College Algebra 2nd ed by Addison Wesley  CH: R
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 Numbers that can be expressed in the form p/q, where p and q are integers and pâ‰ 0. Decimal notation for rational numbers either TERMINATES or REPEATS.
 rational numbers
 Real numbers that are not rational. Decimal notation neither treminates nor repeats.
 irrational numbers
 Positive and negative whole numbers, including zero.
 integer
 Whole numbers that are not negative, including zero.
 whole numbers
 Posivive whole numbers.
 natural numbers

a + b = b + a
and
ab = ba  commutative properties of addition and multiplication

a + (b + c) = (a + b) + c
and
a(bc) = (ab)c  associate properties of addition and multiplication
 a + 0 = 0 + a = a
 additive identity property
 a + a = a + a =0
 additive inverse property
 a * 1 = 1 * a = a
 multiplicative identity property

if aâ‰ 0, then:
a * 1/a = 1/a * a = 1  multiplicative inverse property

a(b + c) = ab + ac
or
a(b  c) = ab  ac  distributive property
 On a number line, the distance a number is from zero.
 absolute value
 The number of times a factor appears in a product.
 exponent

bª * bª = bª+ª
or
a to the power of m times a to the power of n = a to the power of m+n  product rule
 if aâ‰ 0, then a to the power of m Ã· by a to the power of n = a to the power of mn
 quotient rule
 a to the power of m * the power of n = a to the power of m*n
 power rule
 (a * b) to the power of m = (a to the power of m) * (b to the power of m)
 raising a product to a power
 if bâ‰ 0, then (a/b) to the power of m = (a to the power of m) Ã· (b to the power of m)
 raising a quotient to a power