MTEL Elementary Math

Decimal

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problem - list the numbers shown below from least to greatest - 1/3, square root of 3, 3, .3

1/3 - 0.33333333 square root of 3 - 1.73205 therefore .3,1/3,square root of 3,3

examples of rational numbers

2,3,5,10,32,-2,-4,-18,-25,1/4,1/2,2/3,-1/4,101/635

problem - write each integer as a product of its primes 2,12,5,22,18,36

2=2x1 12=4x3=2x2x3 5=5x1 22=11x2 18=6x3=2x3x3 36=6x6=3x2x3x2 or 18x2=9x2x2=3x3x2x2

Real Numbers (reals)

Most of the numbers in algebra belong to a set called real numbers. Real numbers can be thought of as points on an infinitely long line called the number line or real line, where the points corresponding to integers are equally spaced.

Integers

The integers (from the Latin integer, literally "untouched", hence "whole": the word entire comes from the same origin, but via French[1]) are formed by the natural numbers (including 0) (0, 1, 2, 3, ...) together with the negatives of the non-zero natural numbers (−1, −2, −3, ...).They are known as Positive and Negative Integers respectively. Viewed as a subset of the real numbers, they are numbers that can be written without a fractional or decimal component, and fall within the set {..., −2, −1, 0, 1, 2, ...}. For example, 21, 4, and −2048 are integers; 9.75, 5½, and 14% are not integers

Natural Numbers

The set of integers starting with 1 and increasing: Ne 1,2,3,4,......

irrational number

a number that cannot be written as a simple fraction. It is an infinite and non repeating decimal

Fractions

a number that expresses parts of a whole or a group

prime number

a number that has no factors other than itself and 1 - examples - 1,3,5,7

Rational Numbers

any number that can be written in the form a/b where a is any integer and b is any integer except 0. All rational numbers can be expressed ad decimals by dividing b into a.

repeating decimal

b continues to divide into a so that the decimal has a repeating pattern of integers

Examples of irrational numbers

pie = approx - 3.14159 e - approx 2.71828 square root of 2 approx 1.41421

Absolute Value

represented by two vertical lines around the number and is equal to the given number regardless of sign

Order of operations

the order in which operations in an expression to be evaluated are carried out. 1. parentheses 2. exponets 3. multiplication and divison 4. addition and subtraction - pneumonic: please excuse my dear aunt sally

Numerator

the part of a fraction above the line, which tells how many parts are being counted.

Denominator

the part of a fraction below the line, which tells how many equal parts there are in the whole or in the group.

Terminating decimal

the result of dividing b into a in a rational number with a remainder of 0 after a certain point

Even Integers

the set of integers divisible by 2 - - -4,-,0,2,4,6

Negative Numbers

the set of integers starting with -1 and decreasing z = -1,-2,-3

Whole Numbers

the set of integers starting with 0 and increasing 0,1,2,3....

Prime Numbers

the set of positive integers greater than 1 that are divisible only by 1 and themselves 2,3,5,7,11

Simplify Fractions

to reduce the numerator and the denominator in a fraction to the smallest numbers possible