Properties Flashcards

0
Q

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

A

associative property of addition

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1
Q

a+b=real #

A

closure property of addition

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2
Q

a+b=b+a

A

commutative property of addition

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3
Q

a+0=a.

A

identity property of addition

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4
Q

a+(-a)=0

A

inverse property of addition

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5
Q

ab= real #

A

closure property of multiplication

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6
Q

(ab)c=a(bc)

A

associative property of multiplication

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7
Q

Ab=ba

A

commutative property of multiplication

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8
Q

a(1)=a

A

identity property of multiplication

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9
Q

a(1/a)=0

A

multiplicative inverse

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10
Q

a(b+c) = ab+av

A

distributive property

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11
Q

if a+b=c & x-y=z,

then (a+b)-y=x-y=z

A

substitution principle

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12
Q

a=a

A

reflexive

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13
Q

a=b, b=a

A

symmetric property

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14
Q

if a=b & b=c, then a=c

A

transitive property

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15
Q

a, | -(-a) = a

A

cancellation property of additive inverse

16
Q

ac=bc, then a=b

A

cancellation property of multiplication

17
Q

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

A

cancellation property of addition

18
Q

-(a+b)=(-a)+(-b)

A

property of opposites of a sum

19
Q

a/b = a(1/b)

A

definition of division

20
Q

ax=0

A

multiplicative property of zero

21
Q

a(-1)=-a

A

multiplicative property of -1

22
Q

(-a)b=-ab & (-a)(-b)=ab

A

property of opposites in products

23
Q

a-b=a+(-b)

A

definition of subtraction