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Absolute Value

The distance a number is away from zero

Distance vs. Change

Distance is always positive
To find:
Find absolute value of difference (#'s can be in any order)
*OR*
Subtracting the smaller # from the larger #
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Change in elevation/temperature may be pos. or neg. depending on if it's increasing or decreasing (going up or down)
Find just like distance, but pos. or neg. answer depending on direction

Commutative Property (addition and multiplication only)

You can swap numbers around and still get the same answer
(Only for all adding or all multiplying)
**Order does not matter **
Examples:
-5 + 3 = 3 + -5
(4)(2) = (2)(4)

Associative Property (addition and multiplication only)

It doesn't matter how we group the numbers
(i.e. which we calculate first)
You will still get the same answer. (Only for all adding or all multiplying)
Examples:
(3 + 4) + 5 = 3 + (4 + 5)
(3 x 4) x 5 = 3 x (4 x 5)

Distributive Property

The distributive property: we get the same answer when we:
added first, then multiply
5(1 + 3) = 5(4)= 20
**OR**
multiply each separately then add them
5(1 + 3) = 5(1) + 5(3) = 5 + 15 = 20

Identity Property of Addition

Adding zero to a number leaves it unchanged
Example:
-4 + 0 = -4

Identity Property of Multiplication

Multiplying a number by one leaves the number unchanged
Example:
3(1) = 3

Inverse Property of Addition

What you add to a number to get zero.
Example:
The additive inverse of -5 is 5
because -5 + 5 = 0.
The additive inverse will be the opposite sign.

Inverse Property of Multiplication

"When you multiply a number by its Multiplicative Inverse you get 1.
Example:
8 x (1/8) = 1
The multiplicative inverse is also called the reciprocal.

How do you change a decimal to a fraction?

1) Place the digits you see in the numerator
2) The denominator will be the place value that the last digit is in
3) Simplify
Example:
0.015 = 15/1000 = 3/200

How do you change a fraction to a decimal?

You can always divide the numerator (top) by the denominator (bottom)
**Remember:**
numerator goes in the house AND numerator goes in calculator first
OR:
Change the denominator to a power of ten. (This will not always work)

Adding and Subtracting Fractions

You MUST have a common denominator before you add or subtract fractions
Follow rules for rational numbers once denominators are the same

Multiplying Fractions

***Don't get a common denominator***
1) Simplify a numerator with a denominator if you can
2) Multiply numerators together, then multiply denominators
3) Simplify the fraction if you can

Dividing Fractions

Remember: Dividing is the same as multiplying by the reciprocal
1) Change the division to multiplication
2) Flip the second fraction over
3) Follow the rules for multiplying fractions

Even/Odd Rule of Multiplication

If there are an even number of negative signs, the product will be positive.
Ex. -2 x -3 x -4 x -5 = 120
If there are an odd number of negative signs, the product will be negative.
Ex. -2 x -3 x -4 = -24

Order of Operations

MUST be followed when multiple operations are in an expression.
Following the Order of Operations:
Remember it with *PEMDAS*
1st
*P*arentheses and brackets
2nd
*E*xponents
3rd
*M*ultiply or
*D*ivide from left to right
4th
*A*dd or
*S*ubtract from left to right