246 Index
Reciprocals
in dividing of algebraic fractions, 145–146
of exponential expression, 50–51
multiplication by, 11
perpendicular line slopes, 181–182
simplifying, 51–52
Rise, 178, 178f, 187, 188
Run, 178, 178f, 187, 188
Sets
correspondence between, 196
dots in, 1
function, 195 –196
of integers, 3
“is an element of ” symbol for, 11
of natural numbers, 1
of rational numbers, 4
of whole numbers, 2
Seventh root, 39
Signed numbers. See Real numbers
Sixth root, 6, 39
Slope of a line
defi nition of, 178
parallel lines, 181
perpendicular lines, 181–182
through two points
basics, 178–181
from graph, 178f, 187, 188
negative, 178, 180, 185
point-slope equation for, 190–193
posit ive, 178 –179, 18 5
y-intercept equation for, 184–190
zero, 178, 180 –181, 185
Special products
difference of two cubes, 102, 134, 136
difference of two squares, 102, 134–135
perfect cubes, 36, 102
perfect squares. See Perfect squares
sum of two cubes, 102, 134, 136
Square root
absolute value and, 32, 36, 164
categorization of, 5–7
of decimals, 34, 53
fi nding, 32–36
of fractions, 34–35, 41–42
function with, 198–200
in monomials, 85
of negative numbers, 6, 32, 36, 163
on number line, 6
of one, 33
of positive numbers, 5, 7, 32–35, 39–42
principal, 32–36, 38, 53, 164
simplifying, 39–42
symbol for. See Square root
symbol
of zero, 5, 32
Square root function, 202, 202f
Square root symbol
categorization of, 58
in order of operations
with addition, 35, 119
algebraic expressions, 67–70
with multiplication, 36, 37, 39–42
PEMDAS, 60
sign with, 5, 32
Squares, diagonal length in unit, 5, 5f
Substitution method, 206–208
Subtraction
of algebraic fractions, 146–150
commutative property of, 24
within complex fractions, 151–152
difference of two cubes, 102, 134, 136
difference of two squares, 102, 134–135
of integers, 4
of like terms, 88–89
linear equation rules, 155
linear inequality rules, 160
of monomials, 88–89
of natural numbers, 1
of negative numbers, 21–25
opposite numbers in, 21–25, 92–93
in order of operations
with absolute value, 120
algebraic expressions, 68–70
PEMDAS, 58–63
parentheses in, 147
of polynomials, 92–93
power of a difference rule, 80, 81, 220
in rational expressions, 141–150
sign for, 21, 25
signed numbers rules, 21–25
in slope formula, 178
of whole numbers, 2
of zero, 22, 24
Sum of two cubes, 102, 134, 136
Sum of two squares, 134, 135