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### 25 Cards in this Set

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 Natural Numbers Natural numbers are 1,2,3,4,... where the 4,... represents to positive infinity. Whole Numbers Whole numbers are the natural numbers (1,2,3,4,... pos. infinity) and zero. Integers The integers are natural numbers, their opposites (negative numbers), and zero. Example- ...-2, -1, 0, 1, 2, ... Rational Numbers Rational numbers are numbers that can be written as a fraction a/b with a and b being integers and b≠0. Rational numbers either terminate or end with a repeating decimal. Example- 1.5 or 2 1/3 = 2.33... Irrational Numbers Irrational numbers are numbers that cannot be written as a fraction a/b with a and b being integers and b≠0. Irrational numbers do not terminate and do not end with a repeating decimal. Example- pi (3.14...), and the square root of 2. Real Numbers Real numbers are all rational and irrational numbers. Prime Numbers Prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, etc. These numbers have only two factors (1 and the number itself). Composite Numbers Composite numbers have three or more factors. Examples- 4, factors are 1, 2, 4. 12, factors are 1, 2, 3, 4, 6, 12. Equivalency Equal in value. Examples- 1/2=5/10 or .5 etc. Scientific Notation Used to express very large or very small numbers, usually in science. Positive exponent= large number, Negative exponent = small number. Commutative Property Allows for changing of the order (commuting the values from one place to another). Addition- a+b=b+a. Multiplication- a x b= b x a. Associative Property Allows for grouping. Addition- (a+b)+c = a+(b+c). Multiplication- (a x b)c = a(b x c). Identity Property This property does not change the value (identity) of a number. Addition- a+0=0+a. Multiplication- times positive 1, a x 1 = 1 x a = a. Inverse for Addition The inverse property for addition is adding the opposite of a number to result in zero: a + -a = 0. -a and a are additive inverses. Inverse for Multiplication The inverse property for multiplication is multiplying by the reciprocal to result in 1. (3/2)(2/3)=1, (-5)(-1/5)=1 since -5 = -5/1. This is a(1/a)=(1/a)(a). Density Property There are an infinite amount of rational numbers between any two rational numbers. Closure Property An operation of any two numbers in a certain set of numbers will result in a number that is also in that same set. Example- the multiplication of two counting numbers results in another counting number. a+b is in the same set as a and b, or a x b is in the same set as a and b. Distributive Property Combines addition and multiplication. States that a(b+c)=ab+ac, and that (b+c)a=ba+ca. Complex Number System Written as a+bi, where a is a real number and bi is and imaginary number part. The i is the square root of negative 1 so that i squared = -1. Imaginary Number A number like 14i where i is the square root of -1, or a complex number where a=0 and b≠0. Complex Number An imaginary number with a real number. Example- a + bi. Real Numbers A complex number where b = 0. Equality Property a+bi=c+di when a=c and b=d. FOIL Method Multiplying complex numbers using first, outer, inner, and last. Example- (a + bi)(c + di) Algorithms A series of steps or repetitive steps to solve a certain type of problem.