#### Study sets matching "algebra 2 number properties"

#### Study sets matching "algebra 2 number properties"

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

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

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**12Closure 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

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

Natural Numbers

Whole Numbers

Intergers

Rational Numbers

1,2,3,4,.... doesnt include zero

0,1,2,3,4,... includes zero

....-2,-1,0,1,2 includes negative numbers

can be written as a fraction using Intergers

Natural Numbers

1,2,3,4,.... doesnt include zero

Whole Numbers

0,1,2,3,4,... includes zero

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…

2+5=5+2

6•2=2•6

(A+B)+C=A+(B+C)

(A•B)•C=A(B•C)

Commutative property of addition

Commutative property of multiplication

Associative property of addition

Associative property of multiplication

2+5=5+2

Commutative property of addition

6•2=2•6

Commutative property of multiplication

commutative property of addition and m…

associative property of addition and m…

distributive property

identity property of addition and mult…

a+b=b+a

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

a(b+c)=ab+ac

a+0=a

commutative property of addition and m…

a+b=b+a

associative property of addition and m…

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

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

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

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

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…

commutative property of addition

commutative property of multiplication

associative property of addition

associative prop of multiplication

for all real #'s a+b, a+b=b+a

ab=ba

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

(ab)c=a(bc)

commutative property of addition

for all real #'s a+b, a+b=b+a

commutative property of multiplication

ab=ba

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.

Commutative Property

Property

Associative Property

Simplify

The order the numbers are added does not change the sum(+) or…

A rule about an operation on numbers

The way in which numbers are grouped does not changed the sum…

To simplify a variable expression means to combine its like t…

Commutative Property

The order the numbers are added does not change the sum(+) or…

Property

A rule about an operation on numbers

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

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,....

Natural Numbers

Whole Numbers

Integers

Rational Numbers

The set of numbers 1, 2, 3, 4, ... Also called counting numbe…

Natural numbers ( counting numbers) and zero; 0, 1, 2, 3...

whole numbers and their opposites

A number that can be written as a ratio [in the form a/b with…

Natural Numbers

The set of numbers 1, 2, 3, 4, ... Also called counting numbe…

Whole Numbers

Natural numbers ( counting numbers) and zero; 0, 1, 2, 3...

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…

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

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

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

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

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)

closure property

Commutative property

Associative property

Identity property

If A and B are real numbers then A+B or A x B is a unique rea…

If A and B are real numbers, then A+B=B+A ... *order changes... ie.…

(A+B) +C= A+ (B+C)... (A x B) x C = A x (B x C) ... *grouping chang…

A+0=9... A(1)+9... ie. -64+0= -64... 17 x 1= 17

closure property

If A and B are real numbers then A+B or A x B is a unique rea…

Commutative property

If A and B are real numbers, then A+B=B+A ... *order changes... ie.…

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…

Commuative

Associative

Identity

Inverse

7+3=3+7 12x2=2x12 order changes

(1+1)+3=1+(1+3) (1

**1)**6=1**(1**6) parenthesis moves-10+0=-10 5*1=5 original number doesn't change

1/2*2=1 50(1/50)=1 opposite

Commuative

7+3=3+7 12x2=2x12 order changes

Associative

(1+1)+3=1+(1+3) (1

**1)**6=1**(1**6) parenthesis movesReflexive 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…

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)

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…