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1.5 Distributive Property

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

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1.5 Distributive Property

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  1. 1.5 Distributive Property

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

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

  4. Examples: 1. 2. 3.

  5. (2r + 3s – 7t) (-4) • –r (- 5 + 11s) • 2 (7 – b – c) • 5 ( -6m + 4n – 11p) Practice • (4y + 5z) 6 • 5 (2x + 1) • –3 ( 7x + 2) • 4 ( 3 – x) • c ( 2d + 6) • (y – 3) (-2) • 3 (x + 7 – 9y) • ( x + 6 + 3y)5

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

  7. 3 Apples + 2 Bananas Example 1 Example 2 1 Binder + 2 Pencils + 3 Erasers • Mr. Smith has three apples and 2 bananas. • He wants to double all the fruit that he has. • That means he must double each kind of fruit he has. • How much fruit will Mr. Smith have? • A freshman has 1 binder, 2 pencils, and 3 erasers on the first day of school. • On the next day of school he needs to triple the number of supplies. • That means the freshman must triple each type of supply. • How many supplies will freshman have? 2(3 Apples + 2 Bananas) 3(1 Binder + 2 Pencils + 3 Erasers) 2(3 Apples) + 2(2 Bananas) 3(1 Binder) + 3(2 Pencils) + 3(3 Erasers) 6 Apples & 4 Bananas (10 total pieces of fruit) 3 Binders + 6 Pencils + 9 Erasers (18 total supplies)

  8. 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+25,000 4(12,000+15,000+25,000+25,000)= 308,000

  9. 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= 10e + 12m + 6p 12(10e + 12m + 6p)=120e + 144m + 72p

  10. 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 7x + 3 – 4yx + 2 – 8x 5x2 + 7 – 4y + 6y – x 2x - x2 – x + 5 m3 + m2 + m – 5 + 6m2

  11. The number multiplied by a variable What is a coefficient? Identify the coefficients. 7x + 3 m + 2n25x2 + 6y – x What does it mean to combine like terms? • Add or subtract the coefficients of like terms. Combine Like Terms 15x + 18x + 1 10n + 10n2 + 9n2 - 7

  12. Practice 5(x + 3) + 7 (4 + 2x) –9 ( 5r – 3) + 16 – 3 (z + y) – 4 (3 + z) • 3 (x + 4) + 2 • 5(y + 2) + 7y • 6(x – 2) – 8 • x (y – 2) + 2x  

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

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