 | Term | Definition |
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axiom of closure |
If (ab) is real, then a+b is real. ( if 3+4=7 s real, 3(4)=12 is real) |
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commutative of addition |
To change the order of an equation that uses addition or subtraction. (3+4=4+3) |
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commutative of multiplication |
Changes the order of an eqation that uses multiplication and or division. [(3)4=(4)3] |
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associative of addition |
in an equation using additon and subtraction, the order will remain the same but parenthesis groupings will change. [(1+2)+3=1=(2+3)] |
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associative of multiplication |
in an equation using multiplication and division, the order will remain the same but parenthesis groupings will change. [2(3)4=(2)3(4)] |
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reflexive |
Looks exactily the same on both sides. (a=a) |
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symmetric |
You can flip both sides of an equal side to still have a true eqation. (3=a, then a=3) |
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transitive |
Usually used at the end of a proof. To sum up. (if a=b, and b=c, then a=c) |
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distributive |
To multiply a value through parenthesis. Only works if only additon and subtraction are in the parenthesis. [a(b+c)=ab+ac |
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substitution |
To replace a value or actually complete the given operations. ( if a=3, and a=b, then 3=b) |
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cancellation |
To multiply a negative by a negative. [-(-a)=a] |
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identity of addition |
To add zero. (a+0=a) |
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additive inverse |
Adding the opposite the equal zero, and used to praove an opposite. (a+-a=0, a-a=0, and used to prove that if a is real, negative a is real) |
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opposites of a sum |
Like the distributive property, but used when only distributing a negative through. [-(a+3)=-a-3] |
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definition of subtraction |
Just like switch-switch! [a+(-b)=a-b] Just Asking; doesn't switch switch go along with yellow-yellow? |
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identity of multiplication |
To multiply by 1. [a(1)=a] |
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multiplicative property of zero |
To multiply by zero. [a(0)=0] |
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multiplicative property of negative one |
To multiply by negative one. [-1(a)=-a] |
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opposites in products |
The rules of multiplying by integers. [-a(b)=-ab, a(b)=ab, and -a(-b)=ab] |
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multiplicative inverse |
To multiply by the reciprocal, and used to prove recirocals are real. [a(1/a)=1, and to prove that if a is real, then 1/a is real) |
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reciprocal of a product |
Seperating one fraction into two. [1/ab=1/a(1/b)] |
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definition of division |
Rules for dividing fractions. [3/4=(3/4)/1=3(1/4)=3/4] |
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addition property of equality |
Adding the same quantity to both sides of an equation. (If a=b, then a+c=b+c) |
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subtraction property of equality |
Subtracting the same quantity to both sides of an equation. (If a=b, then a-c=b-c) |
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division property of equality |
Dividing the same quantity to both sides of an equation. (If a=b, then a/c=b/c) |
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multiplication property of equality |
Multiplying the same quantity to both sides of an equation. (If a=b, then ac=bc) |
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hypothesis |
To prove that any variable is real. (a, b, and c are real numbers.) |
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