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DeMYSTiFieD / algebra DeMYSTiFieD / HuttenMuller / 000-0 / IndexDecimals (Cont.):
division, 72–73
fractions, 70–72
linear equations, 200
multiplication, 69–70
notation for sum of fractions, as, 66
percent, 224
subtraction, 67–69
terminating/nonterminating, 67
Diagonal formula (rectangle), 417,
418
Difference of two squares, 159
Distance formula, 429, 436
Distance problems, 285–300,
429–441
linear applications
opposite directions, 288, 290
starting at different times, 292
summary (how to), 307
three unknowns, 296
quadratic applications
basic formula, 429
right angles, 436–441
stream problem, 429, 430
type of problems, 429
Distributive property, 134. See also Factoring and the
distributive property
Dividend, 27
Division
decimals, 72–73
exponents, quantities with, 96,
109–112
fractions, 5–6
fractions with variables, 52–54
mixed numbers, 32–34
negative numbers, 84–86
Divisor, 27
Double inequalities, 329–342E
End-of-chapter quizzes, answers to,
457–458
Equations
linear. See Linear equations
quadratic. See Quadratic equations
rational, 210, 373–382
Exponent properties. See also Exponents
adding exponents, 96
algebraic expressions, 98
multiplying exponents, 96
negative exponents, 102, 107
overview (table), 127Exponent properties (Cont.):
reciprocal of the base, 102
rewrite quotient raised to negative power, 107
subtracting exponents, 96
zero power, 97
Exponents, 96–113
defined, 96
dividing quantities with exponents, 96, 109–112
fractions/LCD, 99–101
multiplying quantities with exponents, 96,
109–112
properties. See Exponent properties
roots expressed as exponents, 123–125, 127
write fraction as product, 112–113
Extracting roots, 361–363
Extraneous solutions, 211, 212F
Factoring, 141–143, 145–147, 451–455
difference of two squares, 159–161
grouping, 147–148
negative numbers, 143–145
number facts, 451
prime factors, 452–454
prime numbers (and their squares), 456
quadratic equations, 350–361
quadratic polynomials, 154–159, 162–164
simplifying fractions, 148–151, 166–168
Factoring by grouping, 147–148
Factoring and the distributive property, 133–181
adding fractions, 139–141, 169–175
combining like terms, 137–139
completely factor, 141–143, 145–147
distributive property, 134
factoring by grouping, 147–148
factoring quadratic polynomials, 154–159,
162–164
factoring the difference of two squares, 159–161
factoring to simplify fractions, 148–151,
166–168
FOIL method, 151–154
LCD, 169–171
negative numbers, 135–137, 143–145
quadratic-type expressions, 164–166
subtracting fractions, 139–141, 169–175
Fahrenheit vs. Celsius
basic formula, 236, 340
inequality, 340, 341
same temperature, 236–237
twice as high, 238–240
Falling object problems, 407–416
Finding a common denominator, 14