Up Your Score (31 page)

As you may already know, some calculators are also minicomputers that can store information, such as vocab definitions. But if you were planning to use these to cheat, don’t count on it. No handheld computers or anything else with a lettered keyboard are allowed for the test. (And, yes, the proctor will check.) Also, you can’t keep your calculator on your desk during the critical reading and writing sections.

You’ve done a lot of fractions in math class, so you know, more or less, how to work with them. But do you know what a fraction
means
? Do you completely understand that ⅗ not only means
three-fifths,
it also means
3 divided by 5
? Also, do you completely understand that miles/hour means
miles divided by hours
? If not, read this section extra carefully. Fractions and units are the most important things to master for the math SAT.

The following problem will illustrate why
three-fifths
and
3 divided by 5
are the same thing.

Arnold Schwarzenegger, Russell Crowe, Matt Damon, Bruce Willis, and Hugh Jackman are having dinner together. They order 3 quiches, which they plan to divide equally. How much quiche does each person get?

Step 1:
Cut the first quiche into 5 equal pieces (i.e., into fifths) and give 1 piece to each person.

Step 2:
Do the same thing to the second quiche.

Step 3:
Do the same thing to the third quiche.

Now, as you can see, everyone has 3 slices of quiche. Each slice is a fifth of a quiche, so everyone has three-fifths (⅗) of a quiche. So, 3 quiches were divided equally among 5 people to give each person ⅗ of a quiche.

This is what this problem was designed to demonstrate—that 3 divided by 5 and ⅗ are the same thing: 3 quiches divided by 5 people = ⅗ of a quiche per person. Read this paragraph over and over again until you understand it. Then go eat some quiche.

The Serpent loves testing your ability to work with fractions by creating problems that contain complex fractions. A complex fraction is a regular fraction divided by another regular fraction. Here are some examples of complex fractions:

Since complex fractions are a pain in the neck, you want to make them into regular fractions. There is a simple rule for simplifying complex fractions.

Simple Rule:
Flip the bottom fraction and multiply it by the top fraction.

Simple? Well, actually it is. You just have to recognize each individual fraction. Label the complex fraction like this:

What the Simple Rule says is that you can simplify any complex fraction by flipping the bottom fraction and multiplying it by the top fraction. It works because division is really multiplying by the reciprocal (“reciprocal” means “whatever it was, only flipped over”). This is what the Simple Rule looks like:

You may want to draw arrows:

Another way to think of this is:

Using real numbers:

Here are some problems. Make each complex fraction into a simple (regular) fraction. Practice the Simple Rule.

You should immediately rewrite this as: