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Set

is a collection of distinct "things".

Cardinality

is the number of things in a set

Place Value

the quantity that a digit in a number represents depends - in a very specific way- on the position of the digit in the number

Expanded form

shows how it is composed of its place value parts. ex, 536 is 5 hundred 3 tens 6 ones

Number line

is a line on which we have chosen one location as 0 and another location as 1.

Base ten

the essence of the base ten systems was that every time we move to the left, we multiply by 10

Scale

the choice of a unit

Negative number

-N as the "opposite" of N

Absolute value

is the distance of M (a number) from 0.

Explain greater than and less than numbers

- look at the place value of the digits
- determine if the number is positive or negative
- the number line explanation

explain how to round

if the digit to the right of the place value we are being asked to round is 5 or greater then we round the digit and make every number after it 0.

Multiple

numbers that are the product of counting numbers

Factors

a number that divides another number evenly with no remainder

Even number

a number that is divisible by 2 with no remainder

Odd number

a number that is not evenly divisible by 2

quotient

the answer you get from dividing two numbers

divisor

the number you divide by

Divisibility test

a method for checking to see if a counting number is divisible by another counting number without actually carrying out the division.

divisibility test for 2

If the number is even, yes.
if the number is odd, no

divisibility test for 10

if the ones digit is 0, yes.
if the ones digit is not 0, no.

divisibility test for 5

if ones digit is 0 or a 5, yes.
if ones digit is not a 0 or a 5, no

divisibility test for 3

add the digits of the number.
if the sum of the digits is divisible by 3, yes

divisibility test for 9

add the digits of the number.
if the sum is divisible by 9, yes.

divisibility test for 4

only consider the last two digits.
if the number formed by the last two digits is divisible by 4 then yes.

prime numbers

are the counting numbers that are divisible by only 1 and themselves.

what are the first few prime numbers?

2,3,5,7,11,13,17, 19,23,29,31, and 37

composite numbers

are counting numbers that are not prime.

how to find the list of primes?

Sieve of Eratosthenes - start with 2 and cross out every 2nd number, then do 3 and every 3rd number, then 5, and every 5th number ....

Trial division

division by prime numbers to find out if the given number is prime. stop when your quotient (your answer) is smaller than the divisor (the number you divide by) .

factor tree

is a diagram that shows how to factor a number until the prime numbers are reached.

greatest common factor

- is the greatest counting number that is a factor of all the given counting numbers

least common multiple

is the smallest counting number that is a multiple of all the given counting numbers

The slide method

- make a table with the two numbers in separate columns with one extra column in the front
- write a common factor in the first column and the quotient (so your dividing) in the row beneath your initial numbers.
- repeat this process until the only common factor you have is 1
GCF = multiply all the common factors (the number in the first column)
LCM = multiply all the common factors and the last row of quotients

how to find the GCF of fractions

- find the greatest common factor of the top and bottom number of the fraction
- divide the top and bottom numbers by the GCF
- record results

how to find the LCM of fractions

- to add fractions look at the bottom of the fraction and find the least common multiple of the two numbers
- then create new fractions with the LCM ( multiply the original fraction with the number you multiplied by to get the LCM.)
- then add the product of both the fraction equations.