数学英语 13 How to Use Percentages to Calculate Tips（在线收听）

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by Jason Marshall

A few articles ago, I asked if you ever found yourself at restaurants fumbling to figure out how much to tip; I guessed that you might occasionally resort to seeking advice from your “smart” phone; and I told you that you really didn’t need to. But I didn’t tell you why you didn’t need to because we first needed to cover some basics about fractions. And now that we’ve done that, it’s time to go back and talk about the power of ten percent—soon to be known as: the reason you’ll abandon your favorite tip-calculating iPhone app forever.
What Are Percentages?
Let’s start by figuring out what percentages actually are and where they come from. It might not be obvious, but fractions and percentages are inextricably linked. In fact, percentages are fractions! But they’re not just any old type of fraction—percentages are special: they’re fractions where the denominator (the bottom part) always has a value of 100. And since this denominator is always the same, it doesn’t need to be written down. That’s why percentages only have one number instead of two like normal fractions.
What Does “Percent” Mean?
Now, let’s take a closer look to see where this all comes from. What does “percent” actually mean? Well, let’s split it into two words and see if the meaning becomes clearer: percent = “per cent.” That is the same “cent” as in the word “century,” which means 100 years. So “per cent” means “per 100,” or “for each 100.” What does something like 1 percent—or 1%—actually mean then? Well, 1% literally means 1 per 100. Or, in fractional lingo: one one-hundredth—1/100.（见图一）

How to Use Money to Understand Percentages
Here’s an easy way to think about percentages: The US dollar (and many other currencies around the world) is broken up into 100 parts—called cents! (The use of the word “cent” here is no coincidence.) So, you can think of percentages as portions of $1. For example: What’s 1% of $1? Well, since 1% means 1/100 of something, and 1 cent is 1/100 of $1, 1% of $1 must be 1 cent. Okay, how about 10% of $1. Well, if 1% of $1 is 1 cent, then 10% of $1 must be 10 times that. Which, of course, is 10 cents—also known as a dime.
Okay, so 10% means 10/100 in fractional terms, but we also just said that 10% of $1 is a dime. But a dime, being worth 10 cents, is 1/10 of a dollar. So, the fraction 10/100 must be equivalent to 1/10! This isn’t surprising if you’re familiar with “reducing fractions to lowest terms”—a topic which we’ll talk about in the future. But, for now, the important thing to remember is that 10% and 1/10 are the same fraction. Why is that important?
How to Easily Calculate Ten Percent
Because it leads us to the following quick and dirty tip: To find 10% of any number, all you have to do is divide that number by 10. Here’s what I mean. What’s 10% of $10? Well, $10 divided by 10 is $1. So 10% of $10 is $1. How about 10% of $20? Again, $20 divided by 10 is $2. So 10% of $20 is $2.
Here’s another quick and dirty tip to help you easily calculate 10% of any amount of money. First, write the amount out with the decimal point and the digits representing the number of cents—like you’d see on a cash register. For example: $2.50 or $85.00. Now, to find 10% of that amount, just move the decimal point one position to the left. (We’ll talk a lot more about decimal numbers in the future, so don’t worry if you’re not sure what the decimal point really means yet.) So, what’s 10% of $2.50? Just move the decimal place one position to the left. The result is $0.25, which is the same as 25 cents—or one quarter. What’s 10% of $85.00? Again, move the decimal point one position to the left—the result is $8.50.（见图二）
How to Quickly and Easily Calculate Tips
But why would any of this make you forget your tip-calculating app? Here’s the answer. At restaurants in the US, it’s generally accepted that good service warrants a tip between 15% and 20% of the bill. Let’s say your bill is $34.00. How can you use the power of 10% to calculate the tip? First, calculate 10% of the bill: moving the decimal point one position to the left, 10% of $34.00 is $3.40. Now, if you want to tip 20%, just double this amount since 20% = 10% + 10% (or twice that of 10%). So the total tip would be 2 x $3.40 = $6.80.
If you wanted to leave 15% instead, you could use the fact that 15% = 10% + 5%. So since you already know that 10% of $34.00 is $3.40, you can just take half of that to figure out what 5% of $34.00 is—$3.40 / 2 = $1.70. So a 15% tip would therefore be $3.40 + $1.70 = $5.10. It might take a little practice at first, but soon you’ll find that the power of 10% allows you to quickly and easily calculate tips entirely in your head.
Wrap Up
And on that note, you’ll find several practice problems below to help you sharpen your tip-calculating skills. Look for the answers in this week’s Math Dude Video Extra! episode on Facebook and YouTube.
That’s all the math we have time for today. Please email your math questions and comments to。。。。。。follow the Math Dude on Twitter, and become a fan on Facebook. If you like what you’ve read and have a few minutes to spare, I’d greatly appreciate your review on the iTunes podcast store. And while you’re there, please subscribe to the podcast to ensure you’ll never miss a new Math Dude episode.
Until next time, this is Jason Marshall with The Math Dude’s Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!