Arithmetic & Number Properties 1 Flashcards
Integers
Any counting number including negative numbers (e.g. -3, -1, 2, 7… but not 2.5)
Real numbers
Numbers that appear on the line (i.e. not imaginary) including pi, square root of 2, etc.
Order of operations
Complete any arithmetical operation in following order: 1) Parentheses 2) Exponents 3) Multiplication/Division 4) Addition/Subtraction (PEMDAS)
The Commutative Property
a + b = b + a , a x b = b x a NOTE: does not work with subtraction or division
The Associative Property
(a + b) + c = a + (b + c) , (a x b) x c = a x (b x c) NOTE: does not work with subtraction or division
The Distributive Property
a x (b + c) = ab + ac , a x (b - c) = ab - ac
Prime Numbers
A number that is divisible only by itself and 1. In other words, a positive integer with exactly 2 positive divisors. 1 is not a prime. 2 is the smallest prime and the only even prime.
Factors
If X can be multiplied by Y to get Z, assuming all of these are positive integers, then X and Y are considered factors of Z.
Prime Factorization
Dividing a number into its constituent primes. Ex. 21, is 3 x 7; 60, is 2 x 2 x 3 x 5 (60 = 30 x 2 = 15 x 2 x 2 = 5 x 3 x 2 x 2)
Greatest Common Factor (greatest common divisor)
The biggest factor shared by two numbers. The easiest way to find the GCF is to take the prime factorization and multiply all of the primes that appear in both numbers. If two numbers share no primes, the GCF is 1.
Least Common Multiple
The smallest positive integer with both numbers as a factor. To find the LCM of any two numbers, take the prime factorization of each number, find what prime factors appear in both, and multiply one of each of the shared primes and then by all the unshared primes. The largest possible LCM for any two numbers is one multiplied by the other.
