Chapter 2, Section 2: Distributive Property

Ch. 2, Section 1: Distributive Property Ms. Dewey-Hoffman, 2009

To multiply a sum or difference, multiply each number within the parentheses by the number outside the parentheses.
Distributive Property B ( N + C ) = B N + B C Always distribute the number outside of the parentheses!

Distributive Property Can Look A Lot of Different Ways
a(b + c) = ab + ac
(b + c)a = ba + ca
a(b – c) = ab – ac
(b – c)a = ba - ca

Use Distributive Property Backwards
To make some multiplication problems easier, try doing the Distributive Property Backwards.
20(102) = ?
= 20(100 + 2)  100 + 2 = 102, Break 102 into two parts that are easier to work with.
= 20(100) + 20(2)  Distribute the 20
= 2,000 + 40  PEMDAS, Multiplication
= 2,040  PEMDAS, Addition
20(102) = 2,040
Here we added two numbers to get 102.
Don’t forget that you can subtract too!

Distributive Property Backwards
Find the product of 9 and 199.
9(199) =
= 9(200 – 1)  200 – 1 = 199
= 9(200) – 9(1)  Distribute the 9.
= 1,800 – 9  PEMDAS, Multiplication.
= 1,791  PEMDAS, Subtraction.
9(199) = 1,791

Word Problem: Use The Distributive Property
Lego Robotics Class sold toy robotics for $7 each at a fundraiser. The class sold 204 robots. How much money did they raise?
7(204) =
= 7(200 + 4)  broke down to be easier
= 7(200) + 7(4)  distributed.
= 1,400 + 28  PEMDAS, multiplied.
= 1,428  PEMDAS, addition.
7(204) = $1,428
The Lego Robotics Class made $1,428 off of selling toy robots.

More Backward Distributive Property
12(52) – 12(62) =
= 12(52 – 62)  Pull out 12 and combine the 52 – 62
= 12(-10)  PEMDAS, Simplify in the parentheses
12(52) – 12(62) = -120  PEMDAS, Multiply.
Try This one :
(16)7 – (11)7 =
= (16 – 11)7  Pull out 7 and combine 16 – 11
= (5)7  PEMDAS, Simplify in the parentheses
= 35  PEDMAS, Multiply

Distributive Property and Variables
4(2x – 3) =
Represents x
Represents 1
Represents –1
4(2x – 3) = 8x - 12 Reorganize

More Distributive Property
Multiply:
-5 (4x – 3) =
= -5 (4x) – (-5) (3)  Distribute –5
= -20x – (-15)  PEMDAS, Multiply.
= -20x + (+15)  Add the Opposite.
= -20x + 15  Simplify, this is your answer!
Try This One:
(2x + 5)7 =
= 2x(7) + 5(7)  Distribute 7.
= 14x + 35  PEMDAS, Multiply.

#12
Page 76-77: 1-49 odd.
YOU MUST SHOW YOUR WORK!!!!!!!!!
When it says to Use the Distributive Property to Simplify, break up the big number and show steps.
Example:
#6: 5(18) = 5(20 – 2)
= 5(20) – 5(2)
= 100 – 10
= 90

Chapter 2, Section 2: Distributive Property

by Middle School on Sep 22, 2009

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