文档介绍：CHAPTER 1 REAL NUMBERS AND THEIR BASIC Figure Volume
PROPERTIES
V ϭ lwh
Natural numbers: {1, 2, 3, 4, 5, . . .} Rectangular solid
CylinderV ϭ Bh *
Whole numbers: {0, 1, 2, 3, 4, 5, . . .} 1
ϪϪϪ PyramidV ϭ Bh *
Integers: {. . . , 3, 2, 1, 0, 1, 2, 3, . . .} 3
Rational numbers: {All numbers that can be written as a 1
ConeV ϭ Bh *
fraction with an integer numerator and a nonzero integer 3
denominator} 4
Sphere V ϭ pr 3
Real numbers: {All numbers that are either a rational 3
number or an irrational number}
Prime numbers: {2, 3, 5, 7, 11, 13, 17, . . .} *B is the area of the base.
Composite numbers: {4, 6, 8, 9, 10, 12, 14, 15, . . .}
Even integers: {. . . , Ϫ6, Ϫ4, Ϫ2, 0, 2, 4, 6, . . .} If , b , and ca are real numbers, then
Odd integers: {. . . , Ϫ5, Ϫ3, Ϫ1, 1, 3, 5, . . .} Closure properties:
a ϩ b is a real number.
Fractions: a Ϫ b is a real number.
If there are no divisions by 0, then ab is a real number.
ax a a c ac a
. (ϭؒϭ is a real number(b 0
bx b b d bd b
ϩ
a Ϭ c ϭ ad a ϩ b ϭ a mutative properties:
b d bc d d d a ϩ b ϭ b ϩ a
a b a Ϫ b
Ϫϭ ab ϭ ba
d d d
Associative properties:
(a ϩ b) ϩ c ϭ a ϩ(b ϩ c)
Exponents and order of operations:
(ab)c ϭ a(bc)
If n is a natural number, then
Distributive property:
n factors of x
ϩϭϩ
n p a(b c) ab ac
x ϭ x ؒ x ؒ x ؒؒ x
To simplify expressions, do all calculations within each
pair of grouping symbols, working from the innermost CHAPTER 2 EQUATIONS AND INEQUALITIES
pair to the outermost pair. Let , b , and ca be real numbers.
1. Find the values of any exponential expressions. If a ϭ b, then a ϩ c ϭ b ϩ c .
2. Do all multiplications and divisions from left to right. If a ϭ b, then a Ϫ c ϭ b Ϫ c .
3. Do all additions and subtractions from left to right. a b
If a ϭ b, then ϭ(c 0) .
In a fraction, simplify the numerator and denominator c c
separately and then simplify the fraction, if possible.
If a ϭ b, then ca ϭ cb.
Sale price ϭ regular p