Term
| Additive Identity Property |
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Definition
a+0=a
any term added to 0 remains unchanged |
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Term
| Additive Inverse Property |
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Definition
a+(-a)=0
when opposites are added, the result is always zero |
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Term
| Additive Property of Equality |
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Definition
If a=b, then a+c=b+c
equality is maintained if you add the same amount to both sides of the equation |
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Term
| Associative Property of Addition |
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Definition
a+(b+c)=(a+b)+c
if a sum contains terms that are grouped, then the terms can be grouped differently without affecting the result |
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Term
| Commutative Property of Addition and Multiplication |
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Definition
a+b=b+a
ab=ba
if two terms are added or multiplied, the order is reversible |
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Term
| Multiplicative Identity Property |
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Definition
a*1=a
any term multiplied by one remains unchanged |
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Term
| Multiplicative Inverse Property |
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Definition
(a/b)*(b/a)=1
when multiplying a term by its reciprocal, the result is always one |
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Term
| Multiplicative Property of Equality |
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Definition
If a=b, then a*c=b*c
equality is maintained if you multiply both sides of an equation by the same amount |
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Term
| Associative Property of Multiplication |
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Definition
a*(b*c)=(a*b)*c
if a product contains factors that are grouped, then the factors can be grouped differently without affecting the result. |
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Term
| Transitive Property of Equality |
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Definition
If a=b and b=c, then a=c
if two terms (a and c) are both equal to a third term (b), then they must be equal to each other |
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