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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

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 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…

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

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

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

Commutative property of addition

Commutative property of multiplication

Compatible Numbers

Associative Property of Addition

Changing the order of the addends does not change the sum.

Changing the order of the factors does not change the product.

numbers that are easy to compute mentally

Changing the grouping of the addends does not change the sum.

Commutative property of addition

Changing the order of the addends does not change the sum.

Commutative property of multiplication

Changing the order of the factors does not change the product.

Commutative Property of Addition

Associative Property of Addition

Identity Property of Addition

Commutative Property of Multiplication

States that changing the order of the addends does not change…

States that changing the grouping of the addends does not cha…

States that the sum of 0 and any number is that number

States that changing the order of the factors does not not ch…

Commutative Property of Addition

States that changing the order of the addends does not change…

Associative Property of Addition

States that changing the grouping of the addends does not cha…

commutative property

associative property

identity property of addition... (additiv…

identity property of multiplication... (m…

order does not matter... 1. 3+4 = 4+3... 2. n+4 = 4+n... same with add…

grouping does not matter... 1.(3+4)+5 = 3+(4+5)... 2. 11(3n) = (11*…

any number plus zero is the number... 1. 0+23=23... 2. n+0=n

any number multiplied by one is itself... 1. 2*1=2... 2. 1*x=x

commutative property

order does not matter... 1. 3+4 = 4+3... 2. n+4 = 4+n... same with add…

associative property

grouping does not matter... 1.(3+4)+5 = 3+(4+5)... 2. 11(3n) = (11*…

Reflexive Property of Equality

Symmetric Property of Equality

Transitive Property of Equality

Substitution Property

Any number is equal to itself.... Ex: A=A

Any equality can be reversed.... Ex: B=A A=B

If one number is equal to a second number, and the second num…

For any number a and any number b, if a = b, then b may be su…

Reflexive Property of Equality

Any number is equal to itself.... Ex: A=A

Symmetric Property of Equality

Any equality can be reversed.... Ex: B=A A=B

Natural Numbers

Whole Numbers

Integers

Rational Numbers

The set of numbers that you use to count objects.{ 1,2,3...}

The set of numbers that consists of the set of natural number…

The set of whole numbers and their opposites. {...-3,-2,-1,0,…

The set of numbers that can be written as ab where a and b ar…

Natural Numbers

The set of numbers that you use to count objects.{ 1,2,3...}

Whole Numbers

The set of numbers that consists of the set of natural number…

Commutative Property of Addition

Commutative Property of Multiplication

Associative Property of Addition

Associative Property of Multiplication

2+4=4+2

4 x 6 = 6 x 4

2+(3+4)=(2+3)+4

2 x (4 x 5)=(2 x 4) x 5

Commutative Property of Addition

2+4=4+2

Commutative Property of Multiplication

4 x 6 = 6 x 4

Real numbers

Real number line

Absolute Value

Negative numbers

The set of numbers consisting of the positive numbers, the ne…

A horizontal line that pictures real numbers as points

The distance between the origin and the point representing th…

Points to the left of zero

Real numbers

The set of numbers consisting of the positive numbers, the ne…

Real number line

A horizontal line that pictures real numbers as points

real numbers system

natural numbers

whole numbers

integer numbers

made up of all rational and irrational numbers

numbers you use to count, and so they are also called countin…

all the natural numbers and the number 0

are all the whole numbers, and their negative values

real numbers system

made up of all rational and irrational numbers

natural numbers

numbers you use to count, and so they are also called countin…

Natural numbers

Whole numbers

Integers

Rational numbers

Used for counting... 1,2,3,4...

Natural numbers plus zero

Whole numbers plus negative numbers

All numbers that can be written as quotients of integers... Ter…

Natural numbers

Used for counting... 1,2,3,4...

Whole numbers

Natural numbers plus zero

Equivalent Expressions

Commutative Property

Associative Property

Identity Property

Two algebraic expressions have the same value of all possible…

The property that says changing the order of an expression do…

The property that says changing the grouping of an expression…

The property that says you can add something or multiply by s…

Equivalent Expressions

Two algebraic expressions have the same value of all possible…

Commutative Property

The property that says changing the order of an expression do…

Rational Number

Irrational Numbers

Integers

Whole Numbers

any number written as a ratio; if it is a decimal, it stops o…

Roots that are not perfect; if it is a decimal, it continues

Positive and negative non-decimal numbers and zero

Positive non-decimal numbers and zero

Rational Number

any number written as a ratio; if it is a decimal, it stops o…

Irrational Numbers

Roots that are not perfect; if it is a decimal, it continues

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…