Math 101

You also need a basic grasp of percentages, decimals, and fractions. If you feel you need some help boning up on these skills, I've provided a basic primer below.

Percentages
What are they? The word percent means "parts of 100." If someone says you scored a 70 on a 100-item math test, that means you got 70 out of 100 correct and achieved a 70 percent success rate.

Real Life, Real Money Use
Interest rates, inflation rates, tips in restaurants, and how much interest you're earning on your money are expressed as percentages. You can use them to compare the deals you get on money market accounts from various banks. If one bank is offering 2 percent annually and another is offering 3 or 4 percent, you can easily tell where you'll be getting the better deal.

Math 101 continues...

Decimals
Decimals are also parts of 100, but they are expressed as "points" rather than "percent." Think of taking a child's temperature: 98.6—"ninety-eight point six"—is really 98 and six-tenths (a fraction—we'll get to those in a moment) or 98 and 60 percent.

Real Life, Real Money Use
To use decimals in real life, you need to be able to convert decimals to percentages. When you shop the sales, for instance, you'll see signs (particularly after the holidays) that say items are selling for 40%-off the original price. Suppose the original price of an item is $120. How can you find out how much 40 percent of $120 is?

1. First, convert 40 percent into a decimal. To do that, start at the right-hand side of the number and put a period two digits to the left.
   40% becomes the decimal .40
   (7% would become the decimal .07)
2. Then multiply the decimal by the original price to get the discount.
   $120 x .40 = $48)
3. Finally, subtract the discount from the original price to get the new selling price.
   $120 – $48 = $72.

If you get in the habit of carrying a calculator, you can figure out what sort of prices you'll pay before you get to the checkout counter.

Math 101 continues...

Fractions
Fractions are numbers expressed in parts as well—a numerator over a denominator. A percentage can be stated as a fraction in which the denominator is 100: 50% = 50/100. With fractions, your goal is to reduce the denominator to the smallest possible number so that the fraction becomes easier to deal with. Thus, 50/100 is the same as 1/2, and 25 percent or 25/100 is the same as 1/4.

Often, thinking of these amounts as parts of a dollar—coins—can be very helpful. For example, 50/100 is equivalent to a half-dollar (50 cents), and 25/100 is equivalent to a quarter (25 cents).

Real Life, Real Money use
Fractions, like percentages, show up all the time when stores put things on sale. You often see things marked "1/2 price" or "1/2 off." Fractions also are common in recipes. Once you get good at percentages, decimals, and fractions you'll be able to use them interchangeably. Here are the ones you'll see most often whether you're perusing the stock tables, clearance sales, or a recipe book.

Percentage	Decimal	Fraction
10%	.10	1/10
12.5%	.125	1/8
25%	.25	1/4
33%	.33	1/3
37.5%	.375	3/8
50%	.5	1/2
62.5%	.625	5/8
66%	.66	2/3
75%	.75	3/4
87.5%	.875	7/8
100%	1	1

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Percentage Changes
Percentage changes show you how much more or less something is worth this year than last year—how much money you've made in your 401(k), for example, or how much you've earned on your house. Often, when you deal with brokerage firms and read the stock pages, the percentage changes are computed for you. But knowing how to do it yourself can be helpful—and it's easy.

Figuring out a percentage change is a two-step process.

1. Take today's value and subtract the prior value from it.
2. Divide that answer by the prior value.

Suppose the following: Your house is worth $300,000 now, you bought it for $220,000, and you want to know how much money you made in percentage terms.

1. First, subtract the prior value from today's value:
   $300,000 – $220,000 = $80,000.
2. Then divide that answer by the prior value:
   $80,000 / $220,000 = .363636.
   You made slightly over 36 percent. In other words, you made a killing.

Map to a Million
Make a simple math move that's guaranteed to improve your financial situation.

Move $2,000 a year from a savings account earning 1.5 percent to a money market account earning 4 percent.

	1.5%	4%	EARNINGS DIFFERENCE
10 years	$23,738	$27,076	$3,338
20 years	$48,993	$64,461	$15,468
30 years	$78,332	$120,196	$41,864

Move $2,000 a year from a savings account earning 1.5 percent to an index fund earning 8 percent. 

	1.5%	4%	EARNINGS DIFFERENCE
10 years	$23,738	$33,828	$10,090
20 years	$48,993	$104,475	$55,482
30 years	$78,332	$261,288	$182,956

Math 101 continues...

Let's get one thing straight: When it comes to doing math in the adult world, there will not be any final exams. You don't need to have the answers precisely right. You don't need to use particular formulas. And you don't need to show your work. So by all means, use whatever shortcuts you find helpful.

Rounding
When you are rounding, you bump a number up, or you knock a number down, to the closest big (or round) number. If you think in terms of tens, then 77 becomes 80, and 72 becomes 70. If you think in terms of hundreds, then 267 becomes 300, and 234 becomes 200.

Real Life, Real Money Use
It is absolutely fine to round cents off to the nearest dollar when figuring tips or approximate costs. It's even fine to do this if you're trying to balance your checkbook. As long as you have enough money in your checking account to cover the checks you're writing, no financial police are going to rat you out.

Estimating
When you estimate, you do enough of a calculation to come up with a ballpark answer to a numerical or financial question.

Real Life, Real Money Use
Suppose you need to buy three pair of panty hose and they cost $8.50 a pair. You know you're looking at spending roughly $26. Estimating is a perfectly fine—in fact, time-saving—thing to do. Just be sure to estimate up, not down, to be sure you have enough of a cushion in your credit line or sufficient cash in your wallet to complete the transaction without penalty or embarrassment.