Index 243Monomials
addition of, 88–89
defi nition of, 84
division of polynomials by, 110–113
GCF, 121–126, 139–143
identifying, 84–86
like terms, 87, 88–90
multiplying, 94–98
subtraction of, 88–89
unlike terms, 87
Multiplication
in algebraic expressions, 66
of algebraic fractions, 143–145
associative property of, 10
closure property of, 8–9
commutative property of, 9
distributive property and, 11
division and, 120
factoring and, 119
within fractions, 120, 140, 143
of integers, 4
linear equation rules, 155
linear inequality rules, 159–160
of monomials, 94–98
of natural numbers, 1
by one, 10
in order of operations
with absolute value, 120
algebraic expressions, 67–70
PEMDAS, 60–62
polynomial expressions, 106–109
with square root symbol, 36, 37, 39–42
parentheses in, 8, 58, 144
of polynomials, 94–102
power of a product rule for, 78–80, 119–120
power to a power rule for, 77–78
product rule for, 74–75
by reciprocal, 11
signed numbers rules for, 26–28
symbol for, 8
of whole numbers, 2
by zero, 11, 12, 26, 28, 155
Multiplicative identity property, 10, 11
Multiplicative inverse property, 11
Natural numbers
addition of, 1
defi nition of, 1
division of, 1–2
as exponent, 44–48, 74–81
multiplication of, 1
on number line, 1, 1f
rational. See Rational numbers
roots of, 38
set of, 1
subtraction of, 1
zero and, 2
Negative integer, 3, 3f
Negative numbers
absolute value of, 15–17, 15f
addition of, 17–20
categorization of, 7
comparing, 15
cube of, 36
cube root of, 5–6, 36–37, 39, 53
in division, 29–30
domain of functions and, 196–197
even roots of, 6, 39, 53–54, 196–197
as exponent, 50–52, 77, 84–85,
104 –105, 120
exponentiation of
with fractions, 53–56
with natural numbers, 46–47
with negative numbers, 50, 52
with one, 45
with zero, 49
fi fth root of, 38
as GCF, 123–125
integers, 3, 3f
linear inequality rules, 159–160
in monomials, 84
multiplication of, 26–28
nth root of, 38
on number line, 3–4, 3f, 6, 15, 160f
parentheses with, 25, 58, 67, 176, 178
seventh root of, 39
square of, 32
square root of, 6, 32, 36, 163
subtraction of, 21–25
Negative sign (–)
in division of polynomials, 111
in factoring, 132
in quadratic formula, 168
rules for, 25
when combining like terms, 90
Nonintegers, 6
“Not equal to” symbol (≠), 14t, 120
nth root of a, 38