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What is the Closure Property of Additi…

What is the Commutative Property of Ad…

What is the Associative Property of Ad…

What is the Identity Property of Addit…

a+b is a real number... Ex: 3+5 is a real number

a+b=b+a... Ex: 1+2=2+1

(a+b)+c=a+(b+c)... Ex:1+(2+3)=(1+2)+3

a+0=a... Ex:10+0=10

What is the Closure Property of Additi…

a+b is a real number... Ex: 3+5 is a real number

What is the Commutative Property of Ad…

a+b=b+a... Ex: 1+2=2+1

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

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

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

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

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

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

Real Numbers include..

Rational Numbers

Irrational Numbers

Integers

Rational, integers, whole, and natural

Can be written as a fraction (quotient of integers)... Can be RE…

NONTERMINATING or NON-REPEATING decimals ... Square roots of NON…

Negative numbers , 0 , and positive numbers

Real Numbers include..

Rational, integers, whole, and natural

Rational Numbers

Can be written as a fraction (quotient of integers)... Can be RE…

Reflexive Property

Symmetric Property

Transitive Property

Substitution Property

Any quantity is equal to itself

If one quantity equals a second quantity, then the second qua…

If one quantity equals a second quantity and the second quant…

A quantity may be substituted for its equal in any expression.

Reflexive Property

Any quantity is equal to itself

Symmetric Property

If one quantity equals a second quantity, then the second qua…

Additive Identity

Additive Inverse

Multiplicative Identity

Multiplicative Property of 0

For any number a, a + 0 = a.

For any number a, a + (-a) = 0.

For any number a, a • 1 = a.

For any number a, a • 0 = 0.

Additive Identity

For any number a, a + 0 = a.

Additive Inverse

For any number a, a + (-a) = 0.

real numbers

integers

absolute value

counterexample

the set of all rational and irrational numbers

whole numbers and their opposites

The distance a number is from zero on a number line

an example that proves a statement false

real numbers

the set of all rational and irrational numbers

integers

whole numbers and their opposites

Reflexive Property

Symmetric property

transitive property

Substitution property

any quantity is equal to itself

If one quantity equals a second quantity then the second quan…

if one quantity equals a second quantity and the second quant…

a quantity may be substituted for its equal in any expression

Reflexive Property

any quantity is equal to itself

Symmetric property

If one quantity equals a second quantity then the second quan…

Distributive Property

Commutative Property

Associative Property

Identity Property

the purpose is to get rid of parentheses

only applies to addition and multiplication, order doesn't ma…

only applies to addition and multiplication, the manner in wh…

What you start with, you end up with

Distributive Property

the purpose is to get rid of parentheses

Commutative Property

only applies to addition and multiplication, order doesn't ma…

whole numbers

integers

rational number

absolute value

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

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

a number that can be written as a/b where a and b are integer…

distance between a and 0 on a number line; |a|; always positi…

whole numbers

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

integers

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

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

Real Number (R)

Rational Number (Q)

Irrational Number (I)

Integers (Z)

Any type of number

Can be expressed as a ratio; terminating decimal, or repeatin…

Is a non terminating decimal, or does not repeat; 3.14 or a s…

Any positive or negative number (as long as it isn't a decimal)

Real Number (R)

Any type of number

Rational Number (Q)

Can be expressed as a ratio; terminating decimal, or repeatin…

closure

commutative

associative

indentity

a set of real numbers is closed under addition/multiplication…

change of order

grouping changes

zero for additon, 1 for multiplication

closure

a set of real numbers is closed under addition/multiplication…

commutative

change of order

natural

whole

integers

rational

positive, not decimals or fractions... 1,2,3...

Includes zero... 0,1,2,3

can't be fractions/decimals... includes negatives... -2,-1,0,1,2

any number you can write as a fraction... if it is a decimal and…

natural

positive, not decimals or fractions... 1,2,3...

whole

Includes zero... 0,1,2,3

Commutative Property of Addition

Commutative Property of Multiplication

Associative Property of Addition

Associative Property of Multiplication

Order Changing ... ex: 3+2=2+3

Order Changing... ex: 6x5=5x6

Grouping can Change, but numbers can't move. ... ex: 3(15+50)=(…

Grouping changes, but numbers don't move. ... ex: 6(30x3)=(6x30)3

Commutative Property of Addition

Order Changing ... ex: 3+2=2+3

Commutative Property of Multiplication

Order Changing... ex: 6x5=5x6

Reflexive Property

Substitution Property

Subtraction Property

Multiplication Property

a = a

If a = b, then a may be replaced by b in any equation or expr…

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

If a = b, then ac = bc

Reflexive Property

a = a

Substitution Property

If a = b, then a may be replaced by b in any equation or expr…

Additive Identity Property of 0

Multiplicative Identity Property of 1

Commutative Property of Addition

Commutative Property of Multiplication

g + 0 = g

g x 1 = g

a + b = b + a

a x b = b x a

Additive Identity Property of 0

g + 0 = g

Multiplicative Identity Property of 1

g x 1 = g

Commutative Property of +... CO in commut…

Commutative Property of +... CO in commut…

Commutative Property of x... CO in commut…

Commutative Property of x... CO in commut…

a + b = b + a or 3 +5 = 5 + 3

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

a x b = b x a

(ab)c = c(ab)

Commutative Property of +... CO in commut…

a + b = b + a or 3 +5 = 5 + 3

Commutative Property of +... CO in commut…

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

commutative property of addition

commutative property of multiplication

Associative property of addition

associative property of multiplication

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

ab=ba ... (3) (2)= (2)(3)

(a+b) +c= a+ (b+c) ... (1+2)+3= 1+(2+3)

(ab)c = a(bc) ... (1**2)3= 1(2**3)

commutative property of addition

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

commutative property of multiplication

ab=ba ... (3) (2)= (2)(3)

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

Commutative Property of Addition

Commutative Property of Multiplication

Associative Property of Addition

Associative Property of Multiplication

When adding numbers, changing the order of the numbers doesn'…

When multiplying, changing the order of the factors doesn't c…

When adding numbers, changing the grouping of the numbers doe…

When multiplying, changing the grouping of the doctors doesn'…

Commutative Property of Addition

When adding numbers, changing the order of the numbers doesn'…

Commutative Property of Multiplication

When multiplying, changing the order of the factors doesn't c…

Absolute Value

Algebraic Expression

Associative Property

Base

The distance from zero to any number on the number line. Exam…

An expression consisting of one or more numbers and variables…

Property Example: (a + b) + c = a + (b + c); (ab)c = a(bc)

In an expression of the form x^n, it is the "x"

Absolute Value

The distance from zero to any number on the number line. Exam…

Algebraic Expression

An expression consisting of one or more numbers and variables…

Commutative Property of Addition

Commutative Property of Multiplication

Associative Property of Multiplication

Distributive Property

a + b = b + a

a • b = b • a

(a • b) • c = a • (b • c)

"multiplication distributes over addition/subtraction"... a(b +…

Commutative Property of Addition

a + b = b + a

Commutative Property of Multiplication

a • b = b • a

additive property

commutative property of addition

associative property of addition

multiplicative identity

a + 0 = a; the sum of a number and 0 is that number

a + b = b + a; changing the order of addends doesn't effect t…

a + (b + c) = (a + b) + c; changing the grouping of addends d…

a * 1 = a; the product of a number and 1 is that number

additive property

a + 0 = a; the sum of a number and 0 is that number

commutative property of addition

a + b = b + a; changing the order of addends doesn't effect t…

Commutative Property of Addition

Commutative Property of Multiplication

Properties of Closure Addition

Properties of Closure Multiplication

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

ab = ba... Changing the Order

a+b is a unique real number

ab is a unique real number

Commutative Property of Addition

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

Commutative Property of Multiplication

ab = ba... Changing the Order