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 Numbers we think of when we think of numbers; positive or negative.
 Zero is an integer.



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Name digit and unit in 246 

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 2 = Hundreds digit
 4 = Tens digit
 6 = Units/Ones digit



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Name the digits and unit in 27.63 

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 2 = Tens digit
 7 = Units/Ones digit
 6 = Tenths digit
 3 = Hundreths digit



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The number that is left over at the end of division 


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Integers listed in order of increasing size without any integers missing in between.



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Formula for consecutive integers 

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Numbers that different values (x and y) 


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 Positive integer that can be divided evenly only by two numbers: itself and 1.
 2, 3, 5, 7, 11, 13
 2 is the smallest and only even prime number
 Neither 0 or 1 is a prime number
 All prime numbers are positive (no negatives)



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 When a number can be evenly divided by another number = divisble



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A number is divisible by two if... 

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Its units digit can be divided evenly by two.
Example: 772 is divisible by 2. 


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A number is divisible by 3 if... 

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The sum of its digits can be divided evenly by 3.
216 = 2+1+6= 9
9 is divisible by 3, so 216 is divisible by 3 


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A number is divisible by 4 if... 

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The number formed by its last two digits is divisble by 4.
3,028 > 28
28/4 = 8, so 3,028 is divisible by 4 


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A number is divisible by 5 if... 

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Its final digit is either 0 or 5 


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A number is divisible by 6 if... 

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It is divisble by both 2 and 3, the factors of 6.
318 is even, so it is divisble by 2.
318 = 3+1+8 = 12
12 is divisble by 3 


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A number is a factor of another number if it can be divided evenly into that number.
Factors of 15 = 1,3,5,15 


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A number (x) is considered to be a multiple of another number (y) if y times another integer equals x.
15 is a multiple of 3, since you can multiple 3x5
I would consider this like a "product" of a number
"Factors are few, multiples are many" 


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 Distance between a number and zero
 Always postive
 5 = 5
 6 = 6
 Expressed as a the number sandwiched between two lines l6l



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Best strategy for answering data sufficiency 

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Look at one statement at a time and determine whether you can crack that statement with the information provided. 


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The result of subtraction 

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The result of multiplication 

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In the expression x², the little two is called the 

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exponent (Raising to a power) 


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Order of arithmetic operations 

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Please  Parentheses
Excuse  Exponents
My  Multiplicaiton
Dear  Division
Aunt  Addition
Sally  Subtraction 


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When you are adding or multiplying a series of numbers, you can group or regroup the numbers any way you like. 


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The Distributive Law means that you get the same answer when you multiply a number by a group of numbers added together as when you do each multiplication separately.
a(b+c) = ab + ac 


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If a problem gives you information in "factored form", i.e. a(b+c), you should... 

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Distribute it immediately 


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If a problem gives you information in "distributed form", i.e. ab + ac), you should... 

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Another way of expressing division.
1 over 2 = 1 divided by 2 


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Bottom number in a fraction 


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Important way to think of a fraction... 

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Part/Whole
7/10 = 7 parts out of a total of 10 parts 


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Logic for adding and subtracting fractions with the same demonitor 

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Add: Simply add the nemerators and place them over the common denominator
1/7 + 5/7 = (1+5)/7 = 6/7 


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First thing you must do when adding or subtracting two or more fractions with different denominators 

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You must get them to all have the same denominator 


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How do you make different denominators the same 

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Multiple the numerator and denominator of each fraction by a number that will give it a denominator in common with the others
1/2 + 2/3 =
1/2 * 3/3 + 2/3 * 2/2
3/6 + 4/6 = 7/6 


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How to multiply fractions 

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Just multiply the numerators and put the product over the product of the denominators
2/3 * 6/5
Just multiple 2*6 = 12
3*5 = 15
12/15 


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How do you reduce fractions? 

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Find a factor of both the numerator and the denominator.
12/15
4*3 = 12
5*3 = 15
Remove the number in common (3)
and you just reduced your fraction to 4/5 

