# 1 5 Distributive Property Distributive Property What does

1. 5 Distributive Property

Distributive Property • What does the word distribute mean? Deal out, hand out/around, share, divide up, disperse, spread • What do you think the distributive property means to do? Get rid of the parenthesis, share by multiplication

DISTRIBUTIVE PROPERTY DEFINTION: • If a (b + c), then a (b + c) = ab + ac Arrow Method: Box Method: a ( b + c) =

Examples: 1. 2. 3.

• Does the number of items in the parentheses or a subtraction change the distributive property? No more arrows • More Terms just mean ______. 4 (x + 2 + y) 5 (6 + 3 y + 4 x) 4 x + 8 + 4 y 30 + 15 y + 20 x same addition • Subtraction is the _____ as _______ negative with a ______ number. Subtraction Example: Distributive Property Example: • 12 – 5 = 12 + -5 3(12 – 5) = 3(12) + 3(-5) 36+ -15=21

Example 1 • Mr. Smith has three apples and 2 bananas. 3 Apples + 2 Bananas • He wants to double all the fruit that he has. 2(3 Apples + 2 Bananas) • That means he must double each kind of fruit he has. Example 2 • A freshman has 1 binder, 2 pencils, and 3 erasers on the first day of school. 1 Binder + 2 Pencils + 3 Erasers • On the next day of school he needs to triple the number of supplies. 3(1 Binder + 2 Pencils + 3 Erasers) • That means the freshman must 2(3 Apples) + 2(2 Bananas) triple each type of supply. 3(1 Binder) + 3(2 Pencils) + 3(3 • How much fruit will Mr. Erasers) Smith have? • How many supplies will freshman have? 6 Apples & 4 Bananas (10 3 Binders + 6 Pencils + 9 Erasers total pieces of fruit) (18 total supplies)

The X Games last 4 days in Los Angeles, California. There are BMX, Skateboarding, MOTO, and Rally Car Events. The expected attendance on each day for BMX is 12, 000 people, for Skateboarding 15, 000 people and for both MOTO and Rally Car 25, 000 people. One Day= 12, 000+15, 000+25, 000 4(12, 000+15, 000+25, 000)= 308, 000

In a typical week, the administrative assistance spends 10 hours using email, 12 hours meeting people and 6 hours on the phone. Set up an expression to determine how many hours the administrative assistant spends on these activities after 12 weeks of work. One week= 10 e + 12 m + 6 p 12(10 e + 12 m + 6 p)=120 e + 144 m + 72 p

What is a like term? • Any terms that contain the same variables and the same number of each variable (look at exponents) are called like terms. • Numbers by themselves are like terms together Identify the Like Terms 7 x + 3 – 4 yx + 2 – 8 x 2 x - x 2 – x + 5 5 x 2 + 7 – 4 y + 6 y – x m 3 + m 2 + m – 5 + 6 m 2

What is a coefficient? • The number multiplied by a variable Identify the coefficients. 7 x + 3 m + 2 n 2 5 x 2 + 6 y – x What does it mean to combine like terms? • Add or subtract the coefficients of like terms. Combine Like Terms 15 x + 18 x + 1 10 n + 10 n 2 + 9 n 2 - 7

HOMEWORK • Pg. 30 20 -28 EVEN, 37 -38, 39 -41

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