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(Ch. 10) GRE Arithmetic and Number Properties Review
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Kaplan Chapter 10
Terms in this set (37)
Commutative Laws of Addition and Multiplication
switching the order of any two numbers being added or multiplied together does not affect the result
Associative Laws of Addition and Multiplication
regrouping the numbers does not affect the result
Distributive Law
allows you to distribute a factor over numbers that are added or subtracted, by multiplying that factor by each number in the group. Also works for the numerator in division, but not when the sum or difference is in the denominator
multiple
the product of a specified number and an integer
An integer is divisible by 3 if...
its digits add up to a multiple of 3
An integer is divisible by 4 if...
its last two digits are a multiple of 4
An integer is divisible by 6 if...
it is divisible by both 2 and 3
An integer is divisible by 9 if...
its digits add up to a multiple of 9
Odd + odd =
even
Even + even =
even
Odd + even =
odd
Odd x odd =
odd
Even x Even =
even
Odd x even =
even
What are the first 10 prime numbers?
2, 3, 5, 7, 11, 13, 17, 19, 23, 29
prime factorization
the expression of a number as the product of its prime factors
To multiply two powers with the same base -->
Keep the base and add exponents together
To divide two powers with the same base -->
Keep the base and subtract the exponent of the denominator from the exponent of the numerator
To raise a power to another power -->
Multiply the exponents
ex. (3²)⁴ = 3⁸
To multiply two powers with different bases but the same power -->
Multiply the bases together and raiser to the power
Raising any non zero number to an exponent of zero equals
1
Raising a fraction between zero and one to a power produces -->
a smaller result
Raising a negative number to an even power -->
produces a positive result
Raising a negative number to an odd power -->
produces a negative result
Raising an even number to any exponent gives ____
an even number
Raising an odd number to any exponent gives ___
an odd number
Powers of 10
When 10 is raised to an exponent that is a positive integer, that exponent tells how many zeros the number would contain if it were written out
consecutive numbers
numbers of a certain type (integers, even, odd, prime) following one another without interruption
cube
number raised to the third power
decimal system
numbering system based on powers of 10; only numbering system used on the GRE. Each digit in a decimal number occupies a particular position (its place value)
decimal
a fraction written in decimal system format
digit
one of the numerals 0-9, a number can have several digits
distinct
different from each other
element
one of the members of a set
operation
a function or process performed on one or more numbers
part
a specified number of the equal sections that compose a whole
sequence
lists that have an infinite number of terms, in order. The terms are often indicated by a letter with a subscript indicating the position of the number in the sequence. Ex. a₃ denotes the third number in a sequence; aⁿ (but subscript) indicates the nth term
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