Distributive Property 1.8
Another Friend
You can make equivalent (equal expressions) using the Distributive Property... this property allows you to multiply each term inside the ( ) instead of doing the ( ) first.
Distributing literally means giving... so think of DP as giving the multiplication to each term inside the ( )
You can make equivalent (equal expressions) using the Distributive Property... this property allows you to multiply each term inside the ( ) instead of doing the ( ) first.
Distributing literally means giving... so think of DP as giving the multiplication to each term inside the ( )
It's Halloween and you are giving
candy to each child who comes in the door. Every ghost, vampire, and princess
wants the candy... you can’t just stop somewhere in the middle
c( g + p + v) = cg + cp + cv
a( b + c + d) = ab + ac + ad
a(b – c- d) = ab – ac – ad
How is this property different
from Order of Operations?
Aunt Sally or PEMDAS) says Please
( ) first... do the operations inside the parenthesis first but the DP allows
you to multiply the number/variable outside the parenthesis by each term inside
to get the same results.
REMEMBER you must have the following characteristics
for the DP:
1. a number of variable outside the ( ) that is multiplied
2. terms inside that are separated by +
or -
2(3 + 5)
Aunt Sally ( order of operations) says 2 (8) = 16
Distributive property says 2 (3)
+ 2(5) = 6 + 10 = 16
Both are correct—just different
ways to arrive at the same answer. Now in this case—Aunt Sally was
smarter—using her method we arrived at the solutions faster... right?
So when does the DP help the
most?
When variables are present
2( y + 5)
Now Aunt Sally can’t do
ANYTHING... She is stuck
But the DP can help you simplify
to 2y + 2(5) which equals 2y + 10
The DP is also great for mental
math
15(23)
with this you just need to multiply out but using the distributive property you can change 23 into 20 + 3
15( 20 + 3) you probably can multiply 15(20) in your head thinking well 15 (2) is 30 so 15(20) must be 300 and 15(3)
is 45 so I add 300 + 45 ... and I can do that in my head 345
15(20+3) = 15(20) + 15(3) = 300 +
45 = 345
You can also use the DP
Backwards = FACTORING the GCF in Algebra
You are given
11(24) + 11 (76)
What do you normally do?
Instead look at this
expression... you notice that 11 is a COMMON FACTOR in each term....
The DP allows you to go BACKWARDS
BEFORE the 11 was distributed to both the 24 and 76.
Think: What would that look
like????
Se up a pair of parentheses
( )
Place the common factor in front
11( )
Place the two other factors
inside with the SAME operation given
11( 24 + 76 )
BUT WHY WOULD YOU WANT TO DO
THIS????
Because it easier to do the math
this way using Order of Operations
look
11( 24 + 76 )
= 11(100) = 1100
So the DP can also be stated this
way
ab + ac = a( b + c)
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