Math Chapter 1

common factor

all factors that two number have in common; for instance 12 and 30 have: 12:1x12, 2x6, 3,4 30:1x30, 2x15, 3x10, 5x6 12:1,12,2,6,3,4 30:1,30,2,15,3,10,5,6 resulting in common factors of 1, 2, 3, 6

factor

all of the possible combinations of numbers that can be multiplied to create a number

numerical expression rule order

1: Evaluate inside Parenthesis 2: Evaluate Exponents 3: Multiply and divide from left to right 4: Add and Subtract from left to right

prime number

A number that is only divisible by itself and one. It only has 2 factors, itself and one. for instance 3

cube root

A number that, when multiplied by itself, then multiplied by itself again, equals a given number; To find a cube root, find the prime factors of a number. if they can be grouped into 3 equal sets then it is a perfect cube and you can find the cube root. for example: 64= 2*2*2*2*2*2= (2*2)*(2*2)*(2*2)=(2*2)^3 64= 4^3 therefore 4 is the cube root of 64

perfect cube

Cubes which are a product of cubing an integer. For example, 27 is a perfect cube because 3x3x3=27 and 3 is an integer.

multiple

Multiples of a number are the number times a whole number from 1 continuing upward. Multiple of 5: 5, 10, 15, 20, 25, ....

perfect square

Numbers whose square roots are integers. for instance 9, 25, 36, 49

greatest common factor

The largest factor that two or more numbers have in common. Find the prime factorization then the greatest common factor (GCF) is the product of those factors which they have in common. 45= 3*3*5 75= 3*5*5 GCF=3*5=15

common multiple

The multiple of a set of numbers that they have in common Multiples of 8: 8, 16, 24, 32, 40, 48, ... Multiples of 12: 12, 24, 36, 48, ... Common multiples are: 24, 48, ...

square (of a number)

The product of a number with itself. Example: 81 is the square of 9, because 9 time 9 = 81

least common multiple

The smallest multiple (other than zero) that a set of numbers have in common. Find the prime factorization then the least common multiple (LCM) is the product of the largest number of factor (most 2's, most 3's, etc.). 45= 3*3*5 75= 3*5*5 LCM=3*3*5*5=225

square root

a number that when multiplied by itself equals a given number, for instance the square root of 25 = 5. To find a square root, find the prime factors of a number. if they can be grouped into 2 equal sets then it is a perfect square and you can find the square root. for example: 64= 2*2*2*2*2*2= (2*2*2)*(2*2*2)=(2*2*2)^2 64= 8^2 therefore 8 is the square root of 64

composite number

a number which has more than two different whole-number factors; for instance 18 has 6 factors, so it is a composite number

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base

`

exponent A mathematical notation indicating the number of times a quantity is multiplied by itself.

inverse of square root

square (of a number)

inverse of square (of a number)

square root

prime factor

the set of prime numbers that can be multiplied to create a number

cube (of a number)

the value of the number raised to an exponent of three for instance:

prime factorization

writing a composite number as only its prime factors