chapter 2, section 2: distributive property
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Chapter 2, Section 2: Distributive PropertyTRANSCRIPT
Ch. 2, Section 1: Distributive Property
Ms. Dewey-Hoffman, 2009
Page 2
To multiply a sum or difference, multiply each number within the parentheses by the number outside the parentheses.
Distributive Property
B(N + C) = BN + BC
Always distribute the number outside of the parentheses!
Page 3
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
Page 4
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!
Page 5
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
Page 6
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.
Page 7
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
Page 8
Distributive Property and Variables
4(2x – 3) =
Represents x
Represents 1
Represents –1
4(2x – 3) = 8x - 12
Reorganize
Page 9
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.
Page 10
#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