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Commutative Property

Associative Property

Distributive Property

Identity Property

Says that the ORDER in an addition or multiplication problem…

Says that the GROUPING in an addition or multiplication probl…

Multiplying a number by a group of numbers added together is…

Any number multiplied by 1 will equal itself.

Commutative Property

Says that the ORDER in an addition or multiplication problem…

Associative Property

Says that the GROUPING in an addition or multiplication probl…

18 + 35 + 2 = 18 + 2 + 35

5 × 43 × 20 = 5 × 20 × 43

13 + (7 + 25) = (13 + 7) + 25

5 × (20 × 13) = (5 × 20) × 13

CA commutative property of addition

CM commutative property of multiplication

AA associative property of addition

AM associative property of multiplication

18 + 35 + 2 = 18 + 2 + 35

CA commutative property of addition

5 × 43 × 20 = 5 × 20 × 43

CM commutative property of multiplication

18 + 35 + 2 = 18 + 2 + 35

5 × 43 × 20 = 5 × 20 × 43

13 + (7 + 25) = (13 + 7) + 25

5 × (20 × 13) = (5 × 20) × 13

commutative property of addition

commutative property of multiplication

associative property of addition

associative property of multiplication

18 + 35 + 2 = 18 + 2 + 35

commutative property of addition

5 × 43 × 20 = 5 × 20 × 43

commutative property of multiplication

commutative (property of addition)

commutative (property of multiplication)

associative (property of addition)

associative (property of multiplication)

a + b = b + a

a × b = b × a

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

(a × b) × c = a × (b × c)

commutative (property of addition)

a + b = b + a

commutative (property of multiplication)

a × b = b × a

Commutative Property of Addition

Commutative Property of Multiplication

Associative Property of Addition

Associative Property of Multiplication

4+2 = 2+4 ... 6=6... The order that the numbers are added does not…

2 X 3 = 3 X 2... 6 = 6... The order that the numbers are multiplied…

(5+8) + 2 = 5 + (8+2) ... 13+2 = 5+ 10... 15 = 15... The way in which…

(4 X 6) X 3 = 4 X (6 X 3)... 24 X 3 = 4 X 18... 72 = 72... The way in…

Commutative Property of Addition

4+2 = 2+4 ... 6=6... The order that the numbers are added does not…

Commutative Property of Multiplication

2 X 3 = 3 X 2... 6 = 6... The order that the numbers are multiplied…

Reflexive Property

Symmetric Property

Transitive Property

Substitution Property

A quantity is congruent (equal) to itself. a = a

if a=b, then b=a

If a=b and b=c, then a=c

If a=b, then a can be substituted for b in any equation or ex…

Reflexive Property

A quantity is congruent (equal) to itself. a = a

Symmetric Property

if a=b, then b=a

Commutative Property Addition

Commutative Property Multiplication

Associative Property Addition

Associative Property Multiplication

C stands for change O is for order

C stands for Change O is for order

Change Parenthesis

Change Parenthesis

Commutative Property Addition

C stands for change O is for order

Commutative Property Multiplication

C stands for Change O is for order

Commutative Property

Associative Property

Identity Property

Inverse Property

The order in which you add two numbers does not change the su…

The way you group three numbers in a sum does not change the…

The sum of a number and 0 is the number ex: a+0=a

The sum of a number and its opposite is 0. ex: a+(-a)= 0

Commutative Property

The order in which you add two numbers does not change the su…

Associative Property

The way you group three numbers in a sum does not change the…

Coefficient

Base

Evaluate

Numerical Expression

A number that is multiplied by a variable.

A number used as a repeated factor.

To find the value of a numerical or algebraic expression.

A mathematical phrase that uses only numbers and operation si…

Coefficient

A number that is multiplied by a variable.

Base

A number used as a repeated factor.

Associative Property of Addition

Associative Property of Multiplication

Commutative Property of Addition

Commutative Property of Multiplication

changing the grouping of terms will not change the sum, (a +…

changing the grouping of factors will not change the product,…

In a sum, you can add terms in any order, a + b = b + a

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

Associative Property of Addition

changing the grouping of terms will not change the sum, (a +…

Associative Property of Multiplication

changing the grouping of factors will not change the product,…

Reflective Property

Symmetric Property of Equality

Substitution Property

Transitive Property

Reflects Itself. EX: 4 = 4

Lets the left side move to the right and the right side to th…

Equal values can be substituted for each other. EX: If X = Y…

If A = B, and B = C then A = C.

Reflective Property

Reflects Itself. EX: 4 = 4

Symmetric Property of Equality

Lets the left side move to the right and the right side to th…

Additive Identity

Additive Inverse

Multiplicative Identity

Multiplicative Property of 0

Any amount plus zero is itself.... Ex: a + 0 = a.

Any number plus it's opposite is zero.... Ex: a + (-a) = 0

Any amount multiplied by one is itself.... Ex: a * 1 = a

Any number multiplied by zero is zero.... ... Ex: a * 0 = 0

Additive Identity

Any amount plus zero is itself.... Ex: a + 0 = a.

Additive Inverse

Any number plus it's opposite is zero.... Ex: a + (-a) = 0

distributive property

associative property of multiplication

associative property of addition

comm. prop. of add.

distribution of a number into other numbers in parenthasis

changing the GROUPING of factors does not change the product

changing the GROUPING of addends does not change the sum

changing the Order of addends does not change the sum.

distributive property

distribution of a number into other numbers in parenthasis

associative property of multiplication

changing the GROUPING of factors does not change the product

Closure Property

Commutative Property of Addition

Associative Property of Addition

Distributive Property

a + b = unique real number ex. 4 + 6 = 10

a + b = b + a ex. 4 + 6 = 6 + 4

a + (b + c) = (a + b) + c ex. 4 + (6 + 2) = (4 + 6) + 2

a(b + c) = ab + ac ex. 4(6 + 2) = 4(6) + 4(2)

Closure Property

a + b = unique real number ex. 4 + 6 = 10

Commutative Property of Addition

a + b = b + a ex. 4 + 6 = 6 + 4

Additive Property of equality

Multiplicative Property of equality

Identity property

Distributive Property

add or subtract the same quantity from both sides and retain…

multiply or divide by the same quantity on both sides and ret…

for any number a, a + 0 = 0 + a = a and a x 1 = 1 x a =a

for any numbers a, b, and c, a(b + c) = ab + ac and a(b - c)…

Additive Property of equality

add or subtract the same quantity from both sides and retain…

Multiplicative Property of equality

multiply or divide by the same quantity on both sides and ret…

Properties

Commutative of Addition

Commutative of Multiplication

Associative Property of Addition

statements that are true for ANY numbers

the order in which numbers are ADDED does NOT change the sum…

the order in which numbers are MULTIPLIED does NOT change the…

the way in which numbers are grouped when ADDED does NOT chan…

Properties

statements that are true for ANY numbers

Commutative of Addition

the order in which numbers are ADDED does NOT change the sum…

Commutative property

Associative

Distributive property

Additive inverse property

The order of the number does not affect the sum or the product

The way the numbers are paired does not affect the sum or the…

Multiplication can be distributed over addition or subtraction

The sum of a number and it's additive inverse(also called its…

Commutative property

The order of the number does not affect the sum or the product

Associative

The way the numbers are paired does not affect the sum or the…

Identity Property of addition

Inverse Property of addition

Commutative Property

Associative Property

The sum of a number and 0 is the number ex: a+0=a

The sum of a number and its opposite is 0. ex: a+(-a)= 0

the order in which you add/multiply two numbers does not chan…

the way you group three numbers together does not change the…

Identity Property of addition

The sum of a number and 0 is the number ex: a+0=a

Inverse Property of addition

The sum of a number and its opposite is 0. ex: a+(-a)= 0

Reflexive Property

Symmetric Property

Transitive Property

Commutative Property of Addition

For any number a, a=a... Ex: 5=5; 4+7=4+7

For any numbers a and b, if a=b, then b=a... Ex: If 8=2+6 then 2…

For any numbers a,b, and c, if a=b and b=c, then a=c... Ex: If 6…

For any numbers a and b, a+b=b+a... Ex: 4+8+8+4

Reflexive Property

For any number a, a=a... Ex: 5=5; 4+7=4+7

Symmetric Property

For any numbers a and b, if a=b, then b=a... Ex: If 8=2+6 then 2…

What does PEMDAS mean?

Algebraic Expression

Substitution

The commutative Property (for addition…

P- please,... E- excuse,... M- my,... D-dear,... A-aunt,... S-sally.

Contains at least one variable and at least one operation.

Replacing a variable with a given number to evaluate (solve)…

to "move it move it"... Ex: a+b=b+a

What does PEMDAS mean?

P- please,... E- excuse,... M- my,... D-dear,... A-aunt,... S-sally.

Algebraic Expression

Contains at least one variable and at least one operation.

Commutative Property

Associative Property

Distributive Property

Additive Property Of Equality

The word "commutative" comes from "commute" or "move around",…

The associative property states that you can add or multiply…

"multiplication distributes over addition"

The property that states that if you add the same number to b…

Commutative Property

The word "commutative" comes from "commute" or "move around",…

Associative Property

The associative property states that you can add or multiply…

Commutative Property of Addition

Commutative Property of Multiplication

Associative Property of Addition

Associative Property of Multiplication

a + b = b + a

a x b = b x a

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

(a x b) x c = a x (b x c)

Commutative Property of Addition

a + b = b + a

Commutative Property of Multiplication

a x b = b x a

Multiplicative Identity

Multiplicative Property of Zero

Multiplicative Inverse

Reflexive

For any number (a), the product of a and 1 is a... Ex: a**1=a 12**…

For any number (a), the product of a and 0 is 0.... Ex: a**0=0 0**…

For every number a/b, where a, b is not equal to 0, there is…

Any quantity is equal to itself... Ex: a=a 7=7 2+3=2+3

Multiplicative Identity

For any number (a), the product of a and 1 is a... Ex: a**1=a 12**…

Multiplicative Property of Zero

For any number (a), the product of a and 0 is 0.... Ex: a**0=0 0**…

Commutative Property

Associative Property

Distributive Property

Additive Identity

The order in which you add or multiply numbers does not chang…

The way you group three or more numbers when adding or multip…

To distribute the number outside of the parentheses into each…

For any number a, the sum of a and 0 is a. ex: a + 0 = 0 + a…

Commutative Property

The order in which you add or multiply numbers does not chang…

Associative Property

The way you group three or more numbers when adding or multip…

Equivalent expressions

reflexive property

symmetric property

transitive property

Expression equals the same problem

something that is equal to itself. A=A

You can flip it around. A=B, B=A

Shoot right through. A=B, B=C, A=C

Equivalent expressions

Expression equals the same problem

reflexive property

something that is equal to itself. A=A

Reflexive Property of Equality

Symmetric Property of Equality

Transitive Property of Equality

Substitution

a=a

a=b then b=a (like commutative)

a=b and b=c, then a=c

if a=b, then a can be substituted for b at any time

Reflexive Property of Equality

a=a

Symmetric Property of Equality

a=b then b=a (like commutative)

division property of equality

additive identity property

multiplicative inverses

associative property of multiplication

if a=b and c=/0, then a/c=b/c

a+0=0+a=a

a x 1/a=1/a x a = 1

(a x b) x c=a x (b x c)

division property of equality

if a=b and c=/0, then a/c=b/c

additive identity property

a+0=0+a=a

commutative (property of addition)

commutative (property of multiplication)

associative (property of addition)

associative (property of multiplication)

a + b = b + a

a × b = b × a

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

(a × b) × c = a × (b × c)

commutative (property of addition)

a + b = b + a

commutative (property of multiplication)

a × b = b × a

Closure

Associative (Grouping)

Commutative (Ordering)

Identity

When two real numbers are added or multiplied, the result wil…

Numbers may be grouped differently without affecting the fina…

The numbers on each side of an operation sign may be commuted…

Find a number that will produce an identical answer to the or…

Closure

When two real numbers are added or multiplied, the result wil…

Associative (Grouping)

Numbers may be grouped differently without affecting the fina…

Commutative property (addition and mul…

Associative property of addition and m…

Distributive property

Identity property of addition

You can move the terms in an additionj problem and still get…

You can move, put in or take out parenthesis in an addition p…

If you have multiplication on the outside of parentheses you…

Addition- anything added to zero is the same thing

Commutative property (addition and mul…

You can move the terms in an additionj problem and still get…

Associative property of addition and m…

You can move, put in or take out parenthesis in an addition p…

Addition Property of Equality

Subtraction Property of Equality

Multiplication Property of Equality

Division Property of Equality

-If a=b, then a+c=b+c... -if x=-4, the x+4=-4+4

-If a=b, then a-c=b-c... -If r+1=7, then r+1-1=7-1

-If a=b, then ac=bc... -If k/2=8, then k/2(2)=8(2)

-If a=b, c≠0, then a/c=b/c... -If 6=3t, then 6/3=3t/3

Addition Property of Equality

-If a=b, then a+c=b+c... -if x=-4, the x+4=-4+4

Subtraction Property of Equality

-If a=b, then a-c=b-c... -If r+1=7, then r+1-1=7-1

Commutative Property of Multiplication

Associative Prperty of Multiplication

Identity Property of Multiplication

Property of Zero

a(b) = b(a)

(a x b) x c = a x (b x c)

a x 1 = 1 x a= a

a x 0 = 0

Commutative Property of Multiplication

a(b) = b(a)

Associative Prperty of Multiplication

(a x b) x c = a x (b x c)

Addition prop. of equality

Multiplication prop. of equality

Additive inverse prop.

Multiplicative inverse prop.

If a=b, then a+d = b+d

If a=b, then d•a = d•b

a + (-a) = 0

If a does not equal 0, then 1/a • a = 1

Addition prop. of equality

If a=b, then a+d = b+d

Multiplication prop. of equality

If a=b, then d•a = d•b