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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…

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

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

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

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…

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,…

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

Associative Properties

Commutative Properties

Expanded Form

Expression

The Associative Property of Addition states that changing the…

The Commutative Property of Addition states that changing the…

The expanded form of a number is the sum that shows the place…

An expression is a mathematical phrase containing numbers and…

Associative Properties

The Associative Property of Addition states that changing the…

Commutative Properties

The Commutative Property of Addition states that changing the…

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

Commutative Property

Associative Property

Distributive Property

Zero is the additive identity. Any num…

You could switch the order of numbers and the product/sum wou…

You could switch the groupings and the product/sum would be t…

Addition and multiplication together... a(b+c)=a(b) + a(c)

Identity Property (addition)

Commutative Property

You could switch the order of numbers and the product/sum wou…

Associative Property

You could switch the groupings and the product/sum would be t…

Common Factor

Highest Common Factor (HCF) or Greates…

Prime Numbers

Composite Numbers

A number that is a factor of 2 or more other numbers

The largest Common factor of 2 or more numbers

A natural number that has exactly 2 different Factors. (1 and…

A natural number that has more than 2 factors. 1 is not a com…

Common Factor

A number that is a factor of 2 or more other numbers

Highest Common Factor (HCF) or Greates…

The largest Common factor of 2 or more numbers

Additive Identity Property of Addition

Multiplicative Identity Property of Mu…

Additive Inverse

Multiplicative Inverse

Any number added to 0 is itself/x+0=x

Any number times one is itself/x*1=x

Adding the opposite/a+(-a)=0

Multiplying the reciprocal/x*(1/x)=1

Additive Identity Property of Addition

Any number added to 0 is itself/x+0=x

Multiplicative Identity Property of Mu…

Any number times one is itself/x*1=x

Additive Identity

Multiplicative Identity

Commutative Property of Addition

Distributive Property

The sum of any number and zero will always equal itself.

The product of a number and one will always equal itself.

adding any numbers in any order will still give you the same…

Multiplying the number outside of the parenthesis to the numb…

Additive Identity

The sum of any number and zero will always equal itself.

Multiplicative Identity

The product of a number and one will always equal itself.

6(2x+5)-x... 6(2x)-6(5)-x

12x+30-x... 12x+30+(-x)

2a+3b+(-2a)... 2a+(-2a)+3b

3+5x+8c... [3+5x]+8c

Distributive property

Add the opposite

Commutative property of addition

Associative property of addition

6(2x+5)-x... 6(2x)-6(5)-x

Distributive property

12x+30-x... 12x+30+(-x)

Add the opposite

Commutative Property of Addition

Commutative Property of Multiplication

Associative Property of Addition

Identity Property of Addition

Order of the numbers change... ex. 3+7=7+3

Order of the numbers change... ex. 5**8=8**5

The numbers stay in the SAME order but the parentheses move.…

You get what you start with... ex. 5+0=5

Commutative Property of Addition

Order of the numbers change... ex. 3+7=7+3

Commutative Property of Multiplication

Order of the numbers change... ex. 5**8=8**5

Undefined

Real

Imaginary

Integer

Almost always means division by zero

A number that has a location on the number line

A number that involves the square root of a negative number

Whole numbers including negative whole numbers and zero

Undefined

Almost always means division by zero

Real

A number that has a location on the number line

commutative property

associative property

identity property

inverse property

order of values does not matter

grouping of values does not matter

the number stays the same

using opposited to "cancel" out a value

commutative property

order of values does not matter

associative property

grouping of values does not matter

Commutative Property of Addition

Commutative Property of Multiplication

Associative Property of Addition

Associative Property of Multiplication

Changing the Order... a+b = b+a

Changing the Order... ab = ba

Moving Parentheses - keep order the same... (a+b)+c = a+(b+c)

Moving Parentheses - keep order the same... (ab)c = a(bc)

Commutative Property of Addition

Changing the Order... a+b = b+a

Commutative Property of Multiplication

Changing the Order... ab = ba

Undefined

Real/Imaginary

Integers

Rational Numbers

When something is divided by zero

A number that has a location on the number line - positive, n…

Whole numbers, which means no fractions, decimals, or mixed n…

Any number that can be expressed as a fraction or a repeating…

Undefined

When something is divided by zero

Real/Imaginary

A number that has a location on the number line - positive, n…

How do you know something is divisible…

How do we know if it's divisible by 6?

What is a multiple similar to

What does the multiple of an integer m…

Adding up all the numbers

-divisible by 2 AND 3... -Look to see if the last number is an e…

-factor of... -divisible ... -divisor

-you can add it by the multiple over and over again and creat…

How do you know something is divisible…

Adding up all the numbers

How do we know if it's divisible by 6?

-divisible by 2 AND 3... -Look to see if the last number is an e…

Commutative Property of Addition

Commutative Property of Multiplication

Associative Property of Addition

Identity Property of Addition

when you can switch the numbers and it does not change the sum

when you can switch the numbers and it does not change the pr…

states that the way the numbers are grouped ( were the parent…

it states that when 0 is added to any number the number stays…

Commutative Property of Addition

when you can switch the numbers and it does not change the sum

Commutative Property of Multiplication

when you can switch the numbers and it does not change the pr…

Real Numbers

Irrational Numbers

Integers

Whole Numbers

Q- terminate or repeat decimal

I- does not repeat or terminate(square roots that aren't perf…

Z- number line

W- 0,1,2,3,...

Real Numbers

Q- terminate or repeat decimal

Irrational Numbers

I- does not repeat or terminate(square roots that aren't perf…

Commutative Property of Addition

Associative Property of Addition

Identity Property of Addition

Commutative Property of Multiplication

x + y = y + x

x + (y + z) = (x + y) + z

x + 0 = x

xy = yx

Commutative Property of Addition

x + y = y + x

Associative Property of Addition

x + (y + z) = (x + y) + z

The Reflexive Property of Equality

The Symmetric Property of Equality

The Transitive Property of Equality

The Substitution Property

Any number is equal to itself

Any equality can be reversed

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…

The Reflexive Property of Equality

Any number is equal to itself

The Symmetric Property of Equality

Any equality can be reversed

Closure Property of Multiplication

Commutative Property of Multiplication

Associative Property of Multiplication

Identity Property of Multiplication

The product of a number (ab) is a unique real number.... Ex: 5(6…

ab = ba... Ex: 5(6) = 6(5)

ab(c) = a(bc)

a x 1 = 1 x a

Closure Property of Multiplication

The product of a number (ab) is a unique real number.... Ex: 5(6…

Commutative Property of Multiplication

ab = ba... Ex: 5(6) = 6(5)

Multiplicative identity property

Additive identity property

Commutative property of addition

Commutative property of multiplication

If you multiply a number by one, the number will stay the same.

If you add zero to a number, the number will stay the same.

The order in which you add numbers doesn't matter.

The order in which you multiply numbers doesn't matter.

Multiplicative identity property

If you multiply a number by one, the number will stay the same.

Additive identity property

If you add zero to a number, the number will stay the same.

Reflexive Property of Equality

Symmetric Property of Equality

Transitive Property of Equality

Commutative Property of Addition and M…

Mirror; any number is equal to itself: a=a

An equality may be reversed: ... If a=b, then b=a

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

We may change the order in which two numbers are added/multip…

Reflexive Property of Equality

Mirror; any number is equal to itself: a=a

Symmetric Property of Equality

An equality may be reversed: ... If a=b, then b=a

communicative property of addition (or…

communicative property of multiplicati…

associative property of addition (grou…

Associative property of multiplication…

a+b=b+a

a**b=b**a

(a+b)+c=a+(b+c)

(a**b) c = a (b**c)

communicative property of addition (or…

a+b=b+a

communicative property of multiplicati…

a**b=b**a

Reflexive property of equality

Symmetric property of equality

Transitive property of equality

Communitive property of addition

a=a ... A number is equal to itself (missior)... 4=4

If a=b, then b=a... If numbers are equal, the will still be equa…

If a=b and b=c, then a=c... If numbers are equal to the same num…

A+b=b+A... The order in which two numbers are added does not cha…

Reflexive property of equality

a=a ... A number is equal to itself (missior)... 4=4

Symmetric property of equality

If a=b, then b=a... If numbers are equal, the will still be equa…