e numbers 1, 2, 3, and so on, together with their negatives, and 0. Thus, the set of integers is - - - 1, 2, 3, . . . ,{. . . , 3, 2, 1, 0, 1, 2, 3, . . . . - - - }
factor or divisor
when integers are multiplied, the multiplied integers is called a factor or divisor of the resulting product.
The integers 4, 15, 5, and 12 are also factors of 60, since (4 15 60 )( ) = and (5 12 60. )( ) = The positive factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. The negatives of these integers are also factors of 60, since, for example, (- - = 2 30 60 )( ) .
multiple
all the numbers which a number can be multiplied into (ex 25: 25, 50, 75, 100, 125, 150...)
divisible
All numbers which are divide into a number (ex 25, 1,5, 25)
least common multiple
f two nonzero integers a and b is the least positive integer that is a multiple of both a and b.
For example, the least common multiple of 30 and 75 is 150. This is because the positive multiples of 30 are 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, etc., and the positive multiples of 75 are 75, 150, 225, 300, 375, 450, etc. Thus, the common positive multiples of 30 and 75 are 150, 300, 450, etc., and the least of these is 150.
greatest common divisor (or greatest common factor)
two nonzero integers a and b is the greatest positive integer that is a divisor of both a and b.
For example, the greatest common divisor of 30 and 75 is 15. This is because the positive divisors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30, and the positive divisors of 75 are 1, 3, 5, 15, 25, and 75. Thus, the common positive divisors of 30 and 75 are 1, 3, 5, and 15, and the greatest of these is 15.
prime number
an integer greater than 1 that has only two positive divisors: 1 and itself.
prime factorization
Every integer greater than 1 either is a prime number or can be uniquely expressed as a product of factors that are prime numbers, or prime divisors
composite number.
An integer greater than 1 that is not a prime number
numerator
top number of a fraction
denominator
bottom number of a fraction
common denominator
a common multiple of two denominators of different fractions
To divide one fraction by another
first invert the second fraction—that is, find its reciprocal—then multiply the first fraction by the inverted fraction.
mixed number
consists of an integer part and a fraction part
base
the whole number in an expression with a power (3^4- 3)
exponent
The power number in an expotential expresion. (ex 4^3- 3)
square root
nonnegative number n is a number r such that For example, 4 is a square root of 16 because Another square root of 16 is -4 since (-4 )^2=16 All positive numbers have two square roots, one positive and one negative. The only square root of 0 is 0.
True or false: Square roots of negative numbers are not defined in the real number system.
True
cube root cube
a root raised to the 3rd level 3 cube 3√n
fourth root
A number raised to the 4th power 4√n
True or false: there is exactly one root for every number n, even when n is negative.
True
For example, 8 has exactly one cube root, 3√8=2
True or False: For even-order roots, there is exactly one root for every positive number n and no roots for any negative number n
False. For even-order roots, there are exactly two roots for every positive number n and no roots for any negative number n4√8 and -4√8 and -8 has one cube root 3√-8=-2 but -8 has no fourth root because it is negative
irrational numbers
decimal numbers which do not terminate or repeat.
real numbers
consists of all rational numbers and all irrational numbers
absolute value
The distance between a number x and 0 on the number line