Math for Grownups (33 page)

Reflexive Property of Equality

Any number is equal to itself.
a
=
a
. Example: 3 = 3

Remainder

The amount left over after division. Example: 15 / 4 = 3 with a remainder of 3. If a divisor is a factor of the dividend, the remainder is 0.

Rounding

Reducing the number of digits in a number (or making them 0) but keeping the value of the rounded number close to the value of the original number. Numbers can be rounded to a variety of places, including the ones place, 10ths, 1000ths, etc. Examples: 3.56 3.6 and 7.13 7

Sequence

A list of objects or numbers in a special order. Example: 6, 12, 24, 48, … is a geometric sequence.

Side

One of the line segments that defines a two-dimensional shape, or one of the surfaces that defines a three-dimensional shape.

Simplify

In mathematics, this means to put in the simplest form. Example: Simplify the fraction. (Answer: ½) Example: Simplify the algebraic expression 2(
x
+ 7) (Answer: 2
x
+ 14)

Square

Multiplying a number by itself. Example: 4
²
= 4
•
4 = 16

Sum

The answer in an addition problem. Example: The sum of 4 and 7 is 11.

Surface Area

The total area of a three-dimensional figure, such as a cube, cylinder, or prism.

Symmetric Property of Equality

If
a
=
b
, then
b
=
a
. Example: If
x
= 3, then 3 =
x
.

Term

Part of an algebraic expression that includes a number, a variable, or the product of numbers and variables. Terms are separated by addition or subtraction symbols. Example: The terms of 6
x
²
+ 4
x
–2 are 6
x
²
, 4
x
, and 2.

Transitive Property of Equality

If
a
=
b
and
b
=
c
, then
a
=
c
. Example: If
x
=
y
and
y
= 2, then
x
= 2.

Variable

A symbol for an unknown number. A variable is usually a letter. Example: The variable in 2
x
+ 9 is
x
.

Vertex

A point where two or more line segments meet. The plural of vertex is vertices. Angles, squares, triangles, rectangles, cubes, prisms, and pyramids have vertices.

Volume

The amount of three-dimensional space an object occupies. Volume is expressed in cubic units.

Whole Number

A positive number with no fractional or decimal parts. The set of whole numbers is {0, 1, 2, 3, 4, … }. Examples: 4, 17, and 399

Index

A

Addition

doing same thing to both sides of equation, 41

estimating answers.
See
Estimating

of fractions, 113-14, 115-16, 144

inverse of, 44

of negative numbers, 7

order of operations (PEMDAS acronym), 36

rounding before, 3

of time, 108-9

word clues indicating, 134

Amount-due formula (A=P(1 + r)
ⁿ
, 35-37

Appliance (refrigerator) measurements, 87-88

Area calculations

carpet requirements, 83-85

circles, 221

formulas, 81, 221

oddly shaped areas, 123-25

paint requirements, 78-82

perimeter calculations, 123

rectangles, 221

scale drawings and, 86

square feet, 78-80, 84, 125

squares, 221

square yards, 84

subscripts in, 85

surface area, 81, 129, 135-36, 224

triangles, 221

windows, doors and, 79-82

Art, hanging, 88-92

B

Basal metabolic rate (BMR), 185-88, 192, 222

Birdhouse calculations, 153-54

Body mass index (BMI), 182-84, 192, 222

Bottled water vs. filtered water costs, 21

Brzycki formula, 198, 222

Budget.
See also
Debt; Retirement

adjusting spending based on, 159

average percents of select expenses, 158

expenses and, 156-59

increasing income, 159-60

need for, 156

negative totals, 158

for vacation, 208-14

Bulk, buying in, 22

C

Calculators

calculating monthly payments, 40-46

myth about, 6-7

using, 6-7

Calories.
See also
Weight loss

BMR and, 185-88

bodies handling differently, 185

intake scenarios for weight loss, 190-91

nutrition labels and, 191-93

Olympic swimmer consumption example, 189

reducing, to lose one pound, 188-90

weight-loss formula, 181

Canning jar requirement calculation, 98

Car financing

calculating interest and total costs, 35-37, 45-46

calculating monthly payments, 40-46

down payment calculation, 37-40

20% rule, 39

used vs. new cars, 35-37

Car leasing, 46-53

advantages of, 46

buy/lease decision and, 51-53

calculations for, 47-51

components and considerations, 46-47

Carpet requirement calculations, 83-85

Car purchases, 29-53.
See also
Car financing; Interest calculations

about: overview of, 29

calculating total cost, 31-32, 33-34

fees and option costs, 30-33

lease/buy decision and, 51-53.
See also
Car leasing

phony fees, 32-33

sales taxes on, 30, 32, 33-34

title, licensing fee and, 30, 32

used vs. new, 34-37

Casinos.
See
Gambling

Celsius/Fahrenheit conversions, 110-12

Cones, volume of, 225

Constants, 192

Container gardening, 126-29

Converting

cubic inches/feet/yards, 131-32

inches and feet, 144, 182

inches and yards, 146-48

metric and standard units, 147, 204

minutes and hours, 203

percents/fractions/decimals, 17, 147

temperatures (Celsius and Fahrenheit), 110-12

volume measurements (teaspoons, cups, etc.), 101, 116

Coupon savings, 18-19

Crafts, 139-54

about: overview of, 139-40

approach to, 142

birdhouse calculations, 153-54

changing knitting patterns, 140-42

economies of, 153

photo proportions and sizing, 152

scrapbooking calculations, 148-50

sewing calculations, 143-48

Credit card payments and interest, 161-64

Cubes

surface area of, 224

volume of, 225

Cubic units, 127, 129, 130-32

Cup conversions, 101

Curtains, measuring and hanging, 92-94

Cylinders

surface area of, 224

volume calculations, 128-29, 225

D

Debt

compound interest and, 163-64

credit card payments and interest, 161-64

debt-to-income ratio, 165-66, 222

minimum monthly payments, 166-68

paying down, 168-69

Decimals

common fraction conversions, 147

converting fractions and percents to/from, 16-17, 147.
See also
Fractions; Percents

dividing, 10-11

Decorating.
See
Remodeling and decorating

Departure time calculation, 201-3

Deriving formulas, 207

Diameter

calculating area of circle and, 135-36

radius relative to, 128

Distributive property, 34

Division

of decimals, 10-11

doing same thing to both sides of equation, 41

estimating answers.
See
Estimating

factorials and, 176

factors and, 151

of fractions, 118-19

multiples and, 151

order of operations (PEMDAS acronym), 36

rounding rules, 137

solving for
x
using, 38-40

undoing multiplication, 40

Down payments

for car loans, 37-40

for mortgage, 56-58, 74

Drapes, measuring and hanging, 92-94

E

Ease of everyday math, vi-vii

Equals, synonyms for, 134

Equations

basic problem-solving skills, 95

calculating monthly payments, 40-46.
See also
Interest calculations; Mortgage(s)

common-sense approach to, 211

constants in, 192

deriving formulas for, 207

doing same thing to both sides of, 41

formulas for.
See
Formulas;
specific topics

rounding rules, 137

showing parentheses or not, 44

solving for
x
, 38-40, 99-101, 141-42

variables (dependent and independent) and, 110

word clues for solving, 134

Equity, 58-59

Estimated time of arrival (ETA), 205-8

Estimating

annual savings, 26-27

benefits of, 1-2, 15

coupon savings, 18-19

deciding whether to use, 125

decimal division and, 10-11

grocery cost in cart, 2-8

length of trips, 205-8

methods of, 12-15

percents.
See
Percents

reasonableness and, 125

rounding before adding, 3