Welcome to a lesson on
the meaning of a variable in mathematics.
A variable can be used to represent a changing value
as well as a value that doesn't change, or a placeholder.
Let's look at these two meanings of a variable.
Let's first look at the definition
of a variable as a changing value.
A variable is a letter that represents
a number or value that may change within
the context of a mathematical problem.
As an example, the temperature inside an oven once
it is turned on, the temperature changes until
it reaches the set temperature,
and then changes again once the oven is turned off.
So if we use a variable to represent
the temperature in the oven, the variable represents
a changing value because the temperature is changing.
And now let's look at the definition
of a variable as a placeholder.
A variable is a letter that represents a number or value
that will remain unchanged, or constant,
based on the confines of the mathematical problem.
As an example, the area of your mathematics classroom.
For each specific classroom, the area will not change,
so if a variable is used to represent this area,
the variable is a placeholder.
Typically we use a single letter for a variable.
Many times we use a letter that makes sense to
the meaning of the value, like t for time, or w for width.
Let's look at some examples.
Here we're asked to determine if the description describes
a changing value, or a placeholder,
then determine a possible variable.
So enter CV if the variable represents
a changing value, and P if the variable is a placeholder,
meaning a value that doesn't change.
First we have the elevation of Mount Humphrey's,
if we use a variable to represent the elevation,
because the elevation doesn't change, the variable would be
a placeholder, and therefore we enter P.
For the variable let's use e to represent the elevation.
Next we have the water level of a pool
as it is being filled, so as the pool is being filled
the water level rises, and therefore changes,
so if we use a variable to represent the water level,
the variable represents a changing value, we enter CV.
For a possible variable we could use l or w
to remind us it represents the water level, let's use w.
Next we have the number of calories
consumed throughout the day.
Throughout the day as you eat food
the number of calories consumed increases,
so if we use a variable for the number of calories consumed,
because this value changes throughout the day,
the variable would represent a changing value, and let's use
the variable c to represent the calories consumed.
Next the monthly car payment with a fixed-interest loan.
So because we have a fixed-interest loan,
this means the car payment is always the same amount,
and therefore if we use a variable for
the car payment it would be a placeholder,
and let's use the variable p for payment.
Next the amount of gas consumed by your car as you drive,
well the more you drive a car the more gas it consumes,
and therefore the amount of gas consumed changes
as you drive, as a variable this would be a changing value.
As a possible variable we could use a for
the amount of gas, or just g for gas, let's use g.
And then finally we have the cost of a new textbook
for a specific class from the bookstore
at the beginning of the semester.
So because the cost of the book remains constant
or doesn't change, if we use a variable for
the cost it would be a placeholder.
As a possible variable we could use c for cost
or t to remind us it's the cost of a textbook.
Let's use c for cost.
I hope you found this lesson helpful.