Beginning Algebra, 11th Edition

Mathematical model, 27
Mean, 58
Means of a proportion, 131
Measure of an angle, 114, 122–123
Minuend, 39
Mixed number, 2
Mixture problems, 111, 139–141, 274
Model(s)
mathematical, 27
quadratic, 403
using a linear equation to, 194
Money problems, 142–143
Monomial, 70, 321
Motion problems, 144–145, 275
Multiplication
associative property of, 61
of binomials, 331
commutative property of, 60
of complex numbers, 576
of conjugates, 525, 577
FOIL method of, 331
of fractions, 4
identity element for, 62
identity property of, 62
inverse for, 51, 63
of a monomial and a polynomial, 329
in order of operations, 16
of polynomials, 329
properties of, 60–61
of radicals, 504
of rational expressions, 429
of real numbers, 49, 59
of signed numbers, 50, 59
of sum and difference of two terms, 336
summary of properties of, 66
word phrases for, 54–55
by zero, 49
Multiplication property
of equality, 92
of inequality, 154
Multiplicative identity element, 62
Multiplicative inverse, 51, 63
Multivariable polynomial, 320, 324
addition of, 324
subtraction of, 324

Natural numbers, 2, 28
negative of, 28
opposite of, 28
Negative exponents, 303–304
changing to positive, 305–306
Negative infinity, 151
symbol for, 151
Negative numbers, 28
addition of, 37
as exponents, 304
simplifying square roots of, 575
Negative of a number, 28

Negative slope, 202

Negative square roots, 494

Not equal, 17

Notation

function, 233

interval, 151

scientific, 312

set-builder, 29, 250

subscript, 200

nth root, 499

Null set, 103, 597

symbols for, 103, 597

Number(s).See alsoReal numbers

absolute value of, 32–33

additive inverse of, 31–32, 40, 63

complex, 574–575

composite, 3

cube of, 15

divisibility tests for, 58, 360

factors of, 2, 360

fractions, 2

graph of, 28

greatest common factor of, 360

imaginary, 575

integers, 28–29

irrational, 30, 496

mixed, 2

natural, 2, 28

negative, 28

opposite of, 28, 31–32, 40, 63

ordering of, 31

perfect square, 496

positive, 28

prime, 2, 360

prime factors of, 3

rational, 29

real, 30

reciprocal of, 5, 51

signed, 28

square of, 15, 494

square roots of, 494

whole, 2, 28

Number line, 28, 151

addition on, 37

graphing a number on, 28

graphing intervals on, 151

subtraction on, 39

Numerator, 2, 421

Numerical coefficient, 70, 320

Numerical expressions

evaluating, 53

from word phrases, 41–42, 54–55

Odd consecutive integers, 113, 401

Opposite(s)

of a number, 28, 31–32, 40, 63

quotient of, 424

Order

of operations, 15–16, 40–41

of a radical, 499

Ordered pairs, 177, 229

completing, 178

components of, 229

graphs of, 180

input of, 230

output of, 230

plotting, 180

table of, 179

Ordering of real numbers, 31

Origin, 180

Outer product, 331

Output for a function, 230

Pairs, ordered, 177, 229

Parabola, 325

axis of, 325, 580

axis of symmetry of, 580

graph of, 325

intercepts of, 581

line of symmetry of, 325

steps to graph, 582

vertex of, 325, 580

Parallel lines, 204

slopes of, 205

Parentheses, 15

Percentage, 134

Percent(s), 133, 139

applications of, 135

converting to decimals, 134

solving equations with, 134

using to find percentages, 140

Perfect cube, 499

Perfect square, 496

Perfect square trinomial, 382, 560

factoring of, 383

Perimeter of a geometric figure, 12, 121

Perpendicular lines, 205

slopes of, 205

Pi ( ), 30, 126, 496

Pie chart, 9

Pisa, Leonardo of, 494

Plane, 180

Plotting points, 181

Plus or minus symbol, 555

Point-slope form, 213–214, 216

Polynomial(s)

binomial, 321

classifying, 321

degree of, 321

of degree two, 324

in descending powers, 321

division by a monomial, 340

division by a polynomial, 342

evaluating, 322

factoring summary, 389

graphing equations defined by, 324

long division of, 342–346

monomial, 321

multiplication by a monomial, 329

multivariable, 320, 324

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