# Study sets matching "algebra properties real"

Study sets

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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

Natural Number

Whole numbers

Integers

Rational numbers

numbers used for counting 1,2,3...

are natural numbers and 0

natural numbers (positive integers),0, negative integers

All numbers that can be written as quotients of integers. ... Mus…

Natural Number

numbers used for counting 1,2,3...

Whole numbers

are natural numbers and 0

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Commutative Property of Addition

Commutative Property of Multiplication

Associative Property of Addition

Associative Property of Multiplication

Changing the order in which numbers are added, but not changin…

Changing the way in which numbers are multiplied, but not chan…

Changing the grouping of numbers in addition, but not changing…

Changing the grouping of numbers in multiplication, but not ch…

Commutative Property of Addition

Changing the order in which numbers are added, but not changin…

Commutative Property of Multiplication

Changing the way in which numbers are multiplied, but not chan…

Commutative Property of +

Commutative Property of x

Associative Property of +

Associative Property of x

Order doesn't matter.... a+b=b+a... (a+b)+c=c+(a+b)

Order doesn't matter.... a•b=b•a... (ab)c=c(ab)

Grouping doesn't matter.... (a+b)+c=a+(b+c)

Grouping doesn't matter.... (a•b)•c=a•(b•c)

Commutative Property of +

Order doesn't matter.... a+b=b+a... (a+b)+c=c+(a+b)

Commutative Property of x

Order doesn't matter.... a•b=b•a... (ab)c=c(ab)

Commutative Property of Addition

Associative Property of Addition

Identity Property of Addition

Commutative Property of Multiplication

Changing the order of the addends does not change the sum.... a +…

Changing the grouping of addends does not change the sum.... (a +…

The sum of 0 and any number is that number.... 0 + c = c

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

Commutative Property of Addition

Changing the order of the addends does not change the sum.... a +…

Associative Property of Addition

Changing the grouping of addends does not change the sum.... (a +…

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

Natural Numbers (N)

Whole Numbers (W)

Integers (Z)

Rational Numbers (Q)

All numbers that are positive starting at 1. ... Ex: 1, 5, 7, 10

All numbers that are positive starting at 1 and including 0.…

All numbers that are positive, negative, and including 0. ... Ex…

All numbers that are positive, negative, zero, terminating dec…

Natural Numbers (N)

All numbers that are positive starting at 1. ... Ex: 1, 5, 7, 10

Whole Numbers (W)

All numbers that are positive starting at 1 and including 0.…

Commutative property

Associative property

Distributive property

Additive Identity

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

(a+b) +c = a+(b+c) , Changing the grouping of numbers will NOT…

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 switched…

Associative property

(a+b) +c = a+(b+c) , Changing the grouping of numbers will NOT…

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 r…

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

Real Numbers

All rational and irrational numbers

Rational Numbers

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

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

Commutative Property of Addition

Commutative Property of Multiplication

Associative Property of Addition

Associative Property of Multiplication

a + b = b + a ... Ex: 6+3=3+6

a x b = b x a... Ex: 4x5=5x4

(a + b) + c = a + (b + c)... Ex: (3+4)+7 = 3+(4+7)

(a x b) x c = a x (b x c)... Ex: (2 x 5) x 8 = 2 x (5 x 8)

Commutative Property of Addition

a + b = b + a ... Ex: 6+3=3+6

Commutative Property of Multiplication

a x b = b x a... Ex: 4x5=5x4

Commutative Property

Associative Property (of addition or mu…

Identity property

Inverse Property (of addition or multip…

Order of values does not matter!

Grouping of values does not matter!

Stays the same!

Using opposite(+)/reciprocal (*) to cancel a value!

Commutative Property

Order of values does not matter!

Associative Property (of addition or mu…

Grouping of values does not matter!

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Commutative Property of addition and mu…

Associative Property of addition and mu…

Distributive Property of multiplication…

Identities for addition and multiplicat…

-order doesn't matter ... 2+5= 5+2

-the way numbers are grouped doesn't matter... 5+(2+4)= (5+2)+4

6(3+2)= 6(5)= 30

3+0= 3

Commutative Property of addition and mu…

-order doesn't matter ... 2+5= 5+2

Associative Property of addition and mu…

-the way numbers are grouped doesn't matter... 5+(2+4)= (5+2)+4

Real Number

Natural (Counting) Numbers

Whole Numbers

Integers

any number that can be written as a decimal

{1,2,3...}

{0,1,2,...}

{...,-3,-2,-2,0,1,2,3,...}

Real Number

any number that can be written as a decimal

Natural (Counting) Numbers

{1,2,3...}

Commutative

Associative

Identity

Inverse

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)

a+0 = a = 0+a... a x 1 = a = 1 x a

a+(-a) = 0 = (-a)+a... a x 1/a = 1 = 1/a, a =/0

Commutative

a+b = b+a... a x b = b x a

Associative

(a+b)+c = a+(b+c)... (a x b) x c = a x (b x c)