Texes Mathematics 4-8 #115

Front 1

Natural Numbers

Back 1

Natural numbers are 1,2,3,4,... where the 4,... represents to positive infinity.

Front 2

Whole Numbers

Back 2

Whole numbers are the natural numbers (1,2,3,4,... pos. infinity) and zero.

Front 3

Integers

Back 3

The integers are natural numbers, their opposites (negative numbers), and zero. Example- ...-2, -1, 0, 1, 2, ...

Front 4

Rational Numbers

Back 4

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...

Front 5

Irrational Numbers

Back 5

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.

Front 6

Real Numbers

Back 6

Real numbers are all rational and irrational numbers.

Front 7

Prime Numbers

Back 7

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).

Front 8

Composite Numbers

Back 8

Composite numbers have three or more factors. Examples- 4, factors are 1, 2, 4. 12, factors are 1, 2, 3, 4, 6, 12.

Front 9

Equivalency

Back 9

Equal in value. Examples- 1/2=5/10 or .5 etc.

Front 10

Scientific Notation

Back 10

Used to express very large or very small numbers, usually in science. Positive exponent= large number, Negative exponent = small number.

Front 11

Commutative Property

Back 11

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.

Front 12

Associative Property

Back 12

Allows for grouping. Addition- (a+b)+c = a+(b+c).
Multiplication- (a x b)c = a(b x c).

Front 13

Identity Property

Back 13

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.

Front 14

Inverse for Addition

Back 14

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.

Front 15

Inverse for Multiplication

Back 15

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).

Front 16

Density Property

Back 16

There are an infinite amount of rational numbers between any two rational numbers.

Front 17

Closure Property

Back 17

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.

Front 18

Distributive Property

Back 18

Combines addition and multiplication. States that a(b+c)=ab+ac, and that (b+c)a=ba+ca.

Front 19

Complex Number System

Back 19

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.

Front 20

Imaginary Number

Back 20

A number like 14i where i is the square root of -1, or a complex number where a=0 and b≠0.

Front 21

Complex Number

Back 21

An imaginary number with a real number. Example- a + bi.

Front 22

Real Numbers

Back 22

A complex number where b = 0.

Front 23

Equality Property

Back 23

a+bi=c+di when a=c and b=d.

Front 24

FOIL Method

Back 24

Multiplying complex numbers using first, outer, inner, and last. Example- (a + bi)(c + di)

Front 25

Algorithms

Back 25

A series of steps or repetitive steps to solve a certain type of problem.