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Study sets matching "algebra 1 axioms equality"

21 terms
Algebra 1 - axioms & properties of equality
commutative axiom for addition
commutative axiom for multiplication
associative axiom for addition
associative axiom for multiplication
x+y = y+x
xy = yx
x+(y+z) = (x+y)+z
x(yz) = (xy)z
commutative axiom for addition
x+y = y+x
commutative axiom for multiplication
xy = yx
21 terms
Algebra 1 - axioms & properties of equality
commutative axiom for addition
commutative axiom for multiplication
associative axiom for addition
associative axiom for multiplication
x+y = y+x
xy = yx
x+(y+z) = (x+y)+z
x(yz) = (xy)z
commutative axiom for addition
x+y = y+x
commutative axiom for multiplication
xy = yx
21 terms
Algebra 1 Properties and Axioms
Substitution Principle
Commutative Axiom(+)
Commutative Axiom(*)
Associative Axiom (+)
If a = b, then a can be substituted for b in any expression.
a + b = b + a
ab = ba
(a +b) + c = a + (b + c)
Substitution Principle
If a = b, then a can be substituted for b in any expression.
Commutative Axiom(+)
a + b = b + a
21 terms
Algebra 1 Properties and Axioms
Substitution Principle
Commutative Axiom(+)
Commutative Axiom(*)
Associative Axiom (+)
If a = b, then a can be substituted for b in any expression.
a + b = b + a
ab = ba
(a +b) + c = a + (b + c)
Substitution Principle
If a = b, then a can be substituted for b in any expression.
Commutative Axiom(+)
a + b = b + a
24 terms
Algebra 1 Axioms
Multiplication Property of equality
factors
multiplicative identity axiom
definition of division
x=y,xz=yz
parts of an expression that are multiplied or divided
x*1=x
multiplication by the reciprocal x/y = x*1/y
Multiplication Property of equality
x=y,xz=yz
factors
parts of an expression that are multiplied or divided
15 terms
Algebra 1: Axioms/Properties
Closure Axiom of Addition
Commutative Axiom of Addition
Associative Axiom of Addition
Identity Axiom of Addition
For all real number, a and b, a+b is a real numer
For all real number a and b, a+b = b+a
For all real numbers a,b, and c, (a+b)+c = a+(b+c)
For all real numbers a, a+0=a and 0+a=a
Closure Axiom of Addition
For all real number, a and b, a+b is a real numer
Commutative Axiom of Addition
For all real number a and b, a+b = b+a
16 terms
Algebra 1 Axioms and Properties
transitive axiom of equality
multiplicative property of -1
multiplicative identity axiom
additive identity axiom
if x=y and y=z, then x=z
x(-1) = -x
x*1 = x
x+0 = x
transitive axiom of equality
if x=y and y=z, then x=z
multiplicative property of -1
x(-1) = -x
Algebra 1 - Property and Axioms
Distributive Axiom for Multiplication…
Common Factor
Multiplication Property for 0
Multiplication property for -1
x(y +z) = xy + xz
The factor that's the same in each term in an expression
0 * x = 0
-1 * x = x
Distributive Axiom for Multiplication…
x(y +z) = xy + xz
Common Factor
The factor that's the same in each term in an expression
12 terms
Algebra 1 Axioms and Properties
Def. of Sub.
Def. of Div.
Comm. Ax +
Comm. Ax. x
x+(-y) = x-y
x÷y = x×¹/y
x+y = y+x
xy = yx
Def. of Sub.
x+(-y) = x-y
Def. of Div.
x÷y = x×¹/y
20 terms
Algebra 1 Properties and Axioms
Substitution Principle
Commutative Axiom of Addition
Commutative Axiom of Multiplication
Associative Axiom of Addition
If a = b, then a can be substituted for b in any expression.
a + b = b + a
ab = ba
(a +b) + c = a + (b + c)
Substitution Principle
If a = b, then a can be substituted for b in any expression.
Commutative Axiom of Addition
a + b = b + a
23 terms
Axioms for Algebra 1
Commutative Axiom for Addition
Commutative Axiom for Multiplication
Associative Axiom for Addition
Associative Axiom for Muiltiplication
a+b=b+a
ab=ba
(a+b) +c = a+ (b+c)
(ab) c=a (bc)
Commutative Axiom for Addition
a+b=b+a
Commutative Axiom for Multiplication
ab=ba
21 terms
Algebra 1 Properties and Axioms
Substitution Principle
Commutative Axiom(+)
Commutative Axiom(*)
Associative Axiom (+)
If a = b, then a can be substituted for b in any expression.
a + b = b + a
ab = ba
(a +b) + c = a + (b + c)
Substitution Principle
If a = b, then a can be substituted for b in any expression.
Commutative Axiom(+)
a + b = b + a
18 terms
axioms for algebra 1 honors
a+b ∈ R
ab ∈ R
a+b=b+a
ab=ba
closure for addition
closure for multiplication
commutative addition
commutative multiplication
a+b ∈ R
closure for addition
ab ∈ R
closure for multiplication
14 terms
Algebra 1 Properties and Axioms
Substitution Property of Equality
Commutative Axiom of Addition
Commutative Axiom of Multiplication
Associative Axiom of Addition
If a = b, then a can be substituted for b in any expression.
a + b = b + a
ab = ba
(a +b) + c = a + (b + c)
Substitution Property of Equality
If a = b, then a can be substituted for b in any expression.
Commutative Axiom of Addition
a + b = b + a
Algebra 1 Axioms, Definitions, and Properties
x + y = y + x
x y = y x
(x + y) + z = x + (y + z)
(x y) z = x (y z)
Commutative Axiom of Addition
Commutative Axiom of Multiplication
Associative Axiom of Addition
Associative Axiom of Multiplication
x + y = y + x
Commutative Axiom of Addition
x y = y x
Commutative Axiom of Multiplication
16 terms
Algebra- Chapter 1 (Properties and Axioms)
Axiom
Axioms of closure of additions
Communative Property Axiom of Addition
Associate Property Axiom of Addition
An accepted truth, that doesn't require evidence
A+B is a real number and a unique number
A+B=B+A ... the order doesn't matter
(A+B)+C= A+(B+C) ... again the order doesn't matter
Axiom
An accepted truth, that doesn't require evidence
Axioms of closure of additions
A+B is a real number and a unique number
13 terms
Properties of Equality - Algebra 1
Reflexive Property
Symmetric Property
Transitive Property
Substitution Principle
For all real numbers, a=a. ... "Every number equals itself"... 7=7…
For all real numbers, if a=b, then b=a.... x=2, 2=x
For all real numbers, if a=b, and b=c, then a=c.... 6+1=7, and 7…
An expression may be replaced by another expression that has…
Reflexive Property
For all real numbers, a=a. ... "Every number equals itself"... 7=7…
Symmetric Property
For all real numbers, if a=b, then b=a.... x=2, 2=x
17 terms
Algebra 1- properties of equality
reflexive property
symmetric property
substitution property
addition property
5 = 5
if 8 = 2 + 6 then 2 + 6 = 8
if n = 11 then 4n = 4 x 11
if 5x - 6 = 14 then 5x = 20
reflexive property
5 = 5
symmetric property
if 8 = 2 + 6 then 2 + 6 = 8
13 terms
Properties of Equality - Algebra 1
Reflexive Property
Symmetric Property
Transitive Property
Substitution Principle
For all real numbers, a=a. ... "Every number equals itself"... 7=7…
For all real numbers, if a=b, then b=a.... x=2, 2=x
For all real numbers, if a=b, and b=c, then a=c.... 6+1=7, and 7…
An expression may be replaced by another expression that has…
Reflexive Property
For all real numbers, a=a. ... "Every number equals itself"... 7=7…
Symmetric Property
For all real numbers, if a=b, then b=a.... x=2, 2=x
10 terms
Algebra 1: Properties of equality
Distributive Properties
Commutative Properties of Addition
Commutative Properties of Multiplication
Associative Properties of Addition
a(b+c)=a(b)+a(c)
a+b=b+a
ab=ba
a+(b+c)=(a+b)+c
Distributive Properties
a(b+c)=a(b)+a(c)
Commutative Properties of Addition
a+b=b+a
24 terms
Honors Algebra 1- Properties, Definitions, Axioms
Definition of a property
Definition of an axiom
Definition of Subtraction
Definition of Division
A property of a mathematical system is a fact that is true co…
An axiom is a property that forms the basis of a mathematical…
Subtracting a number means adding its oppostite. That is, x-y…
Dividing by a number means multiplying by its reciprocal. Tha…
Definition of a property
A property of a mathematical system is a fact that is true co…
Definition of an axiom
An axiom is a property that forms the basis of a mathematical…
16 terms
parnassus prep algebra 1 properties and axioms- 4L
commutative axiom for addition
commutative axiom for multiplication
associative axiom for addition
associative axiom for multiplication
x+y=y+x
xy=yx
(x+y)z = x(y+z)
(xy)z = x(yz)
commutative axiom for addition
x+y=y+x
commutative axiom for multiplication
xy=yx
25 terms
Algebra 1 (H) Theorems, Axioms, and Rules
Axioms of Closure (p. 53)
Commutative Axioms (p. 53)
Associative Axioms (p. 54)
Axioms of Equality (p. 55)
For all real numbers a and b:... a + b is a unique real number.…
For all real numbers a and b:... a + b = b + a... ab = ba
For all real numbers a, b, and c:... (a + b) + c = a + (b + c)…
For all real numbers a, b, and c:... Reflexive Axiom: a = a... Sym…
Axioms of Closure (p. 53)
For all real numbers a and b:... a + b is a unique real number.…
Commutative Axioms (p. 53)
For all real numbers a and b:... a + b = b + a... ab = ba
12 terms
Yonekawa Algebra 1 Honors Final - Axioms and Properties
Commutative axioms
Associative axioms
Reflexive axiom
Symmetric axiom
a+b=b+a or ab=ba
(a+b)+c=a+(b+c) or (ab)c=a(bc)
a = a
if a=b, then b=a
Commutative axioms
a+b=b+a or ab=ba
Associative axioms
(a+b)+c=a+(b+c) or (ab)c=a(bc)
16 terms
Algebra Unit 1 Test (properties & axioms)
Reflexive Property of Equality
Symmetric Property of Equality
Transitive Property of Equality
Addition Property of Equality
Anything equals itself: 3 = 3
If 3y = 9, then 9 = 3y
If 2x = 8 and 8 = 2^3 (to the third power), then 2x = 2^3
Kerry is solving the one-step equation x - 8 = 10. This prope…
Reflexive Property of Equality
Anything equals itself: 3 = 3
Symmetric Property of Equality
If 3y = 9, then 9 = 3y
8 terms
Algebra 1-3 Properties of Equality
Reflexive Property
Transitive Property
Symmetric Property
Addition Property
A=A
If a = b and b = c then a =c
If a = b and b = a
If a = b, then a + c = b + c
Reflexive Property
A=A
Transitive Property
If a = b and b = c then a =c
10 terms
Algebra 1 Properties of Numbers and Equalities
Identity
Inverse
Multiplicative Property of 0
Commutative
a + 0 = a or a x 1 = a
a + (-a) = 0 or a x 1/a = 1
a x 0 = 0
a + b = b + a or ab = ba
Identity
a + 0 = a or a x 1 = a
Inverse
a + (-a) = 0 or a x 1/a = 1
11 terms
Algebra 1: 1.8 Properties of Equality
Communative Property
Associative Property
Additive Identity
Additive Inverse
Numbers can be multiplied or divided in any order. ... Ex. a + b…
Numbers that can be grouped together in any order when added…
Zero is added to any number; the number stays the same.... Ex. 7…
Adding a number to its opposite gives a sum of zero. ... Ex. 7 +…
Communative Property
Numbers can be multiplied or divided in any order. ... Ex. a + b…
Associative Property
Numbers that can be grouped together in any order when added…
14 terms
Algebra 1-4 Identity and Equality Properties
*what is multiplicative identity prope…
*what is additive identity property
*what is multiplicative property of zero
*what is multiplicative inverse property
the product of any number and 1 is the number
the sum of any number and 0 is the number itself
the product of any number and 0 is 0
any number times its reciprocal is 1
*what is multiplicative identity prope…
the product of any number and 1 is the number
*what is additive identity property
the sum of any number and 0 is the number itself
6 terms
Properties of Equality 3.6 Algebra 1 AH
Transitive Axiom of Equality
Symmetric Axiom of Equality
Reflective Axiom of Equality
Addition Property of Equality
for all real numbers x, y, and z... if x=y and y=z, then x=z
if x=y then y=x... 14=x+3 then x+3=14
x=x... 5=5
x=y the x+z=y+z... x-4=20 is also x-4+4=20+4
Transitive Axiom of Equality
for all real numbers x, y, and z... if x=y and y=z, then x=z
Symmetric Axiom of Equality
if x=y then y=x... 14=x+3 then x+3=14
7 terms
Geometry CH2QUIZ1 Algebraic Property of Equality
**** If a=b, c=d, then a+c = b+d
If a=b, ac=bc
If a = b, then a can be substituted fo…
If a=a
Addition Property
Multiplication Property
Substitute Property
Reflexive Property
**** If a=b, c=d, then a+c = b+d
Addition Property
If a=b, ac=bc
Multiplication Property
11 terms
Axioms for Algebra I
Commutative Axiom for Addition
Commutative Axiom for Multiplication
Associative Axiom for Addition
Associative Axiom for Multiplication
x + y = y + x
x•y = y•x
(x + y) + z = x + (y + z)
(x•y) •z = x•(y •z)
Commutative Axiom for Addition
x + y = y + x
Commutative Axiom for Multiplication
x•y = y•x
19 terms
Properties & Axioms - Algebra I
Commutative Property of Addition
Commutative Property of Multiplication
Associative Property of Addition
Associative Property of Multiplication
Add in any order;... 12 + 5 + 8 = 12 + 8 + 5
Multiply in any order;... 5 x 8 x 2 = 5 x 2 x 8
Add by regrouping;... 8 + (2 + 3) = (8 + 2) + 3
Multiply by regrouping:... (8 x 5) x 6 = 8 x (5 x 6)
Commutative Property of Addition
Add in any order;... 12 + 5 + 8 = 12 + 8 + 5
Commutative Property of Multiplication
Multiply in any order;... 5 x 8 x 2 = 5 x 2 x 8
19 terms
Properties & Axioms - Algebra I
Commutative Property of Addition
Commutative Property of Multiplication
Associative Property of Addition
Associative Property of Multiplication
Add in any order;... 12 + 5 + 8 = 12 + 8 + 5
Multiply in any order;... 5 x 8 x 2 = 5 x 2 x 8
Add by regrouping;... 8 + (2 + 3) = (8 + 2) + 3
Multiply by regrouping:... (8 x 5) x 6 = 8 x (5 x 6)
Commutative Property of Addition
Add in any order;... 12 + 5 + 8 = 12 + 8 + 5
Commutative Property of Multiplication
Multiply in any order;... 5 x 8 x 2 = 5 x 2 x 8
19 terms
Properties & Axioms - Algebra I
Commutative Property of Addition
Commutative Property of Multiplication
Associative Property of Addition
Associative Property of Multiplication
Add in any order;... 12 + 5 + 8 = 12 + 8 + 5
Multiply in any order;... 5 x 8 x 2 = 5 x 2 x 8
Add by regrouping;... 8 + (2 + 3) = (8 + 2) + 3
Multiply by regrouping:... (8 x 5) x 6 = 8 x (5 x 6)
Commutative Property of Addition
Add in any order;... 12 + 5 + 8 = 12 + 8 + 5
Commutative Property of Multiplication
Multiply in any order;... 5 x 8 x 2 = 5 x 2 x 8
19 terms
Algebra II Axioms/Properties
commutative axiom for addition
commutative axiom for multiplication
associative axiom for addition
associative axiom for multiplication
a+b=b+a
ab=ba
(a+b)+c=a+(b+c)
(ab)c=a(bc)
commutative axiom for addition
a+b=b+a
commutative axiom for multiplication
ab=ba
11 terms
Algebra 1
Power
Exponent
Base
Simplify
A number produced by raising a base to an exponent
A mathematical notation indicating the number of times a quan…
a number that is multiplied repeatedly
to write an expression in a simpler form
Power
A number produced by raising a base to an exponent
Exponent
A mathematical notation indicating the number of times a quan…
39 terms
Algebra 1
variable
algebraic expression
numerical expression
sum
A letter that stands in place of a value
a phrase (or expression) that includes one or more variables
a phrase (or expression) that only includes numbers and opera…
variable
A letter that stands in place of a value
algebraic expression
a phrase (or expression) that includes one or more variables
16 terms
AXIOMS/AXIOM EQUALITY
The distributive axiom
Commutative axiom for addition
Commutative axiom for multiplication
Associative axiom for addition
X(Y+Z)=XY+XZ/TDA Abbreviation.
X+Y=Y+X/CAFA Abbreviation
XY=YX/CAFM Abbreviation
(X+Y)+Z=X+(Y+Z)/AAFA Abbreviation
The distributive axiom
X(Y+Z)=XY+XZ/TDA Abbreviation.
Commutative axiom for addition
X+Y=Y+X/CAFA Abbreviation
26 terms
Properties and Axioms for Algebra I
Commutative Axiom for addition
Commutative Axiom for Multiplication
Associative Axiom for addition
Associative Axiom for multiplication
x+y=y+x
xy=yx
(x+y) + z= x + (y+z)
(xy)z=x(yz)
Commutative Axiom for addition
x+y=y+x
Commutative Axiom for Multiplication
xy=yx
12 terms
Algebraic Properties of Equality, Algebraic Properties
Addition Property of Equality
Subtraction Property of Equality
Multiplication Property of Equality
Commutative of Addition
a+b = b+a
Addition Property of Equality
Subtraction Property of Equality
39 terms
Algebra 1
variable
algebraic expression
numerical expression
sum
A letter that stands in place of a value
a phrase (or expression) that includes one or more variables
a phrase (or expression) that only includes numbers and opera…
variable
A letter that stands in place of a value
algebraic expression
a phrase (or expression) that includes one or more variables
88 terms
Algebra 1
binomial
constant
factor
monomial
a polynomial with two terms
a value that does not change
a number or expression that is multiplied by another number o…
a number or a product of numbers and variables with whole-num…
binomial
a polynomial with two terms
constant
a value that does not change
10 terms
Algebra 1 - Chapter 10
conclusion
conditional
conjugates
converse
the part following then in a conditional.... EX: If I have tw…
an if-then statement.... EX: If I have two apples, then I hav…
expressions that are the same but have opposite signs.
like a conditional, but when you switch the conclusion and th…
conclusion
the part following then in a conditional.... EX: If I have tw…
conditional
an if-then statement.... EX: If I have two apples, then I hav…
14 terms
Algebra 1 - Chapter 12
bias
bivariate
box-and-whisker plot
element
a survey question that contains assumptions that may or may n…
a set of data that uses two variables.
a graph that summarizes a set of data by displaying it along…
a number or variable within a matrix.
bias
a survey question that contains assumptions that may or may n…
bivariate
a set of data that uses two variables.
17 terms
Algebra Unit 2 CC Algebraic Properties of Equality
Addition Property of Equality
Subtraction Property of Equality
Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality
15 terms
Algebra 1 Vocabulary.
Sequence
common difference
least
Greatest
an ordered list of numbers
The difference between the terms in a sequence
smallest
largest
Sequence
an ordered list of numbers
common difference
The difference between the terms in a sequence
17 terms
Algebraic Properties of Equality, Algebraic Properties
Addition Property of Equality
Subtraction Property of Equality
Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality
30 terms
Algebra 1 Chapter 1
algebraic expression
base
coefficient
coordinate system
An expression consisting of one or more numbers and variables…
In an expression of the form x^n, it is the x.
The numerical factor of a term.
The grid formed by the intersection of two number lines, the…
algebraic expression
An expression consisting of one or more numbers and variables…
base
In an expression of the form x^n, it is the x.
11 terms
Algebra 1 - Module 2 Vocabulary
Algebraic Expression
Coefficient
Compound Inequality
Compound Statement
is an expression that contains at least one variable.
is the numerical factor of a variable term.
is formed by combining two or more simple inequalities.
is formed by combining two or more simple statements.
Algebraic Expression
is an expression that contains at least one variable.
Coefficient
is the numerical factor of a variable term.
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