Math for Grownups (6 page)

3. Division
undoes
multiplication.

With these rules in mind, can you guess what you need to do to find out what
x
is? How about if you divide each side of the equation by 0.20?

When you divide 0.20
x
by 0.20, you get
x
—and remember that getting
x
by itself on one side of the equals sign is the key to solving the equation. Here’s what you’ll end up with:

x
= 21,000

Whew! That’s a lot of work to find out that with a $4,200 down payment, the most expensive car you can afford is one that costs $21,000. The good news is that there’s an easier way: Just divide the down payment by the percent.

$4,200 / 20%
=
$4,200 / 0.20
=
$21,000

So now you have two options for finding the down payment. You can remember to divide the down payment by the percent, or you can remember how to set up and solve a simple algebraic equation.

You might think you can afford a $21,000 vehicle, but if you’re financing, it’s smart to look at your monthly costs before you sign off on the deal. If you can’t afford the monthly payment, it doesn’t matter how great a price you’ve negotiated.

Whatever you do to one side of an equation, you have to do to the other side. But why? It’s because of those two little horizontal, parallel lines: the equals sign.

Think of an equation as a teeter-totter. Let’s say identical 8-year-old twins Truman and Nixon climb on—one on each side. Because they weigh the same, they can balance in mid-air. But if their older sister Reagan jumps on behind Nixon, the teeter-totter is no longer balanced.

Truman = Nixon

Truman ≠ Nixon + Reagan

The same thing happens with equations. Here’s an easy one:

2
=
2

What happens when we add to one side of the equation only?
Does 2
=
2
+
1? Of course not.

2
≠
3

But if we do the same thing to both sides of the equation, we keep the balance.

2
=
2

Now, let’s add the same thing to both sides of the equation.
Does 2
+
1
=
2
+
1?

Yes! 3
=
3

This works for any operation: addition, subtraction, multiplication, and division. Don’t believe it? Try it out on your own.

Online calculators can help you find your monthly payment, but you can also figure it out on your own. Let’s look at the formula. It’s pretty ugly but not hard to use.

M
is the monthly payment

P
is the principal, or the total amount borrowed

r
is the interest rate

n
is the number of months in the loan

Dear Aunt Sally has her eye on a car that, with taxes, fees, and options, costs a nice, round $21,000. She can put down 20%, which is $4,200. That means she needs to finance $16,800. Before even setting foot on the lot, she contacted her bank and was approved for a 3-year loan with 4.5% interest.

Always organized, Aunt Sally first lists her variables—the letters that are in her formula and that change depending on how much she’s borrowing, at what interest rate, and so on:

Now she can substitute.

“That’s one doozy of an equation!” dear Aunt Sally exclaims. And then she gets to work, using PEMDAS. (Remember PEMDAS from earlier in the chapter?)

First she takes care of anything in parentheses:

Now she can take care of the exponent. She has a scientific calculator, so she just plugs in the numbers to find out that 1.000375
^-36
is 0.873. If she didn’t have a scientific calculator, she could find one online
(
www.calculator-tab.com
would be a good choice).

The rest of the calculations are pretty simple. She needs to multiply on the top and then subtract on the bottom.

Then she can divide, which will give her monthly payment.

M
= 496.06

Dear Aunt Sally has discovered that her monthly car payment would be $496.06.

You may have wondered why Aunt Sally did all of the calculations in the numerator
—
the top part of the formula—and all of the calculations in the denominator
—
the bottom part of the formula—before she actually divided. That’s because the parentheses in this situation were understood.

If she put all of the parentheses into the formula, it would look like this:

And that’s an even uglier formula. It’s much easier to consider the numerator of this formula as one part and the denominator as another part. The parentheses around each of those expressions are understood, so it is not necessary to write them.

It may have been a long while since you last saw a negative exponent. Heck, it may have been so long ago that you don’t remember ever seeing such a thing.

Negative exponents aren’t so scary actually—if you know the rule that applies to them. A negative is just the inverse of a positive. Think of an inverse as turning something upside down. The inverse of addition is subtraction (the inverse of subtraction is addition). The inverse of multiplying is dividing.