Math 7( Period 4)

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 (  )

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)