102 Part 2: Into the Unknown
Using Variables
A variable is any symbol that stands for a number. In algebra, the symbol is usually a letter, but
that doesn’t have to be the case. You might have looked at questions that said 3 +? = 5 and you
understood that you were supposed to find the number that replaced the? to make the statement
true. In that case,? is a variable. You might have seen puzzles that said ' + ¢ = 9. There are
many different right answers for that one, but the ' and the ¢ are acting as variables.DEFINITION
A variable is a letter or symbol that takes the place of a number.A variable is used to take the place of a number because the value of the number is unknown,
or because the number that goes in that place may be changing. Perhaps a pattern is being
represented in which different values are possible.
For example, imagine you are taking a test with 20 questions. Each question is worth 5 points,
so if you get all the questions correct, you earn 100 points. But what if you don’t get them all
right? Your teacher might use a rule or pattern that says your score is 5 points times the number
of questions you answer correctly. Using the variables S for your score and n for the number of
questions you answer correctly, you can write the rule as S = 5×n. That rule will apply to every-
one who takes the test, but each person may get a different number of questions correct. The
variable n can have many different values. It varies. That’s where the name variable comes from.
Suppose on a different test you got your paper back with a grade of 87 on it. You want to know
how many points each question was worth. You can find out by counting the number of questions
you answered correctly and using the variable p to stand for the point value of one question. If
you answered 29 questions correctly, you can say 29×p = 87. Here you’re using a variable because
you don’t know the number of points. The variable stands for a number that is unknown.The Language of Variables
When you start to use variables in your phrases and sentences, it’s a lot like learning a new
language. You need to learn your vocabulary, understand the grammar of the language, including
the idioms, and practice, practice, practice.
Let’s start with parts of speech: nouns, verbs, and such. In algebra, numbers and variables are
your nouns, and symbols like =, <, and u serve as verbs. Operation signs, like + and –, act as
conjunctions, the way “and” and “or” would in English.
To translate algebra into English, you can usually just read the symbols and make a few shifts,
like saying “and” for + and “is” for =. The sentence x + 3 = 8 is the algebra language equivalent
of “some number and three combine to make eight.” The x, the 3, and the 8 are nouns. The x and