Up Your Score (32 page)

You should immediately rewrite this as:

Miles per hour is a way we measure speed. You’ve probably seen miles per hour written as a fraction: miles/hour. Using the quiche problem, we just confirmed that
fractions
mean “division.” So
miles per hour
must mean “miles divided by hours.” But what does that mean? How do you divide a mile by an hour? What does it mean to travel 400 miles divided by 8 hours? The following problem will attempt to answer all these questions.

After our quiche eaters finish eating, they get into the car to go to an ice cream shop. The ice cream shop is 500 miles away. If it takes them 10 hours to get there, what was their average speed?

Answer: The key is to realize that if they drive 500 miles in 10 hours then they have 500 miles to divide among 10 hours of driving. (It’s just like having 3 quiches to divide among 5 people.) So rewrite it as:

Now you know why
miles per hour
is the same thing as miles/hour.

Anything you can count or measure has a unit associated with it.
Pounds
are units,
miles
are units,
hours
are units,
miles/hour
are units, even
noodles
can be units if you are counting or measuring with noodles.

Knowing the tricks of working with units can help you do problems faster and can show you how to do problems that you otherwise wouldn’t know how to do. The rule for working with units is that you can multiply and divide them just as you would numbers. For example, when you multiply (or divide) fractions containing units you can cancel units in the numerator with units in the denominator:

And you can divide using the Simple Rule:

After some practice, multiplying and dividing units will be
as simple and as natural to you as multiplying and dividing numbers.

We will now do a few practice problems from real SATs that show the procedure for doing units problems.

A gasoline tank on a certain tractor holds
16 gallons. If the tractor requires 7 gallons
to plow 3 acres, how many acres can the
tractor plow with a tankful of gasoline?
(A) 6
(B) 7⅙ (C) 7⅓ (D) 10⅔ (E) 37⅓

There are two steps to all units problems:

1. Figure out what information is given.

2. Pick, from only three options, what to do with that information in order to get the correct unit in the answer.

Step 1: Figure out the information given.

a. “7 gallons to plow 3 acres” =

b. “A gasoline tank holds 16 gallons” = 16 gallons

c. “How many acres?” means . . . answer in
acres
.

Step 2: Do the right thing with the information given.

In all units problems, you have three options for what to do with the given information:

1. Multiply the first thing × the second thing.

2. Divide the first thing/the second thing.

3. Divide the second thing/the first thing.

The great thing about units problems is that it is not necessary to understand what’s going on in order to know which of the three options to use. You automatically know which one to
choose because only one of the options will give you the answer in acres (the unit you want). Look at the three options:

Nope! The answer has to be in terms of acres, not in terms of

Nope! We want acres in the numerator.