January 25, 2016
Distributive Property
Many mathematical expressions can be
written in two different ways. The
distributive property will help us write
these equivalent expressions.
Let's look at some problem examples
January 25, 2016
Example #1: Yesterday Steve bought 5 DVD's at
the store. DVD's cost $8 each. Today he bought 7
more. How much money did he spend on DVD's?
Which method did you use?
5x8 + 7x8
or
8 x (5 + 7)
Will you get the same answer?
January 25, 2016
Let's check to see if the answers are the same
Ex 1: Yesterday Steve bought 5 DVD's at the store. DVD's
cost $8 each. Today he bought 7 more. How much
money did he spend on DVD's?
8x5 + 8x7
40 + 56
$96
or
8 x (5 + 7)
8 x (12)
$96
Pull
January 25, 2016
January 25, 2016
Example #2: There are four
children. Each has 2 blue pens
and 3 black pens. How many
pens is that altogether?
Can you write this problem two different ways?
4x2+4x3
8 + 12
20
4 x (2+3)
4x5
20
January 25, 2016
January 25, 2016
Example #3: How
many flowers are in
the image?
Can you write the problem two different ways?
4(3+4) = 4(7) = 28
4(3) + 4(4) = 12 + 16 = 28
January 25, 2016
Distributive Property
The preceding examples were all numerical
examples of the distributive property. The
distributive property also holds true algebraically
and can be stated as follows.
a (b + c) = ab + bc
a (b - c) = ab - bc
January 25, 2016
Distributive Property of Multiplication over Addition
a
ex
m
pl
e
3(6 + 2) = 3(6) +3(2)
Distributive Property of Multiplication a over Subtraction
e
pl
am
x
e
5(10 - 3) = 5(10) - 5(3)
Distributive Property of Division over Addition
a
ex
m
pl
e
4
8
_____
4 + 8 = __
+ __
2
2
2
Distributive Property of Division over Subtraction
am
ex
pl
e
12
-9
_____
3
__ - __
9
12
3
3
January 25, 2016
3(b + f + d) =
Pull
A value meal contains a burger plus a fry plus a drink. Show
visually and algebraically what is contained in 3 value meals.
Have t
meals.
algebr
3b + 3
multipl
additio
studen
January 25, 2016
A taco value meal contains 2 tacos plus a fry plus a drink.
Show visually and mathematically what is contained in 2 meals.
2(2t + f + d)=
January 25, 2016
How can you write an equivalent algebraic
expression using the distributive property?
To use the distributive property, you simply
"distribute" the number or variable outside the
parenthesis to each piece within the parenthesis.
January 25, 2016
Use the Distributive property to simplify
3(2x + 1)
3(2x + 1) = 3(2x) + 3(1)
simplify to 6x + 3
January 25, 2016
More Practice:
2(4x - 2)
Distribute to each piece
2(4x - 2)
Don't forget to include the same sign
2(4x
- 2) = 2(4x) - 2(2) = 8x - 4
January 25, 2016
Now let's practice together
1. 3(4a + 5)
4. - (4x + 3)
2. 4(5x - 1)
3. (2 + 7y)5
5. (2a - 7b + 4c)6
January 25, 2016
Use the Distributive property to simplify
9a - 3
3
9a
3
-
3
3
simplify to 3a + 1
January 25, 2016
More Practice:
Distribute to each piece
-5x + 20
5
20
-5x
+
5
5
Simplify and include the same sign
-x + 4
January 25, 2016
Now let's practice together
24 - 9x
1.
3
4. 12x - 9y + 6
3
2.
4d + 12
-4
24 - 6x
3.
-2
5. 10e - 25f + 15g
-5
January 25, 2016
Exit Ticket
Use the Distributive Property.
1. 2(x + 3)
3. 8(2 + 3w)
2. 5(n - 7)
4. -6(a + 4)
January 25, 2016