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Rational Numbers

Natural Numbers

Integers

Whole Numbers

Any number that can be written as a ratio which means it can…

Positive integers and sometimes 0

The number 0 is neither negative or positive. Two of these ar…

a number without a fraction; an integer

Rational Numbers

Any number that can be written as a ratio which means it can…

Natural Numbers

Positive integers and sometimes 0

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

Commutative Property of Addition

Commutative Property of Multiplication

Associative Property of Addition

Associative Property of Multiplication

commute = move to a new place when adding

commute = move to a new place when multiplying

associate = regroup the terms that are associated with each o…

associate = regroup the factors that are associated with each…

Commutative Property of Addition

commute = move to a new place when adding

Commutative Property of Multiplication

commute = move to a new place when multiplying

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

Rational Numbers

Natural Numbers

Integers

Whole Numbers

Any number that can be written as a ratio which means it can…

Positive integers

The number 0 is neither negative or positive. Two of these ar…

a number without a fraction; an integer

Rational Numbers

Any number that can be written as a ratio which means it can…

Natural Numbers

Positive integers

Commutative Property of Addition

Commutative Property of Multiplication

Associative Property of Addition

Associative Property of Multiplication

commute = move to a new place when adding

commute = move to a new place when multiplying

regroup - elements do not move, they group with a new friend…

regroup - elements do not move, they group with a new friend…

Commutative Property of Addition

commute = move to a new place when adding

Commutative Property of Multiplication

commute = move to a new place when multiplying

Commutative Property of Addition

Commutative Property of Multiplication

Associative Property of Addition

Associative Property of Multiplication

8 + 6 = 6 + 8

8 x 6 = 6 x 8

2 + (3 + 7) = (2 + 3) + 7

2 x (3 x 7) = (2 x 3) x 7

Commutative Property of Addition

8 + 6 = 6 + 8

Commutative Property of Multiplication

8 x 6 = 6 x 8

Commutative Property of Addition (1)

Additive Identity (1)

Zero Property of Multiplication (1)

Associative Property of Addition (2)

(b + 8) + 1 = (8 + b) + 1

7c + 0 = 7c

27 + 6a × 0 = 27 + 0

(-1 + 4) + 7 = -1 + (4 + 7)

Commutative Property of Addition (1)

(b + 8) + 1 = (8 + b) + 1

Additive Identity (1)

7c + 0 = 7c

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

Commutative Property of Addition

Commutative Property of Multiplication

Associative Property of Addition

Associative Property of Multiplication

The order of the addends does not matter when adding. Ex: a+b…

The order of the factors does not matter when multiplying. Ex…

the way in which you group three or more numbers when adding…

Changing the grouping of three or more factors does not chang…

Commutative Property of Addition

The order of the addends does not matter when adding. Ex: a+b…

Commutative Property of Multiplication

The order of the factors does not matter when multiplying. Ex…

Commutative Property of Addition

Commutative Property of Multiplication

Associative Property of Addition

Associative Property of Multiplication

commute = move to a new place when adding

commute = move to a new place when multiplying

associate = regroup the terms that are associated with each o…

associate = regroup the factors that are associated with each…

Commutative Property of Addition

commute = move to a new place when adding

Commutative Property of Multiplication

commute = move to a new place when multiplying

Integers

Rational Numbers

Irrational Numbers

Additive Identity

..., -3, -2, -1, 0, 1, 2, 3,... and denoted Z

A rational number is the division of any two integers ... (i. e.…

A real number that is not rational is called irrational. For…

Integers

..., -3, -2, -1, 0, 1, 2, 3,... and denoted Z

Rational Numbers

A rational number is the division of any two integers ... (i. e.…

commutative property

associative property

identity property

Inverse property

Addition Multiplication... a+b=b+a a times b= b times a

Addition Multiplication... (a+b) +c= a + (b+c) (a times b) times…

Addition Multiplication... a + 0 = a = 0 + a a times 1 = a = 1 t…

Addition Multiplication... a + (-a) = 0 = (-a) + a a times 1/a =…

commutative property

Addition Multiplication... a+b=b+a a times b= b times a

associative property

Addition Multiplication... (a+b) +c= a + (b+c) (a times b) times…

Associative Property of Addition

Associative Property of Multiplication

Distributive Property

Inverse

Allows you to re-group addends using grouping symbols:... ( ) o…

Allows you to re-group number factors using grouping symbols:…

Multiplying the factor outside the parentheses by every term…

another word for "opposite"

Associative Property of Addition

Allows you to re-group addends using grouping symbols:... ( ) o…

Associative Property of Multiplication

Allows you to re-group number factors using grouping symbols:…

Integers

Rational Numbers

Irrational Numbers

Additive Identity

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

A rational number is the division of any two integers ... (i. e.…

A real number that cannot be written as a fraction.

Integers

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

Rational Numbers

A rational number is the division of any two integers ... (i. e.…

Commutative Property of Addition

Associative Property of Addition

Identity Property of Addition

Inverse Property of Addition

a + b = b + a

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

a + 0 = a

a + -a = 0

Commutative Property of Addition

a + b = b + a

Associative Property of Addition

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

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

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

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

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

Commutative Property of Addition

Commutative Property of Multiplication

Associative Property of Addition

Associative Property of Multiplication

commute = move to a new place when adding

commute = move to a new place when multiplying

associate = regroup the terms that are associated with each o…

associate = regroup the factors that are associated with each…

Commutative Property of Addition

commute = move to a new place when adding

Commutative Property of Multiplication

commute = move to a new place when multiplying

Commutative property of addition

Commutative property of multiplication

Associative property of addition

Associative property of multiplication

(commute = move to new place)... a+b=b+a or 6+4=4+6

(commute = move to new place)... a**b=b**a or 5**7=7**5

(regroup - elements do not move, they group with a new friend…

(regroup - elements do not move, they group with a new friend…

Commutative property of addition

(commute = move to new place)... a+b=b+a or 6+4=4+6

Commutative property of multiplication

(commute = move to new place)... a**b=b**a or 5**7=7**5

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

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

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

Commutative Property of Addition

Commutative Property of Multiplication

Associative Prop of Addition

Associative Prop of Multiplication

2 + 3 = 3 + 2

2 x 3 = 3 x 2

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

(2 x 3 ) x 4 = 2 x (3 x 4 )

Commutative Property of Addition

2 + 3 = 3 + 2

Commutative Property of Multiplication

2 x 3 = 3 x 2

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

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 (change the grouping) - keep order the sam…

Moving Parentheses (change the grouping) - keep order the sam…

Commutative Property of Addition

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

Commutative Property of Multiplication

Changing the Order... ab = ba

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

Associative Property of Addition

Associative Property of Multiplication

Commutative Property of Addition

Commutative Property of Addition

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

Numbers added any way to get the same sum

(6 + 10) + 3 = (10 + 6) + 3

Associative Property of Addition

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

Associative Property of Multiplication

commutative property of addition

commutative property of multiplication

associative property of addition

associative property of multiplication

a x b = b x a ... 12 x 1/2 = 1/2 x 12

commutative property of addition

commutative property of multiplication

a x b = b x a ... 12 x 1/2 = 1/2 x 12

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

Associative Property of Addition

Commutative Property of Additions

Additive Identity Property

Additive Inverse Property

When adding more than two numbers we can "group" any two numb…

We can add numbers in any "order".... a + b = b + a

Zero added to any number is the number itself.... a + 0 = a or 0…

The sum of a number and its opposite is zero.... a + (-a) = 0 or…

Associative Property of Addition

When adding more than two numbers we can "group" any two numb…

Commutative Property of Additions

We can add numbers in any "order".... a + b = b + a