Operations with Integers...

If you are having trouble working with integers here are some notes to help!

Addition:

RULE:  

If the signs are the SAME you ADD the values and keep the same sign

ex/ -4 + -8 = -12

If the signs are DIFFERENT you SUBTRACT the values and take the sign from the number with the greater absolute value

ex/ +9 + -15 = -6 (15 - 9 = 6 and the 15 is greater so the answer is negative)

Subtraction:

RULE:

1. Change the subtraction sign to an addition sign

2. Switch the sign of the second number (+ to - or - to +)

3. Follow the rules for addition!

Multiplication and Division:

RULE:
1. Multiply or divide the numbers normally

2. To decide the sign follow these rules:

~if the signs are the SAME the answer is POSITIVE

~if the signs are DIFFERENT the answer is NEGATIVE

Graphing:

Remember, the numbers stand for (x,y) which means go (left/right, up/down)

ORDER OF OPERATIONS

Remember: PEMDAS

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

Hint: - 3³

- (3 X 3 X 3)

-(27)

-27

-2⁴

-(2X2X2X2)

-(16)

-16

(-2)⁴

(-2)(-2)(-2)(-2)

(+4)(+4)

+16

Algebra Graphing:

Remember: the INDEPENDENT  VALRIABLE is the one you ALREADY KNOW before you start an experiment

the DEPENDENT VARIABLE is the one you WANT TO KNOW

Independent goes on the X-axis

Dependent goes on the Y-axis

The steeper the line, the more the Y value is changing, so the faster you are going :) (this will help with your stories!)

Algebra:

Step 1: write a let statement giving letters to the two variables

Step 2: Make a table to find a few values

Step 3: figure out the rule using the pattern, remember it has to go across the table not up and down

(what do you do to the independent variable to get the dependent variable?)

Step 4: write the rule as an equation using letters and numbers

How do you know if a point is on a line?

Step 1: write the equation for the line

Step 2: substitute the x value from the point in for the x variable and the y value from the point in for the y in the equation

Step 3: use PEMDAS to solve each side of the equation

Step 4: if the 2 sides come out equal then the point was on the line, if they dont then it wasnt!

ex/ is the point (4,6) on the line y = 2x - 2

Step 1: y = 2x - 2

Step 2: (6) = 2(4) - 2

Step 3: 6 = 8 - 2

6 = 6

Step 4: since they are equal then the point was on the line