Math 6A (Periods 2 & 5)

Multiplying Integers 11-4


3 ⋅ -2 = -6
Its really repeated addition
or
-2 + -2 + -2 which we learned a few sections ago was equal to -6.

The product of a positive integer and a negative integer is a negative integer.

The product of ZERO and any integer is ALWAYS ZERO!!
a⋅0 = 0

Math imitates life...and Karma(?)
What was the story I told in class... it applies to
Multiplication & Division ...
+ ⋅ + = +
- ⋅ + = -
+ ⋅ - = -
- ⋅ - = +



The product of -1 and any integer equals the opposite of that integer.
(-1)(a) = -a

The product of two negative integers is a positive integer

For a product with NO ZERO factors:
-->if the number of NEGATIVE factors is odd, the product is negative
-->if the number of NEGATIVE factors is even, then the product is positive
Be a sign counter-- count your negatives!
Every integer and its opposite have equal squares!!

Remember-- if its all multiplication use the Associative & Commutative Properties of Multiplication to make your work EASIER!!

Using Exponents

Evaluate (-2)²
Write (-2)² as repeated multiplication

(-2)² = (-2)(-2) = 4

Evaluate
-5²
Notice that the exponent is ONLY touching the 5 so this is really
-(5∙5) = -25

Evaluate
(-4)³  =(-4)(-4)(-4) = 16(-4) = -64

Algebra:
Evaluate the expression when a = -2, b = 3, and c = -8
Always substitute your actual number in with {{Hugs}} that is  (  )
Example 1 ab would be ( -2)(3) = -6
Example 2 │a²c│= │(-2)²(-8)│ = │ (4)(-8)│=│-32│= 32
Example 3 -ab³ –ac  = - (-2)(3)² – (-2)(-8) = -(-2)(27) –(16) = -(-54) – 16 = +54 – 16 = 38
Did you get that one?
Look at each step to see what was done along the way!

Number Sense:
Find the next two numbers in the patterns:
7, -28, 112, -448, …
First what is happening to each?
It looks like each consecutive integer is 4 times the opposite of the previous number.
So the next two integers would be  1792,  -7168