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GEAR RATIO = (number of teeth on the driven gear)/(number of teeth on the driving gear)
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COMPRESSION RATIO= (expanded volume)/(compressed volume)
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COMMON SIGN KEYWORDS  
POSITIVE  NEGATIVE 


Additional examples:
When evaluating mathematical expressions, be sure to follow the order of operations:
1) G: Groupings. These include parentheses, brackets, and braces.
2) E: Exponents. This includes roots and radicals.
3) M and D: Multiplication or Division. These both have the same "weight" so when you get to this step do whichever operation comes first when working from left to right.
4) A and S: Addition or Subtraction. These both have the same "weight" so when you get to this step do whichever operation comes first when working from left to right.
PROPERTY  DESCRIPTION  EXAMPLE 
Commutative Property of Addition  When two numbers are added, the sum is the same regardless of the order in which the numbers are added. 
2 + 3 = 5 3 + 2 = 5 
Associative Property of Addition  When three or more numbers are added, the sum is the same regardless of the way in which the numbers are grouped. 
6 + (4 + 3) = 13 (6 + 4) + 3 = 13 
Commutative Property of Multiplication  When two numbers are multiplied together, the product is the same regardless of the order in which the numbers are multiplied. 
3 • 5 = 15 5 • 3 = 15 
Associative Property of Multiplication  When three or more numbers are multiplied, the product is the same regardless of the way in which the numbers are grouped. 
6 • (4 • 3) = 72 (6 • 4) • 3 = 72 
Distributive Property  The sum of two numbers times a third number is equal to the sum of each addend times the third number. 
5(7 + 2) = 45 5 • 7 + 5 • 2 = 45 
Identity Property of Addition  Adding 0 to any number does not change the original value.  76 + 0 = 76 
Identity Property of Multiplication  Multiplying any number by 1 does not change the original value.  19 • 1 = 19 
Inverse Property of Addition  The sum of any number and its additive inverse is equal to 0.  5 + 5 = 0 
Inverse Property of Multiplication  The product of any number and its reciprocal is equal to 1.  4(1/4) = 1 
Zero Property of Multiplication  Any number multiplied by 0 is equal to 0.  123(0) = 0 
Know the order of operations, basic mathematical properties, and how to use your calculator properly.
Know what you know and know what you don'tespecially when solving a word problem. Clarify for yourself what it is you have and what you're being asked to find.
Don't skimp on writing things down. Write down the problem simply, in your own words. Set aside space to list out the variables in your problem, what they stand for, and what values are known to be associated with them. Color code to help you keep track.
Practice, practice, practice. Practice so much that the word practice no longer feels like a real word. Repeat the same problem multiple times.
Avoid skipping steps and definitely avoid not writing things down. This goes along with writing clearly: write each step on a new line. Don't sacrifice clarity for the sake of saving paper.
As you solve ensure you're following the correct steps and using the correct values. Your instinct might be to rush in order to get the pain over with as fast as possible but please resist this temptation.
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