• · (dot symbol), 7
• = (equal sign), 165
• — (fraction bar), 8
• / (fraction slash), 8
• ∞ (infinity), 168
• ( ) (parentheses)
  • expressions with, 25–28
  • with minus signs, 108
  • with no signs, 108–109
  • overview, 8
  • with plus signs, 107–108
  • removing from algebraic expressions, 107–111
  • removing from equations, 122–124
• 2-D shapes
  • measuring, 139–146
  • overview, 136–137
• 3-D shapes
  • with curves, 138–139
  • measuring, 147–150

A

• A (area), 141–142, 144–146
• A_b (area of the base), 149
• absolute value, 12
• addends, 6
• addition
  • in algebraic terms, 102
  • of decimals, 58–59, 84–85
  • expressions with, 22
  • of fractions, 43–46, 84
  • of mixed numbers, 51–52
  • overview, 6–7
  • of percents, 85
• algebraic equations
  • isolating x, 119–125
  • methods of solving, 115–116
  • overview, 18–20, 113–114
  • solving, 113–125
  • using x in, 114
• algebraic expressions. See also expressions
  • adding terms, 102
  • combining similar terms, 106–107
  • dividing terms, 104–106
  • evaluating, 97–98
  • identifying coefficients and variables, 100–101
  • identifying similar terms, 101–102
  • multiplying terms, 103–104
  • overview, 96–97, 99
  • rearranging terms, 99–100
  • removing parentheses, 107–111
  • simplifying, 106–111
  • subtracting terms, 102–103
• analytic geometry, 165
• area (A), 141–142, 144–146
• area of the base (A_b), 149
• associative operations, 10

B

• b (base), 142, 146
• bar graphs, 152–153
• base (b), 142, 146
• base number, 11
• boxes (rectangular solids), measuring, 148

C

• C (circumference), measuring, 141
• Cartesian coordinate system
  • graph styles, 152–155
  • overview, 151
  • using Cartesian coordinates, 155–161
• Cartesian graph, 165
• center of circles, 140–141
• circles
  • measuring, 140–141
  • overview, 136
• circumference (C), measuring, 141
• coefficients, identifying, 100–101
• commutative operations, 9–10, 100
• cones
  • measuring, 150
  • overview, 138–139
• constant, 95
• counting numbers, 5
• cross-multiplication, 124–125
• cubes, measuring, 148
• cylinders
  • measuring, 149–150
  • overview, 138–139

D

• d (diameter), measuring, 140–141
• decimals
  • adding, 58–59, 84–85
  • converting to/from fractions, 63–68
  • converting to/from percents, 71
  • dividing, 61–63
  • multiplying, 59–60, 88–90
  • non-repeating, 6
  • overview, 57
  • repeating, 67–68
  • subtracting, 59, 84–85
  • terminating, 66–67
• declaring variables, 128–130
• denominator, 41. See also fractions
• diameter (d), measuring, 140–141
• difference, 7
• distributive property, 10–11
• dividend
  • defined, 8
  • zeros in, 62
• division
  • in algebraic terms, 104–106
  • of decimals, 61–63
  • expressions with, 22–23
  • of fractions, 43
  • of mixed numbers, 50
  • overview, 8
• divisor, 8
• dot (·) symbol, 7

E

• equal sign (=), 165
• equations (algebraic)
  • defined, 17, 114
  • methods of solving, 115–116
  • overview, 18–20, 113–114
  • setting up, 129–130
  • solving, 113–125
  • using x in, 114
  • word, 30–33
• evaluations, 19
• exponents
  • expressions with, 24–27
  • overview, 11–12
• expressions. See also algebraic expressions
  • with addition, 22
  • defined, 17
  • with division, 22–23
  • evaluating with order of operations, 21–24
  • with exponents, 24
  • mixed-operator, 23–24
  • with multiplication, 22–23
  • overview, 19–20
  • with parentheses, 25–28
  • with subtraction, 22

F

• factors
  • defined, 7
  • generating, 13–14
  • greatest common factor (GCF), 14
• FOIL (First, Outside, Inside, Last), 110–111
• formulas
  • area (A), 141–142, 144–146
  • circumference (C), 141
  • diameter, 140–141
  • hypotenuse, 143
  • perimeter (P), 143–146
  • pi (p), 141
  • radius, 147
  • volume, 148–150
• fraction bar (—), 8
• fraction slash (/), 8
• fractions
  • adding, 43–46, 84
  • converting to/from decimals, 63–68
  • converting to/from percents, 71–73
  • dividing, 43
  • improper, 49
  • mixed numbers, 48–55
  • multiplying, 42–43, 86–88
  • overview, 41
  • reciprocal of, 43
  • reducing, 42, 65–66
  • removing with cross-multiplication, 124–125
  • subtracting, 47–48, 84
• functions, 166

G

• GCF (greatest common factor), 14
• geometry
  • analytic, 165
  • defined, 135
  • measuring shapes, 139–150
  • plane, 136–137
  • solid, 137–139
• graphs
  • bar, 152–153
  • Cartesian, 165
  • defined, 151
  • line, 154–155
  • pie charts, 153–154
  • styles, 152–155
• greatest common factor (GCF), 14

H

• height (h), 142, 146
• hypotenuse, 142

I

• improper fractions
  • converting between mixed numbers and, 49–50
  • defined, 41
• infinity (∞), 168
• input, 166
• integers, 6
• inverse operations, 9
• irrational numbers, 6, 164, 167
• irregular polygons, 137
• isolating x, 118–125

L

• LCM (least common multiple), 15
• legs (of triangles), 142
• line graphs, 154–155

M

• mixed numbers
  • adding, 51–52
  • converting between improper fractions and, 49–50
  • defined, 41
  • dividing, 50
  • multiplying, 50
  • subtracting, 52–55
• mixed-operator expressions, 23–24
• multiples
  • generating, 14–15
  • least common multiple (LCM), 15
• multiplication
  • in algebraic terms, 103–104
  • cross-multiplication, 124–125
  • of decimals, 59–60, 88–90
  • expressions with, 22–23
  • of fractions, 42–43, 86–88
  • of mixed numbers, 50
  • overview, 7–8
  • of percents, 88–90

N

• natural numbers, 5
• non-repeating decimal, 6
• number line, 167–168
• numbers. See also mixed numbers
  • base, 11
  • counting, 5, 6
  • irrational, 6, 164, 167
  • natural, 5
  • prime, 163
  • rational, 6, 166–167
  • real, 6
  • sets of, 5–6
• numerator, 41. See also fractions

O

• operations
  • absolute value, 12
  • addition, 6–7
  • associative, 10
  • commutative, 9–10, 100
  • division, 8
  • exponents, 11–12
  • inverse, 9
  • multiplication, 7–8
  • properties of, 9–11
  • square roots, 12
  • subtraction, 7
• order of operations
  • defined, 17
  • evaluating expressions, 21–24
  • in expressions with exponents, 24
  • in expressions with parentheses, 25–28
  • overview, 20–21
• order of precedence. See order of operations
• output, 166

P

• P (perimeter)
  • defined, 147
  • measuring, 139–140, 143–145
• parallelograms, measuring, 145–146
• parentheses ( )
  • expressions with, 25–28
  • with minus signs, 108
  • with no signs, 108–109
  • overview, 8
  • with plus signs, 107–108
  • removing from algebraic expressions, 107–111
  • removing from equations, 122–124
• percent circle, 77–81
• percents
  • adding, 85
  • applying problems, 76–81
  • converting to/from, 70–73
  • defined, 69
  • greater than 100, 70
  • increases and decreases in word problems, 91–93
  • multiplying, 88–90
  • solving problems, 73–76
  • subtracting, 85
  • types of problems, 76–77
• perimeter (P)
  • defined, 147
  • measuring, 139–140, 143–145
• pi (p), 141, 164–165
• pie charts, 153–154
• plane geometry, 136–137
• plotting points on Cartesian graphs, 156–157
• polygons, 136–137
• polyhedrons, 137–138, 147
• powers. See exponents
• prime numbers, 163
• prisms, measuring, 149
• problems. See also word problems
  • percent, 73–81
  • solving with Cartesian graphs, 159–161
• properties of operations, 9–11
• pyramids, measuring, 150
• Pythagorean theorem, 142–143

Q

• quadrilaterals, 137
• quotient, 8

R

• radius (r)
  • measuring, 140–141
  • of spheres, 147
• rational numbers, 6, 166–167
• real numbers, 6
• reciprocal of fractions, 43
• rectangles, measuring, 143–144, 148
• regular polygons, 137
• rhombus, measuring, 144–145
• right triangle, 142

S

• sets of numbers, 5–6
• shapes. See also specific shapes
  • defined, 136
  • measuring, 139–150
  • 2-D, 136–137
  • 3-D, 138–139, 147–150
• simplifying
  • combining similar terms, 106–107
  • defined, 106
  • removing parentheses, 107–111
• solid geometry
  • polyhedrons, 137–138
  • 3-D shapes with curves, 138–139
• solving for x, 117–119
• spheres
  • measuring, 147
  • overview, 138–139
• square roots, 12
• squares, measuring, 143
• story problems. See word problems
• subtraction
  • in algebraic terms, 102–103
  • of decimals, 59, 84–85
  • expressions with, 22
  • of fractions, 47–48, 84
  • of mixed numbers, 52–55
  • overview, 7
  • of percents, 85
• sum, 6
• surface area
  • defined, 147
  • of polyhedrons, 147
  • of solids, 147

T

• terms (algebraic)
  • adding, 102
  • combining, 106–107
  • dividing, 104–106
  • evaluating, 97–98
  • identifying coefficients and variables, 100–101
  • identifying similar, 101–102
  • multiplying, 103–104
  • overview, 96–97, 98
  • rearranging, 99–100, 119–125
  • subtracting, 102–103
• 2-D shapes
  • measuring, 139–146
  • overview, 136–137
• 3-D shapes
  • with curves, 138–139
  • measuring, 147–150
• trailing zeros, 59
• trapezoids, measuring, 146
• triangles
  • measuring, 142–143
  • overview, 136

V

• value
  • absolute, 12
  • defined, 17
• variables (x). See also algebraic expressions
  • choosing, 131–133
  • declaring, 128–130
  • identifying, 100–101
  • isolating, 118–125
  • overview, 95–96
  • solving for, 117–119
  • using in equations, 114
• volume
  • defined, 147
  • formulas, 147–150

W

• word equations, 30–33
• word problems. See also problems
  • basic steps to solving, 30–34
  • choosing variables, 131–133
  • decimals and percents, 88–90
  • five-step approach to solving, 128–131
  • overview, 29, 127
  • percent increases and decreases, 91–93
  • solving complex, 34–39, 133–134

X

• x (variables). See also algebraic expressions
  • choosing, 131–133
  • declaring, 128–130
  • identifying, 100–101
  • isolating, 118–125
  • overview, 95–96
  • solving for, 117–119
  • using in equations, 114
• x-y plane. See Cartesian coordinate system

Z

• Zeno’s Paradox, 167–168
• zero, 59, 164