Download The Distributive Property (3-1)

The Distributive Property (3-1)
Understanding the Distributive Property
Ex. A family of 4 is going to the movies. If each of them buys a small popcorn for $2.50 and a
small drink for $1.50, how much will the family spend?
Write an expression to solve this problem
Write a different expression to solve this problem
___________________ = __________
___________________ = __________
Therefore _________________ = __________________
Ex. Find the total area of both rectangles. Remember that A = bh
3
4
2
Method 1
Method 2
3
3
4
+
3
4
2
2
A = _______________
A = _________________
A = _______________
A = _________________
A = ________
A = ________
Therefore _________________ = __________________
Definition: Equivalent Expressions have the same value


The Distributive Property
Combines Addition and Multiplication
Changes an expression to an equivalent expression
a(b + c) = ab + ac or
4(3 + 2) = 43 + 42 or
(b + c)a = ab + ac
(3 + 2)4 = 43 + 42
1
Use the Distributive Property to write each expression as en equivalent expression. Then
evaluate
Ex. 2(6 + 4) = ______________ = ____________ = _____
(equivalent expression)
(evaluate)
Ex. (8 + 3)5= ______________ = ____________ = _____
(equivalent expression)
(evaluate)
You can also use the distributive property with subtraction
Ex. 7(3 – 2) = ______________ = ____________ = _____
(equivalent expression)
(evaluate)
Ex. –3(5 – 2) = ______________ = ____________ = _____
(equivalent expression)
(evaluate)
You can also use the Distributive Property for Algebraic Expressions.
Ex. 3(x +1) = ___________________ = _______________
(equivalent expression) (Simplify)
Ex. (y + 4)5 = __________________ = _______________
(equivalent expression)
(Simplify)
Ex. 4(y – 3) = __________________ = _______________
(equivalent expression) (Simplify)
Ex. –2(x – 5) = __________________ = ______________
(equivalent expression) (Simplify)
Using the Distributive Property for Mental Math
If you are trying to multiply two numbers, you can use the distributive property to change the
problem into a simpler problem to solve
Ex. 24  6 = ( _____ + _____)  _____ = ______ + _____ = _____ + _____ = ______
Ex. 9  75 = _____  ( _____ + _____) = ______ + _____ = _____ + _____ = ______
Ex. 15  14 = _______________________________ = ___
Ex. 106  8 = _______________________________ = ___
2