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Prime Number

Formula for Prime #s > 3

Factor

Factor Properties

2 divisors - 1 and itself

6n+1 or 6n-1

Divisor of an integer n... Integer which divides evenly into n

1. If a is a factor of c and a is a factor of b, then a is a…

Prime Number

2 divisors - 1 and itself

Formula for Prime #s > 3

6n+1 or 6n-1

An integer is said to be divisible by…

An integer is divisible by....

A factor is a positive integer that di…

A multiple of an integer is formed by…

...

- 2 if the integer is even... - 3 if the same of the integer's d…

For example, 1, 2, 3, and 8 are all the factors (also called…

...

An integer is said to be divisible by…

...

An integer is divisible by....

- 2 if the integer is even... - 3 if the same of the integer's d…

An integer is divisible by 3 iff

An integer is divisible by 4 iff

An integer is divisible by 6 iff

An integer is divisible by 8 iff

the sum of the integer's digits is divisible by 3

the integer is divisible by 2 twice, or the integer's last tw…

the integer is divisible by both 2 and 3

the integer is divisible by 2 three times, or the integer's l…

An integer is divisible by 3 iff

the sum of the integer's digits is divisible by 3

An integer is divisible by 4 iff

the integer is divisible by 2 twice, or the integer's last tw…

Interger

Arithmetic Processes that ALWAYS resul…

Arithmetic Process that SOMETIMES resu…

Intergers are Divisible by 2 if

positive and negative numbers that are whole. Includes zero

addition... subtraction... multiplication

division

the interger is even

Interger

positive and negative numbers that are whole. Includes zero

Arithmetic Processes that ALWAYS resul…

addition... subtraction... multiplication

An integer is divisible by 2 if:

An integer is divisible by 3 if:

An integer is divisible by 4 if:

An integer is divisible by 5 if:

It is even

The sum of the integer's digits is divisible by 3

The integer is divisible by 2 twice, or if the last two digit…

The integer ends in 5 or 0

An integer is divisible by 2 if:

It is even

An integer is divisible by 3 if:

The sum of the integer's digits is divisible by 3

Integers ... (Definition)

Real Numbers ... (Definition)

Rational Numbers... (Definition)

Factors/Divisors... (Definition)

Whole numbers (positive and negative and 0); subset of Real/R…

All numbers except unreal numbers (everything on the number l…

All whole numbers and fractions. Any number that can be expre…

a number of +integers that divide perfectly without a remaind…

Integers ... (Definition)

Whole numbers (positive and negative and 0); subset of Real/R…

Real Numbers ... (Definition)

All numbers except unreal numbers (everything on the number l…

Divisibility Rule - 3

Divisibility Rule - 4

Divisibility Rule - 6

Divisibility Rule - 8

If sum of the integer's digits is divisible by 3

If the integer is divisible by 2 twice... OR... If the last two dig…

If divisible by both 2 and 3... (It is an even number that is al…

If divisible by 2 three times... OR... If the last three digits are…

Divisibility Rule - 3

If sum of the integer's digits is divisible by 3

Divisibility Rule - 4

If the integer is divisible by 2 twice... OR... If the last two dig…

Odd +- Odd =... Even +- Even =... Odd +- Eve…

12 is a multiple of

prime factors vs. distinct prime factors

if a certain number is divisible by 12…

Odd +- Odd = EVEN... Even +- Even =EVEN... Odd +- Odd = ODD... Odd x…

3,4,6,2... -because 12 is divisible by 3,4,6,2... -multiple is the…

1,050 = 2 x 3 x 5 x 5 x 7... -5 prime factors... -4 distinct prime…

12 PF = 2, 2, and 3... 10 PF = 5, 2... 2 x 2 x 3 x 5 = 60... 24 is no…

Odd +- Odd =... Even +- Even =... Odd +- Eve…

Odd +- Odd = EVEN... Even +- Even =EVEN... Odd +- Odd = ODD... Odd x…

12 is a multiple of

3,4,6,2... -because 12 is divisible by 3,4,6,2... -multiple is the…

How do you know if a number is divisib…

How do you know if a number is divisib…

How do you know if a number is divisib…

How do you know if a number is divisib…

If the sum of the number's digits is divisible by 3

If it's divisible by 2 twice, or if the last two digits are d…

if it's divisible by both 2 and 3

if the sum of its digit's is divisible by 9

How do you know if a number is divisib…

If the sum of the number's digits is divisible by 3

How do you know if a number is divisib…

If it's divisible by 2 twice, or if the last two digits are d…

0 is odd or even?

When a number is odd or even

Rational Numbers

Irrational Numbers

0 is an even number

it must an integer

All numbers that can be expressed as the ratio of 2 integers:…

All real numbers that are not rational, both postive or negat…

0 is odd or even?

0 is an even number

When a number is odd or even

it must an integer

Bowtie Approach

Lowest Common Denominator Method vs Bo…

Decimal place values

Postive exponent

Adding or subtracting fractions using this formula:... a/b + c/…

Use LCD when all the numbers in the denominators are factors…

6,493.783... thousands, hundreds, tens, units . tenths hundredth…

Move the decimal to the right by the number of places represe…

Bowtie Approach

Adding or subtracting fractions using this formula:... a/b + c/…

Lowest Common Denominator Method vs Bo…

Use LCD when all the numbers in the denominators are factors…

Interger

Arithmetic Processes that ALWAYS resul…

Arithmetic Process that SOMETIMES resu…

Intergers are Divisible by 2 if

positive and negative numbers that are whole. Includes zero

addition... subtraction... multiplication

division

the interger is even

Interger

positive and negative numbers that are whole. Includes zero

Arithmetic Processes that ALWAYS resul…

addition... subtraction... multiplication

Interger

Arithmetic Processes that ALWAYS resul…

Arithmetic Process that SOMETIMES resu…

Intergers are Divisible by 2 if

positive and negative numbers that are whole. Includes zero

addition... subtraction... multiplication

division

the interger is even

Interger

positive and negative numbers that are whole. Includes zero

Arithmetic Processes that ALWAYS resul…

addition... subtraction... multiplication

inverse property of addition

commutative property of addition

associative property of addition

identity property of addition

the sum of a number and its opposite is 0

the ORDER of the addends (numbers being added together) does…

the grouping of addends using parenthesis doesn't affect thei…

the sum of any number and zero is the original number

inverse property of addition

the sum of a number and its opposite is 0

commutative property of addition

the ORDER of the addends (numbers being added together) does…

If 2 different representatives are to…

If n is positive, is sqrt(n) > 100?... 1…

If n and y are positive integers and 4…

A school administrator will assign eac…

Answer: E... 1) More than 1/2 of the 10 employees are women.... T…

TO DO LATER

Answer: 1 only

Answer: B - Statement 2 is sufficient and statement 1 in insu…

If 2 different representatives are to…

Answer: E... 1) More than 1/2 of the 10 employees are women.... T…

If n is positive, is sqrt(n) > 100?... 1…

TO DO LATER

All real numbers are positive or negat…

What kind of numbers correspond to poi…

The distance between a number and zero…

What is the absolute value symbol

Zero

Real Numbers

Absolute Value

| |

All real numbers are positive or negat…

Zero

What kind of numbers correspond to poi…

Real Numbers

inverse property of addition

commutative property of addition

associative property of addition

identity property of addition

add the opposite sign and you get zero

the order is switched

order must stay the same, parentheses move

add zero to keep the number the same

inverse property of addition

add the opposite sign and you get zero

commutative property of addition

the order is switched

Commutative Property of Addition and M…

Associative Property

Distributive Property

Identity Property of Addition

Addition and Multiplication are this: switching the order of…

Addition and multiplication are this: the order that the numb…

This property of multiplication over addition: multiplication…

adding 0 to a number leaves it unchanged. We call 0 the addit…

Commutative Property of Addition and M…

Addition and Multiplication are this: switching the order of…

Associative Property

Addition and multiplication are this: the order that the numb…

Prime numbers

Checking if # <100 is prime

ab < 0 and bc > 0

square root of n^2

factors of itself and 1 (one is NOT prime #)... 2 ,3, 5, 7, 11,…

1. other than 2, all other even #s ruled out... 2. see if divisi…

a & b have different signs ... b & c have the same sign ... Therefo…

n or -n *same for any even root, undefined if x is negative

Prime numbers

factors of itself and 1 (one is NOT prime #)... 2 ,3, 5, 7, 11,…

Checking if # <100 is prime

1. other than 2, all other even #s ruled out... 2. see if divisi…

Perfect Square

Square Root

irrational numbers

rational numbers

A number that is the square of a whole number

a number when multiplied by itself

cannot be written as a fraction, is not a perfect square, doe…

integer, fractions, terminating and repeating decimals

Perfect Square

A number that is the square of a whole number

Square Root

a number when multiplied by itself

Real Number

Imaginary Number

Integer

Is the number 0 an integer

Anything that falls on a number line including all positive a…

Can be defined as the square root of any negative number.

Any number that contains no decimal or fractional part

YES

Real Number

Anything that falls on a number line including all positive a…

Imaginary Number

Can be defined as the square root of any negative number.

Additive Identity

Multiplicative Identity

Commutative Property of Addition

Commutative Property of Multiplication

A number plus zero equals that number... a + 0 = 0

A number times one equals that number... a x 1 = a

Sum remains the same when order is changed around... a + b = b + a

Product remains the same when order is changed around... a x b =…

Additive Identity

A number plus zero equals that number... a + 0 = 0

Multiplicative Identity

A number times one equals that number... a x 1 = a

Additive Identity

Multiplicative Identity

Commutative Property of Addition

Commutative Property of Multiplication

A number plus zero equals that number... a + 0 = 0

A number times one equals that number... a x 1 = a

Sum remains the same when order is changed around... a + b = b + a

Product remains the same when order is changed around... a x b =…

Additive Identity

A number plus zero equals that number... a + 0 = 0

Multiplicative Identity

A number times one equals that number... a x 1 = a

Commutative Property of Addition Def.

Commutative Property of Addition Ex.

Commutative Property of Multiplication…

Commutative Property of Multiplication…

The order of addition does NOT matter

123 + 35 = 35 + 123

The order of multiplication does NOT matter

30 x 234 = 234 x 30

Commutative Property of Addition Def.

The order of addition does NOT matter

Commutative Property of Addition Ex.

123 + 35 = 35 + 123

What integers are a factor of 48?

What integers are a factor of 8748?

How many factor pairs are there for 72…

How many factor pairs for 48? How many…

1 2 3 4 6 8

1 2 3 4 6 9

6 (1 2 3 4 6 8, 9 is a pair with 8 so isnt counted twice) 7 (…

6 (1 2 3 4 6 8) 6 (1 2 3 4 6 8)

What integers are a factor of 48?

1 2 3 4 6 8

What integers are a factor of 8748?

1 2 3 4 6 9

inverse property of addition

commutative property of addition

associative property of addition

identity property of addition

the sum of a number and its opposite is 0

the ORDER of the addends (numbers being added together) does…

the grouping of addends using parenthesis doesn't affect thei…

the sum of any number and zero is the original number

inverse property of addition

the sum of a number and its opposite is 0

commutative property of addition

the ORDER of the addends (numbers being added together) does…

Commutative Property of Addition Def.

Commutative Property of Addition Ex.

Commutative Property of Multiplication…

Commutative Property of Multiplication…

The order of addition does NOT matter

123 + 35 = 35 + 123

The order of multiplication does NOT matter

30 x 234 = 234 x 30

Commutative Property of Addition Def.

The order of addition does NOT matter

Commutative Property of Addition Ex.

123 + 35 = 35 + 123

Additive Identity

Multiplicative Identity

Commutative Property of Addition

Commutative Property of Multiplication

A number plus zero equals that number... a + 0 = 0

A number times one equals that number... a x 1 = a

Sum remains the same when order is changed around... a + b = b + a

Product remains the same when order is changed around... a x b =…

Additive Identity

A number plus zero equals that number... a + 0 = 0

Multiplicative Identity

A number times one equals that number... a x 1 = a

Divisibility

Integers... 1) What are integers?... 2) Exa…

Divisibility... 1) If an integer is divi…

Factors

Start

1) Whole numbers. ... 2) -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4,…

1) Divisibility.... 2) Its factors.

Start

Divisibility

Start

Integers... 1) What are integers?... 2) Exa…

1) Whole numbers. ... 2) -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4,…

Natural Numbers

Whole Numbers

Integers

Rational Numbers

Set of Numbers starting with one

Set of Natural Numbers and 0

contains 0 all natural numbers and their negative equivilants

any fration that can be written as a terminating or repeating…

Natural Numbers

Set of Numbers starting with one

Whole Numbers

Set of Natural Numbers and 0