Download Model of The Distributive Property

Fri. 11/9
Copy the problem.
Starter #2:
Name each property and if
it is for addition or
multiplication.
1.) 8 + 0 = 8
2.) (3 + 2) + 1 = 3 +(2 + 1)
3.) -6 + 7 = 7 + -6
4.) ½ + ¼ = ¼ + ½
5) 3(10 + 2) = 3(10) + 3(2)
USING GENERIC RECTANLGES TO
MODEL THE DISTRIBUTIVE PROPERTY!
Learning Targets
#7: I can explain and use the MODEL for the
Distributive Property
B: 1 2 3
A: 1 2 3
I have these questions:
7.AF1.3
Learning Targets
#8: I can explain and use the Distributive
Property
B: 1 2 3
A: 1 2 3
I have these questions:
7.AF
•The Distributive Property is used
constantly in class for mental Math.
•That means it is used to solve
multiplication problems in your head.
•Just watch!
•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
•Let’s try more mental Math!
16  8
24  7
(10  8)  (6  8)
(20  7)  (4  7)
(80)  (48)
(140)  (28)
 128
So 16  8  128
 168
So 24  7  168
THIS WORKS BECAUSE OF THE DISTRIBUTIVE PROPERTY!!!
Model of The Distributive
Property
•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.
Model of The Distributive
Property
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
Model of The Distributive
Property
Now let’s
try a problem using a
4( x  5)
4(x + 5)
variable.
x + 5
4 4(x)
+ 4(5)
= 4(x) + 4(5)
x + 5
4 4x
+ 20
= 4x + 20
Model of The Distributive Property
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
Simplify using the distributive property.
1) 5(x  3)
4) 4(3  y)
5 x  5  3
43 4 y
12  4y
5x  15
2) 6(y  7)
6  y  6 7
6y  42
5) 10(x  7)
3) 3(m  8)
3 m  3  8
6) 4(k  2)
4 k  4 2
3m  24
10  x  10  7
10x  70
4k  8
Simplify using the distributive property.
1) 4(x  7)
4) 7(8  x)
4  x  4 7
78 7 x
4x  28
2) y(y  3)
y y  y3
y  3y
2
3) x(2x  9)
x  2x  x  9
2x  9x
2
56  7x
5) x(a  b  c)
xa  xb xc
ax  bx  cx
6) 4(3  m  k)
43 4 m  4 k
12  4m  4k
THE END!!!
Take out your
Learning Targets
LT #7
Model of The Distributive Property
A generic rectangle can be used to model the Distributive
Property. The Distributive Property wants you to distribute
(give away) what is on the outside of the parenthesis to the
terms on the inside of the parentheses.
x + 4
3(x + 4)
3(x)3 + 3(4)
= 3x
+ 12
y –7
5(y –7)
5(y) 5– 5(7)
= 5y–
35
LT #8
The Distributive property is very useful for mental math!
a(b + c) = ab + ac
Example:
16  8
(10  8)  (6  8)
(80)  (48)
4(x+5)
6(x-2)
 128
= 4(x)
+ 4(5)
= 6(x) – 6(2)
= 4x + 20
= 6x – 12
-3(x+7) = -3(x) + -3(7) = -3x+ (-21)
Name___________
November 9, 2012
Period___
The Distributive Property and Review
Worksheet