Math 6 Honors Periods 1, 6 & 7

The Distributive Property 1-4

Distributive Property of Multiplication
(with Respect to Addition)

For any whole numbers a, b, and c,

a x (b + c) = (a x b) + (a x c)
and (b + c ) x a = (b x a ) + (c x a)

or written without the multiplication operator symbol
a(b + c) = ab + ac
(b+c)a = ba + bc
Remember that the parentheses indicate which operation to do first.


How could we simplify the following using the distributive property?

a. 13 x 15
13(10 + 5) = 13(10) + 13(5)


b. (11 x 4) + (11 x 6)
11( 4 + 6) = 11(10)

Distributive Property of Multiplication
(with Respect to Subtraction)

For any whole numbers a, b, and c,

a x (b - c) = (a x b) - (a x c)
and (b - c ) x a = (b x a ) - (c x a)

or written without the multiplication operator symbol

a(b -c) = ab - ac
(b-c)a = ba - ca which is better written ab- ac

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

Pre Algebra Period 2 (Monday)

CHAPTER 1-9: MULTIPLYING AND DIVIDING INTEGERS

They have the SAME rules!!!!

Math Book Rules:
If you have 2 signs that are the SAME -
answer is POSITIVE
If you have 2 signs that are DIFFERENT -
answer is NEGATIVE

Good Guy/Bad Guy Rules:
GOOD thing happens to GOOD person= GOOD = POSITIVE

BAD thing happens to BAD person = GOOD = POSITIVE
(they got what they deserved!)

GOOD thing happens to a BAD person = BAD = NEGATIVE
(we hate when good things happen to people who don't deserve it!)

BAD thing happens to a GOOD person = BAD = NEGATIVE
(we hate when that happens because it's so UNFAIR!)

Finger Rules:
If your index finger represents the negative sign, then if you have 2 negatives, you have the index fingers of both your left hand and your right hand and they make a plus sign!
If you just have one negative, it just stays negative because you don't have another finger to cross it!
If you have more than 2 negatives, you just keep using your index fingers to determine the sign.
We did this in class. It's fun! But once you get it, you won't need to keep doing it! (unless you want to keep having fun!!!)

WHAT IF THERE IS MORE THAN 2 SIGNS?
Use Aunt Sally Rules and go left to right
or
BE A SIGN COUNTER:
an ODD number of NEGATIVES = NEGATIVE
an EVEN number of NEGATIVES = POSITIVE

EXAMPLE: (-2) (-5) (-3) = -30 (odd number of negatives)
(2) (-5) (-3) = +30 (even number of negatives)
(2) (5) (-3) = -30 (odd number of negatives)

Averages ( or the Mean): Adding up all the numbers and dividing by the number of numbers

Algebra Period 3 (Monday)

CHAPTER 2-1: ABSOLUTE VALUE
Note:
It is difficult to show the symbol for absolute value here so l n l should be read as “the absolute value of n”

l n l = 5 has 2 possible answers: {-5, 5}
l n l= -5 is impossible! It's the null set and that symbol is either { } or a 0 with a slanted line through it

FORMAL DEFINITION OF ABSOLUTE VALUE:
absolute value of n is n if n was a positive number or zero
absolute value is the opposite of n if n was a negative number
(since absolute value is always positive)

The absolute value is a distance concept- the absolute value is the distance a number is from zero on a number line.

2 words often misunderstood:
withdrawing money is actually considered negative, while depositing is considered positive
The focus is not the money in your wallet, but the money in your bank account!

CHAPTER 2-2: RATIONAL NUMBERS:
Counting Numbers = natural numbers = 1, 2, 3, 4 …..
Whole Numbers = the natural numbers + 0… so 0, 1, 2, 3, 4, ….
Integers = the whole numbers and their opposites… so …-4, -3, -2, -1, 0, 1, 2, 3, 4….
Rational number = any number that can be expressed as the ratio (fraction) of two integers
a/b, where a and b are both integers and b cannot be zero
b cannot be zero because you cannot divide by zero.....IT'S UNDEFINED!
Proof of this was done in class

There are positive and negative rational numbers.
One way to put them in order from least to greatest is to simply place them on the REAL number line. Numbers will be least to greatest if read from the left to the right.
If you have both fractions and decimals, it's often easier to change the fractions into decimals by simply dividing the numerator by the denominator.
REMEMBER: When numbers are NEGATIVE, the closer they are to zero, the bigger they are.
Example: -1/2 is greater than -3/4
-2.3 is greater than -2.5

You can also find the absolute value of rational numbers -
They are ALWAYS POSITIVE unless you're talking about zero (which is neutral)