Algebra Properties
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Created by:
highschoolrox1 on December 14, 2010
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15 terms
Terms | Definitions |
|---|---|
 Symmetric Property | If a=b, then b=a ex: If 3=2x+5 then 2x+5=3 |
| Reflexive Property | For any a, a=a ex: 4=4 ex: 3x+5=3x+5 |
| Transitive Property | If a=b, and b=c, then a=c If 4x+5=2y+9 and 2y+9=10 then 4x+5=10 (3 equal signs to demonstrate) |
| Multiplicative Property | Given a, the product of a and one is a ex: a times 1=a -8 times 1=-8 |
| Associative Property of Multiplication | (ab)c=a(bc) ex: (2 times 3)4=2(3 times 4) |
| Associative Property of Addition | (a+b)+c=a+(b+c) ex: (2+3)+5=2+(3+5) |
| Multiplication Property of Zero | Given a,a times 0=0 ex: 5 times 0=0 |
| Substitution | Given a=b, you can put in b for a in an expression ex: 4x+3y=10 and 4=y then 4x+3(4)=10 |
| Additive Inverse | For any a, a+(-a)=0 (opposite-what do I add to "undo it?") ex: 4+(-4)=0 -2+(2)=0 |
| Multiplicative Inverse | For any a, a times 1 over a=1 (reciprocal!) ex: 4 times one over 4=1 2 thirds times three halves=1 |
| Distributive Property | *Hint: Use Order of Operations a(b+c)=ab+ac This is what allows you to combine terms. ex: -6 times 5 and a half=6(5+a half) -3(x-2)=-3x-6 |
| Commutative Multiplication | a times b=b times a ex: 7 times 3=3 times 7 x times 3=3x Definition of Subtraction is used quite often with commutative property |
| Definition of Subtraction | Add the opposite ex: 7-5 Algebra-7+(-5) *All signs attach to coefficient |
| Additive Identity | Given a, the sum of a and zero is a ex: a+0=a 4+0=4 |
| Commutative Property of Addition | Commute---> move it around a+b=b+a ex: 3+7=7+3 5+x=x+5 |
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