Math for Grownups (32 page)

where
P
is principal,
M
is the monthly payment,
r
is the monthly interest rate
,
and
n
is the number of months in the loan.

Rule of 72 (
Chapter 8
)

y
= 72 /
r
, where
y
is years and
r
is rate

Simple Interest Formula (
Chapter 8
)

I
=
Prt
where
I
is the interest,
P
is the principal,
r
is the rate, and
t
is the length of the loan.

Target Heart Rate (
Chapter 9
)

z
=
p
(
M
–
R
)

Z
=
z
+
R

where
M
is maximum heart rate,
R
is resting heart rate,
p
is the percent from the heart-rate-zones table,
z
is the zone, and
Z
is the zoned heart rate

Total-Payment Formula (
Chapter 3
)

T
=
M
•
n

where
T
is the total payment,
M
is the monthly payment, and
n
is total number of months in the loan

Surface Area (
Chapter 4
)

In general, the surface area of an object is the sum of the areas of its faces or sides.

SURFACE AREA OF A CUBE

SA = 6
s
²
, where SA is surface area and
s
is the length of each edge of the cube.

SURFACE AREA OF A RECTANGULAR PRISM

SA = 2
lw
+ 2
lh
+ 2
wh
, where SA is surface area,
l
is length,
w
is width, and
h
is height

SURFACE AREA OF A CYLINDER

SA = 2
πr
²
= 2
πrh
, where SA is surface area,
π
is 3.14 …,
r
is the radius of the base, and
h
is the height of the cylinder

SURFACE AREA OF A SPHERE

SA
= 4
πr
²
, where SA is surface area,
π
is 3.14 …, and
r
is the radius of the sphere

Volume (
Chapter 6
)

VOLUME OF A CUBE

V
=
s
³
, where
s
is the length of a side

VOLUME OF A RECTANGULAR PRISM

V
=
lwh
, where
l
is the length,
w
is the width, and
h
is the height

VOLUME OF A CYLINDER

V
=
πr
²
h
, where
π
is 3.14 …,
r
is the radius of the base, and
h
is the height of the cylinder

VOLUME OF A PYRAMID

V
= 1∕3(
lwh
), where
l
is the length,
w
is the width, and
h
is the height

VOLUME OF A CONE

V
= 1∕3(
πr
²
h
)

Glossary

Consider this glossary a tool in your mathematical tool belt. If you need to double-check a definition (say, for instance, you want to review what an improper fraction is), you can find the answer here. In some cases, we have included definitions that are related to concepts we discussed, even if the word or phrase itself wasn’t used in this book.

This list is reserved for math terms, so you won’t find definitions for
principal
or
compound interest
here. For that, take a look at the Index, and it will direct you to the pages where the concepts are discussed.

So go ahead. Dig into some meaty math definitions. Soon you’ll be able to impress the kids and be the geeky star at your next cocktail party.

Additive Identity

Adding zero to a number leaves it unchanged.
x
+ 0 =
x
. Example: 3 + 0 = 3

Additive Inverse

The number you add to another number to get zero; the negative value of a positive number and the positive value of a negative number. Example: The additive inverse of 12 is -12, because 12 + (-12) = 0. And the additive inverse of -1 is 1, because -1 + 1 = 0.

Algebra

The field of mathematics in which letters and other symbols are used to represent numbers.

Algorithm

A set of steps used to solve a problem.

Angle

A two-dimensional figure formed by two rays that share a common endpoint called the
vertex
.

Area

The amount of space occupied by a two-dimensional figure. Area is expressed in squared units.

Arithmetic

Basic operations (addition, subtraction, multiplication, and division) with whole numbers, fractions, decimals, and exponents.

Base-10 Number System

The decimal system of numbers, which has 10 as its operating base.

Circumference

The distance around a circle or other closed curve.

Coefficient

A number that is multiplied by a variable. Example: In 5
x
, 5 is the coefficient.

Common Denominator

The same denominator in two or more fractions.

Commutative Property of Addition and Multiplication

a
+
b
=
b
+
a
and
a
•
b
=
b
•
a
. Addition and multiplication are commutative because you can change the order of the numbers and still get the same answer. Examples: 2 + 1 = 1 + 2 = 3 and 4
•
9 = 9
•
4 = 36.

Constant

A fixed value. Example: 10 is a constant in the expression 6
x
²
+ 10.

Decimal Number

A number that includes a decimal point followed by digits. The digits to the right of the decimal point indicate values smaller than 1. Example: 5.7903

Denominator

The bottom number in a fraction. Example: The denominator of 1/5 is 5.

Dependent Variables

Variables whose values are determined by the values of another variable (usually the
independent variable
). Example: In finding the cooking time of a turkey, the time you seek is the dependent variable, because it depends on the weight of the bird (which is the independent variable).

Difference

The answer in a subtraction problem. Example: The difference of 5 and 2 is 3.

Digit

A symbol used to make numerals. Example: 1, 4, and 7 are digits of 147.

Distributive Property of Multiplication over Addition

a
(
b
+ c) =
ab
+
ac
. When a number is multiplied by the sum of two other numbers, the first number can be distributed to both of those numbers (that is, multiplied by each of those numbers independently) and the results then added. Examples: 5(2 + 4) = 10 + 20 = 30 and 3(
x
+ 2) = 3
x
+ 6.

Dividend

In a division problem, the amount being divided into parts. Example: In the problem, 20 / 5 = 4, 20 is the dividend.

Divisor

In a division problem, the number that is being divided into another number (called the
dividend
). Example: In the problem 20 / 5 = 4, 5 is the divisor.

Equation

A mathematical sentence that states equality. Examples: 4 + 2 = 6 and 7
x
– 9 = 27

Estimation

An educated guess, usually based on rounding the numbers before using any operations. An estimate is not an exact answer. Example: An estimate for 19 • 4 is 80.

Exponent

The exponent of a number tells how many times the number is to be multiplied by itself. Example: In
x
⁵
, 5 is the exponent, and
x
⁵
=
x
•
x
•
x
•
x
•
x
.

Expression

Numbers, symbols, and operations grouped together.
Example: 6
x
+ 9

Factor

The numbers you multiply together to get another number. Also, a number that will divide evenly into another number. Example: 2 is a factor of any even number.

Fraction

Part of a whole, written, where
a
is any whole number, and
b
is any whole number. Examples: and

Greatest Common Factor (GCF)

The largest number that will divide evenly into two or more numbers. Example: 12 is the GCF of 60 and 24.

Improper Fraction

A fraction whose numerator is larger than its denominator. An improper fraction is always larger than 1. Improper fractions can be written as
mixed numbers
. Example:

Independent Variable

A variable whose value determines the value of other variables. Example: In finding the cooking time of a turkey, the weight of the bird is the independent variable, because it determines the cooking time (which is the
dependent variable
).

Integer

A number with no fractional part. The set of integers is {…, -4, -3, -2, -1, 0, 1, 2, 3, 4, … }.

Inverse

The opposite. Examples: The inverse of multiplying by 2 is dividing by 2. The inverse of adding 7 is subtracting 7. The inverse of is.

Least Common Denominator (LCD)

In a series of fractions, the smallest number that all of the denominators will divide into evenly. Example: 8 is the least common denominator for,, and.

Least Common Multiple (LCM)

The smallest number that is a common multiple of two or more numbers. Example: The LCM for 3 and 6 is 12.

Mixed Number

A number that includes a whole number and a fraction. Mixed numbers can be written as improper fractions. Example: 4¾

Multiplication Property of Equality

When both sides of an equation are multiplied by the same number, the equation stays true. If
a
=
b
, then
ac
=
bc
.

Multiple

The product of two numbers; also, a number that can be divided evenly by another number. Example: 25 is a multiple of 5.

Multiplicative Identity

Multiplying a number by 1 equals that number. Examples: 4
•
1 = 4 and
a
•
1 =
a
.

Number Sense

The ability to use and understand numbers. Number sense includes an understanding of number values, operations (including their properties), and estimation.

Numerator

The top number of a fraction. Example: 6 is the numerator of.

Operation

A mathematical calculation, most commonly addition, subtraction, multiplication, and division.

Order of Operations

The order in which calculations must be performed in an expression: parentheses, exponents, multiplication, division, addition, and subtraction.

PEMDAS

A way of remembering the order of operations: Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. PEMDAS comes from this mnemonic: Please Excuse My Dear Aunt Sally.

Percent

One part of 100 represented with a percent sign (%). Example: More than 25% of the cars were red.

Percentage

A portion of the whole, usually stated in a general sense. Example: The percentage of red cars on the road has increased significantly over the last year.

Perimeter

The distance around a two-dimensional shape. The perimeter of a circle is called the circumference.

Probability

The chance that something will (or will not) happen.

Product

The answer in a multiplication problem. Example: The product of 2 and 5 is 10.

Quotient

The answer in a division problem. Example: In the problem 20 / 5 = 4, 4 is the quotient.

Ratio

A comparison of two numbers. Ratios can be written with a colon, a fraction line or the word
to
. Examples: 2:1,, and 2 to 1.

Recurring Decimal

A decimal number whose digits behind the decimal point infinitely repeat. Recurring decimals are always rational numbers. Examples: 0.333 … and 0.2388.… Recurring decimals are often shown with a bar over the recurring digit
or digits. The bar indicates which digits repeat. Examples: and