plural of formula in Latin is “formulae,” but it has become more readily accepted as
“formulas.”)
Identity—An identity is a mathematical relationship equating one quantity to
another that initially may appear to differ; it also means an equation that is always
true, such as the Pythagorean theorem (for more about identities, see below).
How can word problemsbe expressed as equations?
There seem to be a gazillion word problems out there—just ask anyone taking such
tests in grade or high school! The one thing most have in common is that they can be
expressed as an equation—many as algebraic equations—in which there are known
and unknown quantities. In almost all instances, there are key words that lead the
reader to determine not only the numbers and variables, but also what operations to
use in the equation to determine the answer. The following lists some simple key
words and their corresponding operation:
Common Key Words Used in Word ProblemsKey Words Operation Examples
sum, total, more than addition The sum of my weight and 10 equals 130
(y 10 130); the groceries at one store
were $3.00 while the total for two stores
was $4.00 (y 3 4); seven more than
the price is $126 (y 7 126)
difference, discrepancy subtraction The difference (or discrepancy) between
her age and her sister’s age, who is 30, is
10 (y 30 10)
times, multiplied by multiplication Three times his brother’s age is 6 (3 y
6); eight multiplied by her weight is 96 (y
8 96); the product of his weight and 6
is 36 (y 6 36)
What are independentand dependent variablesin algebra?
Variables can be broken down into independent and dependent variables. An indepen-
dent variable is a quantity that increases or decreases (is variable), or that has an infi-
nite number of values in the same expression. For example, in the expression x^2 y^2
r^2 , xand yare variables. A dependent variable is a quantity that varies but is pro-
duced by changes in the independent variable. In other words, the dependent vari-
able’s value is dependent on the independent variable. For example, in the expression
f(x) y, xis the independent variable and yis a dependent variable (because yis
dependent on the value of x). 135