us solve multiplication problems mentally. “Distribute” means to share, give out, or split up.

How Distributive Property Works = 8(5) +8(3) 8 (5 + 3)

Distributive Property In a problem like 6 x 53 where we would normally need a think box… ◦ Split up 6 x 53 into 6(50 + 3) ◦ We can solve this MENTALLY!  6 (50) + 6(3)   318

Distributive Property ALGEBRA a(b + c) = ab + ac Or (b + c)a = ba + ca EXAMPLES 4(80 + 2) = 4(80) + 4(2) = = 328 (30 + 8)7 = 30(7) + 8(7) = = 266

Practice With the Distributive Property… 8(62) = 8 (60 + 2) 8(60) + 8(2) (58)3 = (50 + 8)3 50(3) + 8(3)

Now you try… 1) 12 (24) 2)7(10 + 6) 3) (93)5