USING GENERIC RECTANLGES TO MODEL THE
DISTRIBUTIVE PROPERTY!
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The Distributive Property is used
constantly in class for mental Math.
That means it is used to solve hard
Multiplication problems in your head.
Just watch!
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1
Let’s say we want to multiply 53 x 6
Doing 53 x 6 in your head can be a challenge.
So let’s break it apart to make it easier.
We know that:
53 = 50 + 3
(50 • 6) + (3 • 6)
(300) + (18)
= 318
So 53 • 6 = 318
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Let’s try more mental Math!
16 • 8
24 • 7
(10 • 8) + (6 • 8)
(20 • 7) + (4 • 7)
(80) + (48)
= 128
(140) + (28)
= 168
This works because of the DISTRIBUTIVE PROPERTY!!!
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2
A generic rectangle can be used to model
the Distributive Property.
The Distributive Property wants you to
distribute what is on the outside of the
parenthesis to the inside of the
parenthesis.
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Let’s say we want to do the following
problem using mental Math.
3 • 19
3(10 + 9)
10 + 9
3 3(10) + 3(9) = 3(10) + 3(9)
10 + 9
3 30
+
27
= 30 + 27
= 57
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3
Now let’s try a problem using a variable.
4(x + 5)
4(x + 5)
x + 5
4 4(x)
+ 4(5)
= 4(x) + 4(5)
x + 5
4 4x
+ 20
= 4x + 20
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A generic rectangle can be used to model the Distributive
Property. The Distributive Property wants you to distribute
what is on the outside of the parenthesis to the inside of the
parenthesis.
x + 4
5(x + 4)
5
5(x)+ 5(4)
= 5x
+ 20
y –7
3(y –7)
3
3(y) – 3(7)
= 3y– 21
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4
Simplify using the distributive property.
1) 5(x + 3)
2) 6(y + 7)
5• x + 5•3
6• y + 6•7
5x + 15
6y + 42
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Simplify using the distributive property.
3) 3(a − 9)
3• a − 3• 9
4) 4(3 − y)
4•3 − 4• y
12 − 4y
3a − 27
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5
Simplify using the distributive property.
5) 10(x + 6)
10 • x + 10 • 6
10x + 60
6) 4(g − 2)
4•g − 4•2
4g − 8
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Simplify using the distributive property.
7) x(2x − 8)
x • 2x − x • 8
2x 2 − 8x
8) 7(5 − y)
7•5 −7• y
35 − 7y
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6
Simplify using the distributive property.
9) 3(a + b + c)
3 • a +3 • b +3 • c
3a + 3b + 3c
10) 4(x − 2 + m)
4 • x −4 • 2 +4 • m
4x − 8 + 4m
Try these! They are challenging!
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THE END!
Take out your study guide
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7
#7
A generic rectangle can be used to model the Distributive
Property. The Distributive Property wants you to distribute
what is on the outside of the parenthesis to the inside of the
parenthesis.
x + 4
3(x + 4)
3
3(x)+ 3(4)
= 3x
+ 12
y –7
5(y –7)
5
5(y) – 5(7)
= 5y– 35
copyright©amberpasillas2010
#8
a(b + c) = ab + ac
The distributive property is very useful for mental math!
Ex:
16 • 8
(10 • 8) + (6 • 8)
(80) + (48) = 128
4(x+5)
= 4(x) + 4(5)
6(y-2)
= 6(y)– 6(2)
= 4x + 20
= 6y – 12
-3(a+7)
= -3(a) + -3(7)
= -3a + -21
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