# College Algebra 2nd ed by Addison Wesley - CH: R

## Terms

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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
-a + a = a + -a =0
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 m-n
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

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