Download Laws of elementary algebra

Laws of elementary algebra
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Addition is a commutative operation (two numbers add to the same thing whichever order
you add them in).
o Subtraction is the reverse of addition.
o To subtract is the same as to add a negative number:
Example: if 5 + x = 3 then x = − 2.
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Multiplication is a commutative operation.
o Division is the reverse of multiplication.
o To divide is the same as to multiply by a reciprocal:
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Exponentiation is not a commutative operation.
o Therefore exponentiation has a pair of reverse operations: logarithm and
exponentiation with fractional exponents (e.g. square roots).
 Examples: if 3x = 10 then x = log310. If x2 = 10 then x = 101 / 2.
o The square roots of negative numbers do not exist in the real number system.
(See: complex number system)
Associative property of addition: (a + b) + c = a + (b + c).
Associative property of multiplication: (ab)c = a(bc).
Distributive property of multiplication with respect to addition: c(a + b) = ca + cb.
Distributive property of exponentiation with respect to multiplication: (ab)c = acbc.
How to combine exponents: abac = ab + c.
Power to a power property of exponents: (ab)c = abc.
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Laws of equality
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If a = b and b = c, then a = c (transitivity of equality).
a = a (reflexivity of equality).
If a = b then b = a (symmetry of equality).
Other laws
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If a = b and c = d then a + c = b + d.
o If a = b then a + c = b + c for any c (addition property of equality).
If a = b and c = d then ac = bd.
o If a = b then ac = bc for any c (multiplication property of equality).
If two symbols are equal, then one can be substituted for the other at will (substitution
principle).
If a > b and b > c then a > c (transitivity of inequality).
If a > b then a + c > b + c for any c.
If a > b and c > 0 then ac > bc.
If a > b and c < 0 then ac < bc.