Math 6A( Periods 1 & 2)

 The Distributive Property 1-4

The Distributive Property of Multiplication with Respect to Addition 

DP+

For any whole numbers a, b, and c

 a(b + c) = ab + ac

(b+c)a = ba + ca

13(15) … well you could just multiply it out but using the distributive property you might be able to do this in your head…

13(15) = 13( 10+5) = 13(10) + 13(5) = 130 + 65 = 195

9(11)  now we know this but let’s see what happens if we try using the distributive property

9(11) = 9(10 + 1) = 90 + 9 = 99  YAY!!!

We could have completed this another way…

9(11) = (10-1)(11) = 10(11) – 1(11) = 110 – 11= 99

This last example is really  an example of the

Distributive Property of Multiplication with Respect to Subtraction or

DP-

For any whole numbers a, b, and c

 a(b - c) = ab- ac

(b - c)a = ba - ca

What should we do with the following:

(117∙ 4) – (17∙ 4)

Last year you would multiply  (117∙ 4) and then multiply (17∙ 4) and then take the difference… but that is a long process

What happens if we use the distributive property?

(117∙ 4) – (17∙ 4) = (117-17)∙4= (100)4= 400

WOW—that was so much easier

More Examples of the Distributive Property:
(7∙ 9) + (13 ∙9)

They both share a 9 so pull the 9 out

(7 + 13)9

(20)9 = 180

WOW.. look at that!

But… what happens with

57 ∙ 9

There are a number of different ways we might set this up

(50 + 7)(9) = 50(9) + 7(9)

Or

57(10-1) = 57(10) – 57(1)

Or

(60-3)(9) = 60(9) – 3(9)

We could even set it up with the following but this would not help us to solve it easier…

(37 + 20)(9)… remember our discussion in class—it was to make the multiplication easier

The results for all of the above is 513

What about 25 ∙ 38

We could do 25(40 -2) = 25(40) – 25(2)

Now that’s easy…. 1000 – 50 = 950

25(30 + 8) also works but probably isn’t  quite as easy

25(30) + 25(8) = 750 + 200 = 950

101(34) = (100 + 1)(34) = 100(34) + 1(34) = 3434

(89∙ 5) – (19∙ 5)

(89-19)(5)

(70)(5) =350

So much easier than multiplying each separately!

BUT… what happens if you have

4(17 + 42)

Well we would first add the two numbers in the (  )

That gives us 4(59)… but that really did not make it any easier..

So now look at

4(59) and ask yourself what can you do with that number

4(60-1) = 4(60) – 4(1) = 240 -4 = 236!!

YAY!!