How can we help?

You can also find more resources in our Help Center.

COMMUTATIVE Property of Addition ... (com…

COMMUTATIVE Property of Multiplication…

ASSOCIATIVE Property of Addition ... (ass…

ASSOCIATIVE Property of Multiplication…

3 + 5 = 5 +3

9 x 6 = 6 x 9

4 + (6 + 3) = (4 + 6) + 3

7 x (5 x 3) = (7 x 5) x 3

COMMUTATIVE Property of Addition ... (com…

3 + 5 = 5 +3

COMMUTATIVE Property of Multiplication…

9 x 6 = 6 x 9

Commutative Property of Addition

Commutative Property of Multiplication

Associative Property of Addition

Associative Property of Multiplication

a + b = b + a

ab = ba

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

(ab)c = a(bc)

Commutative Property of Addition

a + b = b + a

Commutative Property of Multiplication

ab = ba

additive property of zero

additive property of zero

additive property of zero

commutative property of addition

rule: a+0=0+a=a

means: zero added to the value is that value

example: 9+0=9

rule: a+b=b+a

additive property of zero

rule: a+0=0+a=a

additive property of zero

means: zero added to the value is that value

real numbers

real number line

origin

negative numbers

the set of numbers that includes rational and irrational numb…

real numbers pictured as points on a line

The point labeled 0.

A number less than 0. On a number line, negative numbers are…

real numbers

the set of numbers that includes rational and irrational numb…

real number line

real numbers pictured as points on a line

Commutative Property

Additive and Multiplicative Identity

Multiplicative Inverse

Additive Inverse

If two terms are added or multiplied, the order is reversible.

Any term added to zero remains unchanged. The Multiplicative…

Stated that when multiplying a term by its reciprocal, the re…

States that when opposites are added, the result is always ze…

Commutative Property

If two terms are added or multiplied, the order is reversible.

Additive and Multiplicative Identity

Any term added to zero remains unchanged. The Multiplicative…

Commutative Property (addition)

Associative Property (addition)

Identity Property (addition)

Additive Inverse Property

You can switch the order of the numbers... example : 3+6 = 6+3

You can switch the parenthesis... example: (1+2)+5 = 1+ (2+5)

If you add 0 to any number, the number stays the same ... exampl…

When you add a number and its inverse (opposite) the answer i…

Commutative Property (addition)

You can switch the order of the numbers... example : 3+6 = 6+3

Associative Property (addition)

You can switch the parenthesis... example: (1+2)+5 = 1+ (2+5)

Commutative property

Associative property

Distributive property

Additive Identity

2x3 = 3x2... 2+3 = 3+2 , The order of two numbers may be switche…

(a+b) +c = a+(b+c) , Changing the grouping of numbers will NO…

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

Zero added or subtracted to any number = itself... 4+0= 4 ... 4x1= 4

Commutative property

2x3 = 3x2... 2+3 = 3+2 , The order of two numbers may be switche…

Associative property

(a+b) +c = a+(b+c) , Changing the grouping of numbers will NO…

Commutative Property

Substitution Property

Symmetric Property

Reflexive Property

a+b=b+a... ab=ba

If a=b, then can be replaced by b and vice versa.

If a=b then b=a

a=a

Commutative Property

a+b=b+a... ab=ba

Substitution Property

If a=b, then can be replaced by b and vice versa.

commutative property

additive and multiplicative property o…

multiplicative inverse

additive inverse

addition: a+b=b+a multiplication:(a)(b)=(b)(a)

addition: a+0=a multiplication:(a)(1)=a

(a/b)(b/a)=1

a+(-a)=0

commutative property

addition: a+b=b+a multiplication:(a)(b)=(b)(a)

additive and multiplicative property o…

addition: a+0=a multiplication:(a)(1)=a

commutative property

additive and multiplicative property o…

multiplicative inverse

additive inverse

addition: a+b=b+a multiplication:(a)(b)=(b)(a)

addition: a+0=a multiplication:(a)(1)=a

(a/b)(b/a)=1

a+(-a)=0

commutative property

addition: a+b=b+a multiplication:(a)(b)=(b)(a)

additive and multiplicative property o…

addition: a+0=a multiplication:(a)(1)=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

(6+7)+8=6+(7+8)

(8**9)**7=8(9*7)

Commutative property of addition.

A+B= B+A

Commutative property of multiplication

A**B=B**A

Real Numbers

Rational Numbers

Irrational Numbers

Intergers

All rational and irrational numbers

All integers written in fractions... -intergers Ex. 1/2, 7/12, 2…

Any square root that can be simplified... -non terminating, non…

Whole numbers, their opposites and zero... -Ex. -4, -3, -2, -1,…

Real Numbers

All rational and irrational numbers

Rational Numbers

All integers written in fractions... -intergers Ex. 1/2, 7/12, 2…

Commutative Property

Symmetric Property

Substitution Property

Reflexive Property

If two terms are added or multiplied, the order is reversible…

If two terms are equal, it doesn't matter which is stated fir…

You can replace one expression with another that is equal to…

A term is always equal to itself a=a

Commutative Property

If two terms are added or multiplied, the order is reversible…

Symmetric Property

If two terms are equal, it doesn't matter which is stated fir…

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 a=b, then a-c=b-c

if a=b, then a**c=b**c

if a=b and c is not = to Zero, then a/c=b/c

Addition property of equality

If a=b, then a+c=b+c

Subtraction property of equality

if a=b, then a-c=b-c

Whole Number

Integers

Positive Integers

Negative Integers

The numbers 0,1,2,3,4,......

The numbers..., -3, -2, -1, 0, 1, 2, 3,...., consisting of th…

The integers that are greater than 0.

The integers that are less than 0.

Whole Number

The numbers 0,1,2,3,4,......

Integers

The numbers..., -3, -2, -1, 0, 1, 2, 3,...., consisting of th…

commutative property of addition

commutative property of multiplication

associative property of addition

associative property of multiplication

a + b = b + a... 2 + 3 = 3 + 2

a x b = b x a... 2 x 3 = 3 x 2

(a + b) + c = a + (b + c)... (2 + 3) + 4 = 2 + (3 + 4)

(a x b) x c = a x (b x c)... (2 x 3) x 4 = 2 x (3 x 4)

commutative property of addition

a + b = b + a... 2 + 3 = 3 + 2

commutative property of multiplication

a x b = b x a... 2 x 3 = 3 x 2

Distributive Property

Commutative Property

Associative Property

Identity Property

Purpose is to get rid of parentheses

-Only applies to addition and multiplication ... -Order doesn't…

-Only applies to addition and multiplication... -The manner in w…

What you start with you end up with

Distributive Property

Purpose is to get rid of parentheses

Commutative Property

-Only applies to addition and multiplication ... -Order doesn't…

Commutative Property of Addition

Commutative Property of Multiplication

Associative Property of Addition

Associative Property of Multiplication

a + b = b + a

ab = ba

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

(ab)c = a(bc)

Commutative Property of Addition

a + b = b + a

Commutative Property of Multiplication

ab = ba

Distributive property

Communative property

Associative property

Identity property

Purpose is to get rid of parenthesis.

Applies to only addition and multiplication.

Applies to only addition and multiplication; the manner in wh…

You end up with what you started with.

Distributive property

Purpose is to get rid of parenthesis.

Communative property

Applies to only addition and multiplication.

Commutative Property of Addition

Commutative Property of Multiplication

Associative Property of Addition

Associative Property of Multiplication

Changing the order in addition does not affect the sum ex. a+…

Changing the order when multiplying does not affect the produ…

Changing the grouping when adding does not affect the sum... ex.…

Changing the grouping when multiplying does not affect the pr…

Commutative Property of Addition

Changing the order in addition does not affect the sum ex. a+…

Commutative Property of Multiplication

Changing the order when multiplying does not affect the produ…

Closure Property of Addition

Closure Property of Multiplication

Commutative Property of Addition

Commutative Property of Multiplication

a+b is a real number ... ex. 12+13 is a real number

ab is a real number ... ex. 12*13 is a real number

a+b=b+a ... ex. 12+13=13+12

ab=ba ... ex. 12**13=13**12

Closure Property of Addition

a+b is a real number ... ex. 12+13 is a real number

Closure Property of Multiplication

ab is a real number ... ex. 12*13 is a real number

commutative property of addition

commutative property of multiplication

Associative property of addition

Associative property of multiplication

two real numbers can be added in any order ... a + b = b + a

two real numbers can be multiplied in any order ... ab = ba

when three real numbers are added, it does not matter which t…

when three real numbers are multiplied, it does not matter wh…

commutative property of addition

two real numbers can be added in any order ... a + b = b + a

commutative property of multiplication

two real numbers can be multiplied in any order ... ab = ba

Distributive Property

Commutative Property

Associative Property

Identity Property

-purpose is to get rid of parentheses. ... Ex. 4 (x + 6) = 4x + 24

-order doesnt matter (only applies to multiplication and addi…

-the manner in which terms are grouped doesnt matter. (only a…

-what you start with you end with... Ex. 4 + 0 =4

Distributive Property

-purpose is to get rid of parentheses. ... Ex. 4 (x + 6) = 4x + 24

Commutative Property

-order doesnt matter (only applies to multiplication and addi…

Closure Property of Addition

Closure Property of Multiplication

Commutative Property of Addition

Commutative Property of Multiplication

a + b is a unique real number

ab is a unique real number

a + b = b+ a

ab = ba

Closure Property of Addition

a + b is a unique real number

Closure Property of Multiplication

ab is a unique real number

natural numbers (N)

whole numbers (W)

integers (Z)

rational numbers(Q)

use to count

natural numbers and zero

natural numbers, their opposites and zero

all numbers that can be written as a fraction, terminating, a…

natural numbers (N)

use to count

whole numbers (W)

natural numbers and zero

Real Numbers

Rational Numbers

Irrational Numbers

Integers

All irrational and rational numbers

All integers written in fractions... -integers EX. 1/2, 7/12, 2/…

Any square Root that cant be simplified... -non terminating, non…

Whole numbers, their opposites, and zero... EX. -4,-3,-2,-1,0,1,…

Real Numbers

All irrational and rational numbers

Rational Numbers

All integers written in fractions... -integers EX. 1/2, 7/12, 2/…

commutative property of addition

commutative property of multiplication

associative property of addition

associative property of multiplication

a + b = b + a

ab = ba

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

(ab)c = a(bc)

commutative property of addition

a + b = b + a

commutative property of multiplication

ab = ba

Closure Property of Addition

Closure Property of Multiplication

Commutative Property of Addition

Commutative Property of Multiplication

a + b is a real number

ab is a real number

a + b = b + a

ab = ba

Closure Property of Addition

a + b is a real number

Closure Property of Multiplication

ab is a real number

Communative Property of Addition

Communative Property of Multiplication

Associative Property of Addition

Associative Property of Multiplication

a+b=b+a

aXb=bXa

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

aX(bXc)=(aXb)Xc

Communative Property of Addition

a+b=b+a

Communative Property of Multiplication

aXb=bXa

Distributive Property

Communtative Property

Assotative Property

Identity Property

rule that gets rid of parenthesis

(only applies to multiplication and addition) rule that makes…

(only applies to multiplication and addition) the manner in w…

what you start with... you end up with

Distributive Property

rule that gets rid of parenthesis

Communtative Property

(only applies to multiplication and addition) rule that makes…

Communtative

Associative

Identity

Inverse

Changing the order of the # will not change the result

Changing the grouping of the #s will not change the result

Zero and one preserves identities under addition or multiplic…

For each real # a, there exist a unique #- a and 1/a

Communtative

Changing the order of the # will not change the result

Associative

Changing the grouping of the #s will not change the result