Math 6A ( Periods 2 & 4)

Distributive Property 1-4
Distributive Property of Multiplication with Respect to Addition
DP+
a(b +c) =ab + ac
(b+c)a = ba +ca

Distributive Property of Multiplication with Respect to Subtraction
DP-
a(b -c) = ab -ac
(b -c)a = ba -ca
What's this property all about.. it is about making it easier for you to simplify!!

13(15) you could use your 5th grade skills and multiply it out or...
13(15) = 13(10 +5) = 130 + 65 = 195
OR
(10 +3)(15) = 10(15) = 3(15) = 130 + 45 = 195
SAME SOLUTIONS
What about
23(11) hmmm...
(20+3)11 = 20(11) + 3(11) = 220 + 33 = 253
OR
23(10 +1) = 23(10) + 23(1) = 230 + 23 = 253

we then took a little sidebar and discuss the trick of elevens.... If you missed that explanation.. ask a fellow student to explain multiply 2 digit numbers by 11... You will love it!!


(101)(34) = (100+1)(34) = 100(34) + 1(34)= 3400 + 34 = 3434

What about 54(29) What could you do to make that easier than just multiplying out???
54(29) = (50 +4)(29) = (50)(29) + 4(29) is that any easier? What about...
54(20 +9) = 54(20) + 54(9) ... hmmm... is that easier?? What about..
54(30-1) = 54(30) - 54(1) that looks easier...
We took the time to try all three methods and discovered that the results were all 1566!!
Thank goodness!!
9× 57 What could we do here?
9(50 +7) = 450 +63 =
OR
9(60 -3) = 540 -27
OR
(10-1)57 = 570 - 57
and we discovered again... they all equaled 513


If you have...
(7 × 9) + (13 ×9)
Look and see what they share...
They both have a nine
Pull that out and put one set of HUGS ( ) with the sign that is in the middle of the two
in this case it is +
so you have
( __+ ___)9
Now look at each term, what is the other number in each of the HUGS
7 is in the first one and 13 is in the second so
(7 +13)9    NOW in this case, you want to add them BEFORE you multiply
(7 +13)9 = (20)9= 180 That's TOO easy that way!!

(117 × 4) - (17 × 4)
Ask yourself.. what do they share? 4
Build your HUGS with the sign in the middle --> in this case it's subtraction
( __- ___ )4
Now put the other terms in place
(117-17)4 = (100)4 = 400 ....OMG that is way too easy now!!


(8× 6) + (2 × 6)
well we could just do it.. like 5th grade and get
48 + 12 = 60
or we could start the DP+
(8 + 2)6 and still get 48 + 12 = 60
OR
you could use the DP+ to make it even simpler
(8 +2)6 = (10)6 = 60 in 2 seconds flat!!