Math 6H Period 3, 6 & 7

Distributive Property 1-4

I like to eat...eat...eat..eat Apples and Bananas... now what did that have to do with the distributive property???
The Distributive Property of Multiplication with Respect to Addition
For any whole numbers , a,b, and c,

a(b + c) = ab + ac
and
(b + c)a = ba + ca

so the reason we want to use the Distributive Property is to make our lives easier
for example
13 X 15 could be easily multiply using the distributive property 13(10 + 5) =
13(10) + 13(5) = 130 + 65 = 195

and if you were given (11 X4) + (11 X 6) you could do the reverse and say 11(4 +6) or 11(10) = 110


Similarly, we have the Distributive Property of Multiplication with Resepect to Subtraction

For any whole numbers a, b, and c
a(b - c) = ab - ac
and
(b-c)a = ba - ca

Since multiplication is distributive with respect to both addition and subtraction, we refer to both properties as the DISTRIBUTIVE PROPERTY

99(43) yes, you could multiply it out but if you used the distributive property and thought of two numbers whose difference was 99 -- you could easily do this in your head..
That is,
(100 - 1)43 = 100(43) - 1(43) = 4300 -43 = 4257

51(27) could become (50 + 1)27 = 50(27) + 1(27) = 1350 + 27 = 1377

The distributive property is especially helpful with mental math!!