Math for Grownups (2 page)

A few percents are really easy to calculate in your head, once you know some shortcuts. (If you don’t believe these, check them with a calculator.)

1. To take 10% of a number, just move the decimal point one place to the left.

10% of 57.25

5.725

2. To take 5% of a number, find 10% and then take half.

5% of 38

Note that if the decimal point isn’t shown, you can just add it to the far right of the number: 38.0 (This zero doesn’t change the value of the number at all.)

10% of 38 is 3.8

5% of 38 is 1.9

3. To find 15% of a number—a really handy trick when you’re out to dinner and need to calculate a tip—add 10% and 5% of that number. (To make it über-easy, find 10% first.)

15% of 70

10% of 70 is 7

5% of 7 is 3.5

7
+
3.5
=
10.5

4. To find 20% of a number—for when the service is
really
good—just double 10% (that is, multiply it by 2).

20% of 55

10% of 55 is 5.5

5.5 • 2 = 11

(A quick note about that dot between the 5.5 and 2. You probably learned that multiplication is shown with a symbol that resembles a little x, right? So why aren’t we showing 5.5 × 2? That works in elementary school, because you haven’t done algebra yet. But when you get to middle school and high school, you start using variables—most famously
x
—to stand for unknown quantities
.
To avoid confusion between the × that indicates multiplication and the
x
that represents an unknown quantity, your textbooks probably used a dot, like •, instead of ×. And that’s exactly what you’ll see in this book, too.)

5. To estimate 25% of a number, round the number to one that is easily divisible by 4 and then divide by 4.

25% of 37

25% of 36

36 / 4
=
9

6. To estimate 50% of a number, round the number to an even number and divide in half (that is, divide by 2).

50% of 69.99

50% of 70

70 / 2
=
35

Division can be one of the most challenging operations to do in your head. But if you know the multiplication tables, simple problems like 25 / 2 shouldn’t be too much of a challenge.

A decimal point can throw a wrench in the works, however.

Never fear! Remembering one little rule makes some of these problems child’s play.

When you divide a decimal by a whole number (such as 4, 17, or 352), ignore the decimal point—at first. Divide as you would normally do. When you get your answer, look at the number you divided into. Where is the decimal point? In your answer, you want it to be in the same place.

Confused? Here’s an example:

You and your colleagues are splitting a box of donuts. The donuts are $3.20, and there are 4 of you. How much does each person owe?

$3.20 / 4

320 / 4
=
80 (ignore the decimal point at first)

so $3.20 / 4
=
$0.80 (put the decimal point
back in where it originally was)

Or how about this one? The grocery store has oranges at 5 for $1.25. You only want one. How much is it going to cost?

$1.25 / 5

125 / 5
=
25

so $1.25 / 5
=
$0.25

It may take a little practice before this process comes easily. But give your gray matter a chance: Next time you’re faced with a simple division problem like these, think a moment before you reach for the calculator.

Quick! What’s 20% of $50? If this question sounds like someone shouting at you in a foreign language, don’t panic! You can learn some easy ways to find percents, even if you’ve already lost the tip chart that came with your new wallet.

But why should you? Well, quickly tabulating percents can help you safely navigate the sales rack at your local department store. Or figure state sales tax while you’re on vacation. Or even give your server a decent tip. (Not to mention the warm sensation you have when you know you’re being clever.)

In other words, finding percents can help you make smart (and quick) spending decisions—and keep you in the good graces of the barista who knows you prefer decaf instead of high-test coffee every morning.

Let’s say you’ve been dying to get your hands on the newest gourmet ice cream machine. It’s listed at $499.99, but you’ve only saved up $215. Your sister just texted you with great news—in today’s paper, she saw an ad announcing a 40% off sale at Chilly Charlie’s, your local gourmet ice cream machine store.

Sweet!

You’re in your car, just around the corner from Chilly Charlie’s, and it would take only a minute to stop in. But is it worth it? Can you afford the purchase?

There are a couple of ways to find out—and you won’t need paper and pencil, let alone a calculator. (Keep both hands on the wheel!)

First, let’s look at what you know:

The original price tag on the ice cream maker is $499.99.

It’s on sale for 40% off.

You can spend $215.

The price of the ice cream machine is pretty darned close to $500, so to make things easier, why not do the calculations on $500, instead of $499.99?

Now you have some choices. Try thinking of 40% in a variety of different ways.

• 40% is close to 50%

It’s pretty easy to find 50% of $500. Because 50% is the same as half, all you need to do is divide 500 by 2. So 50% of $500 is $250.

That’s more than $215—the amount you socked away for that ice cream maker. Will 40% off also be more than you’ve saved?

Unfortunately, yes.

50% of the original price is $250

and

40% off the original price is
less than
50% off.

Therefore,

40% off
the original price is
more than
$250.

You still don’t have enough money.

Did you see what happened here? You don’t necessarily need to find the
exact
sale price. You only need to know whether you can afford to buy the ice cream maker.

• 40% is a multiple of 10%

When you’re estimating, zeros are a big, big deal. Remembering how to manipulate numbers with zeros is really helpful—and (thankfully) really simple.

Rule: Thou shalt add zeros when multiplying by multiples of 10, 100, 1,000, and so on.

Suppose you have this problem:

4,000•80,000

To get the answer, find 4 • 8, and then add the zeros on the end. How many zeros, you ask? Why, as many as there are in the original problem!

4,000•80,000

320,000,000 (there are 7 zeros in all)

Rule: Thou shalt drop zeros when dividing by multiples of 10, 100, 1,000, etc.

When you divide with huge numbers that have lots of zeros, just do the opposite of when you multiply—that is, subtract zeros instead of adding them.

120,000 / 6,000

Find 12 / 6, and then add zeros on the end. How many? Subtract the number of zeros in the second number (the number you’re dividing by) from the number of zeros in the first number (the number you’re dividing into). That’s how many zeros will be in your answer.

12 / 6
=
2

120,000 / 6,000 (subtract 3 from 4 to get 1 zero)

20

You probably can find 10% of $500 easily, too. In fact, all you need to do is drop the second zero:

10% of $500
=
$50

What is 40% of $500?

There are 4 tens in 40 (4•10 = 40)

and

10% of $500 is $50

so

4 •
$50 = $200

It’s tempting to think that the sale price of the ice cream maker is $200, but that mistake could be a costly one. Instead, $200 is the amount you’d
save
if you bought the machine. To find the sale price, you need to do one more step:

$500
-
$200
=
$300

Just as we found from the first estimation, the sale price is more than you’ve saved.

• 40%
off
is 60%
of
the original price

When you take 40% off, you’re left with 60% of the original price. That’s because

40%
+
60%
=
100%

Or, if you prefer subtraction,

100%
-
40%
=
60%

Thus, to estimate the sale price of the ice cream maker in one fell swoop, you can use 60% instead of 40%.

Like 40%, 60% is a multiple of 10%.

There are 6 tens in 60 (6•10 = 60)

and

10% of $500 is $50

so

6 •
$50 = $300

The sale price is still $300. And sadly, you still don’t have enough saved up.

You may have thought of other ways to look at 40%. Any of these may help you estimate 40% of $500 without a whole lot of effort. You just need to pick the option that makes most sense to you.

(Go ease your disappointment with a giant banana split.)

Estimation is one of those nifty skills that can help free up your brain for the important stuff—like remembering your debit card PIN or where you parked your car. When you estimate, you don’t get bogged down in unnecessary details.

Try these estimation tips:

1. Remember, “good enough” is good enough. You’re not trying to get the exact answer, so tell your sense of perfectionism to take five.

2. There is no one right way to estimate.

3. Take the path of least resistance—look for patterns in numbers and operations that make sense to you.

4. Concentrate on the first digits of each number. Rounding to those digits will have the most impact.

5. Look for uncomplicated multiplication and division. Consider rounding to numbers that are easily divisible by 2, 5, or 10.

6. Go for as many zeros as you can. It’s easier to multiply 800 by 100 than to multiply 750 by 125.

From the time you get up in the morning until your head hits the pillow at night, you run into percents dozens of times. The too-cheerful weather guy says there’s a 60% chance of rain. (There goes your golf game.) Your cereal has 80% of the recommended daily allowance of fiber. (Yum!) You take home 70% of your gross income. (Thanks, Uncle Sam.) Your boyfriend’s cat shredded your new 100% silk pajamas, which you got at a 70% off sale. (He is so out of here!)

But did you remember that percents can be written as fractions or decimals?

If you think about the word
percent
, that makes perfect sense. (Unless you’re still preoccupied with your newly destroyed silk PJs.)
Per
means “each.”
Cent
means “hundred.” So
percent
means “each hundred” or “out of 100.” An example will probably help jog your memory.

37% is the same thing as 37 out of 100, which can be shown as

37 out of 100, or
, is the same thing as 0.37.