Math 6H (Period 6 & 7)

Distributive Property 1-4
The Distributive Property of Multiplication with Respect to addition
For any whole numbers a, b, c,

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

The Distributive Property of Multiplication with Respect to Subtraction
For any whole numbers a, b, 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

The Distributive Property is used to simplify expressions.
for example
(8 × 6) + (2 × 6) can be solved quickly when you use the distributive property
(8 +2)6 = (10)6 = 60
The following were taken from the Class Exercises on Page 14... Check them out
4(3 + 8) = 4 × 3 + 4 × 8
6(5 + 9) = 6 × 5 + 6 × 9
9(7 - 4) = 9× 7 - 9 × 4
7( 12 + 15) = 7× 12 + 7×15
5(11 - 3) = 5 × 11 - 5 × 3

(9 ⋅ 7) + (9 ⋅ 13) could be solved by multiplying 9× 7 = 63 and adding it to 9× 13= 117
BUT... using the distributive property
(9 ⋅ 7) + (9 ⋅ 13)= 9( 7 + 13) = 9(20) = 180

and
(8 × 9) + (8 × 1) could have been solved by first doing
8 × 9 = 72 and then 8 × 1= 8 and then adding them BUT..
with the distributive property
(8 × 9) + (8 × 1) = 8(9 + 1) = 8(10) = 80 :)
(54 × 11) - (24 × 11) simplifies to
(54 - 24)11 =
30(11) = 330

11(88 - 42) ...
now with this one it doesn't help to separate
that is making 11(88 - 42 ) = 11(88) -11(42) is NOT going to make it easier
so
11(46) = 506... using the trick of 11's that we learned today... do you remember it???

(93 × 5) - (23 × 5) =
(93-23)5 =
(70)5 = 350