In the previous section we used an example where we wanted to
know how many hours a person works over a period of two days if he
each day were to work 4 hours before lunch and 3 hours after lunch.
As we could see this problem could be turned into the
expression
When we want to translate a
verbal phrase like the example above into a mathematical expression
we can look for words that indicate a mathematical operation. For
example words like "sum", "increased by" and "plus" indicates that
we are to use addition. And words like "times" and "multiplied by"
calls for multiplication. When we are writing subtractions and
divisions the order in which we write is important. "The difference
of a number 12 and a" is written 12 - a and not a - 12.
When we have a mathematical
problem as in the example below we can begin by making a verbal
model where we describe the situation in words and relate the words
by usage of mathematical symbols. These words can then be replaced
by numbers or variables to create a mathematical model, or
expression, to describe the situation.
Example 1:
Tony is at a car rental service
to rent a car. There is an administration fee of $50 to rent a car
and then it costs $20 for each day he has the car. Write an
expression for the total cost of renting a car at this particular
car rental service.
Written as a verbal model
Translate the verbal model into
a mathematical model
where x are the number of days
that you've rented the car.
When we measure how fast a car
or something is moving we are usually comparing quantities measured
in different units like comparing distances with time. The fraction
resulting is called a rate. The unit rate is when the denominator
of the fraction is 1 unit.
Example 2:
An airplane travels 760 miles
in 2 hours. Calculate the unit rate.
If you're uncertain as to
whether or not your expression is resulting in the wanted unit you
can always do a unit analysis. In a unit analysis you exchange the
numbers and variables in the expression with the corresponding
units. Here we use the verbal model from example 1.
And to test what the resulting
unit is we only keep the units in the expression:
Videolesson: Write an expression that describes
the situation:
Anna and her parents are going to the movies. Each ticket costs
$8 and Anna also wants popcorn which is an additional $3. How much
did they pay.