GRE Math Fact V.1

• The integers are {...-3, -2, -1, 0, 1, 2, 3...}
• An integer is any negative or postive number

• The sum is the result of an addition.
• The difference is the result of subtraction.
• The product is the result of multiplication.
• The quotient is the result of division.

• When 23/5 it comes out to 4 with a remainder of 3.
• 23=4*5+3

When 35/5 the quotient is 5 and 0 is the remainder, or there is no remainder.

The remainder muts be and integer that is greater than or equal to 0 and less than the number you are dividing by,

• The terms divisor and factor mean the exactly the same thing.
• A divisor (or factor) of an integer, n, is an integer that leaves no remainder when it is divided into n.

For example, the postive divisors (or factors) of 12 are: 1, 2, 3, 4, 6, and 12.

A prime number is a postive integer that has exactly two postive divisors, 1 and itself.

A multiple of an integer, n, is any integer that is the product of n and another integer.

For example: 50 is a multiple of 10 since 50 = 5*10.

An even number is a integer that is a multiple of 2.

An odd number is an integer that is not a multiple of 2.

The expression x^b, x is the base and b is the exponent.

• b^mbⁿ = b^m+n
• b^m/bⁿ = b^m-n
• (b^m)ⁿ = b^mn
• a^m * b^m = (ab)^m
• a^m/b^m = (a/b)^m

For any number, n: x^-n means 1/xⁿ

If x is positive and n is a positive integer: x^1/n means ⁿ

If x is postive, the square root of x, written , is the only postive number.

For any positive numbers x and y:

xy = x * y and a/b = a / b

If the product is equal to 0, then at least one of the factors is 0.

• The distributive law for any numbers a, b, c:
• a(b+c) = ab +ac and a(b-c) = ab-ac

also if a 0: (b+c)/ a = b/a + c/a and (b-c)/a = b/a - c/a

• 0 is the only number that is neither postive nor negative
• If a is negative and b is postitive, then a<0<b
• 0 is a multiple of every integer.
• In particular, 0 is a multiple of 2, so 0 is even.
• For every number a:
• a+0=a a-0=a a*0=0 a/0 is undefined
• For any number b: b=-b if and only if b=0
• If ab=0, then a=0 or b=0

• For any number a: a*1 amd a/1 = a
• For any integer n: 1ⁿ = 1
• 1 is a divisor and factor of every integer
• 1 is the smallest positive odd integer
• 1 is not a prime, since primes have exactly two positive divisors and 1 has only one positive divisor , 1

• A percent is a fractios whose denominator is 100.
• 17% = 17/100

• To convert a percent to a fraction or decimal, write it over 100 and if necessary reduce and divide.
• 50%=50/100=1/2=0.5

• To convert a fraction to a decimal or percent, divide the numerator b the denomiator, and then multiply by 100.
• 1/8 = 1/8 = 0.125 = 12.5%

Write the percent as a decimal and multiply.

To find 35% of 80, write 35% as .35 and multiply: .35*80=28

• The percent increase of a quanity is (actual increase/original amount) * 100%
• The percent decrease of a quanity is (actual decrease/original amount) * 100%

• A ratio is a fraction. Ratios can be expressed using the word "to" or suing a colon, ":", but is is best tro write them as a fraction. For example:
• 3 to 5, 3:5 and 3/5.

A proportion is an equation that states that two ratios are equilivant. Since ratiosi are just fractions, any equation, such as 4/5 = 10/15, in which each side is a single fraction is called a proportion.

By definition , y is directly proportional to x if the quotient y/x is a constant.

By definition y is inversely proportional to x if the product is xy is a constant.

The average (arithmetic mean) is a set of n numbers is the sum of those numbers divided by n.

Average = (sum of numbers) / n.