数学英语 12 How to Use Percentages
by Jason Marshall
In the last article, we applied our knowledge of fractions to begin making sense of percentages, and we used this new tool to quickly and easily calculate how much to tip at restaurants…all in our heads! Today, we’re continuing our exploration of percentages by using the power of 10% to quickly calculate how much money you’ll save the next time you go shopping for sales.
But first, the podcast edition of this tip was sponsored by Go To Meeting. Save time and money by hosting your meetings online. Visit GoToMeeting.com/podcast and sign up for a free 45 day trial of their web conferencing solution.
Review of How to Calculate Ten Percent
Before we get into calculating how much you can save at a sale, let’s briefly review how to easily calculate 10% of any amount of money. For example, what’s 10% of $144? 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: $144.00. Then, to find 10% of that amount, just move the decimal point one position to the left. So, $144.00 becomes $14.40 and, therefore, 10% of $144 is $14.40.
If that makes sense, then you’re ready to move on. If you want a little more practice first, check out the practice problems from the end of the last article. And then be sure to catch the Math Dude Video Extra! episode on YouTube or Facebook to watch me solve the problems.
How to Use Percentages to Figure Out How Much You’ll Save at a Sale
Once you can calculate 10%, figuring out how much you’ll save when things are on sale is easy. For example, say you’re looking at a sweatshirt that has an original price of $40, but is advertised at 30% off. What’s the new price? Well, just as with calculating tips in the last article, start by finding 10% of $40. Moving the decimal point one place to the left in $40.00, we find that 10% of $40.00 is $4.00. So, 30% of $40 must be three times as large since 30% = 3 x 10%. In other words, 30% of $40 is 3 x $4, which is $12.
So, what’s the final price? What do we do with this $12? Well, since we’re talking about a $12 discount here, the final price had better be less than the initial price. So, to get the final price, just subtract the savings, $12, from the original price: $40 - $12 = $28.
How to Round Numbers to Make Estimating Savings Easier
Okay, that’s easy enough. But before we get too excited and run off on a celebratory shopping spree, let’s think about one more problem. This time you’re interested in a shirt on sale for 40% off its normal price of $28. What’s the final price after applying the 40% discount? You could start, as usual, by finding 10% of the initial price—which would be $2.80—and then proceed to calculating the full 40% discount by multiplying this 10% discount by 4. And, if you need a precise answer, that’s a great thing to do. In this case, 4 x $2.80 = $11.20, so the precise final price is $28.00 - $11.20 = $16.80.
But, to be honest, that’s a bit more work than I prefer since I’m usually perfectly content to know only approximately how much the shirt is going to cost me. So, let’s instead choose to work smarter and save ourselves some of the unnecessary effort. After all, unlike many areas of life, doing less work in math isn’t a sign of laziness, but is instead a sign of clever thinking! So, here’s the quick and dirty tip: Let’s pretend the shirt in question isn’t really selling for $28, but is instead selling for $30. In other words, let’s round the price up to the nearest ten dollars.
How does that help? Well, it helps because calculating 40% of $30 (10% of $30 is $3, so 40% of $30 is 4 x $3 = $12) is much faster to do in your head than calculating 40% of $28 (which we did earlier). So back to the initial question: What’s the final discounted price? Well, it’s the initial price minus the discount: $30 - $12 = $18, right? No, not exactly since this was just an estimate. Remember, the actual final price we calculated before was $16.80. But our quick and dirty estimate of $18 isn’t off by much—and it’s a lot faster too. Just remember to keep in mind whether you’re dealing with precise or estimated values to make sure you’re not surprised at the register!
Brain-Teaser Problem
Next time, we’re going to briefly depart from the world of fractions and percentages to take a peak at the surprisingly beautiful world of mathematical sequences. In particular, we’ll be talking about the famous and fascinating Fibonacci sequence.
Until then, here’s a problem dealing with a quirky aspect of percentages for you to ponder:
Your favorite clothing store starts offering a 20% discount on a shirt you’ve been eyeing. The next week, they announce they’ll be offering a second 20% discount off this discounted price. Upon hearing this, the main competitor of your favorite store announces they’ll be selling the same shirt at a discount of 40% off your favorite store’s original non-sale price. Is one store giving you a better deal than the other?
Think about it, and then look for the explanation in this week’s Math Dude Video Extra! episode on YouTube and Facebook.
Wrap Up
That’s all the math we have time for today. Thanks again to our sponsor this week, Go To Meeting. Visit GoToMeeting.com/podcast and sign up for a free 45 day trial of their online conferencing service.
Please email your math questions and comments to...............get updates about the show and my day-to-day musings about math, science, and life in general by following me on Twitter, and join our growing community of social networking math fans by becoming a fan of the Math Dude on Facebook—it’s a great place to ask questions and chat with other math enthusiasts.
If you like what you’ve read and have a few minutes to spare, I’d greatly appreciate your review on iTunes. 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!
In the last article, we applied our knowledge of fractions to begin making sense of percentages, and we used this new tool to quickly and easily calculate how much to tip at restaurants…all in our heads! Today, we’re continuing our exploration of percentages by using the power of 10% to quickly calculate how much money you’ll save the next time you go shopping for sales.
But first, the podcast edition of this tip was sponsored by Go To Meeting. Save time and money by hosting your meetings online. Visit GoToMeeting.com/podcast and sign up for a free 45 day trial of their web conferencing solution.
Review of How to Calculate Ten Percent
Before we get into calculating how much you can save at a sale, let’s briefly review how to easily calculate 10% of any amount of money. For example, what’s 10% of $144? 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: $144.00. Then, to find 10% of that amount, just move the decimal point one position to the left. So, $144.00 becomes $14.40 and, therefore, 10% of $144 is $14.40.
If that makes sense, then you’re ready to move on. If you want a little more practice first, check out the practice problems from the end of the last article. And then be sure to catch the Math Dude Video Extra! episode on YouTube or Facebook to watch me solve the problems.
How to Use Percentages to Figure Out How Much You’ll Save at a Sale
Once you can calculate 10%, figuring out how much you’ll save when things are on sale is easy. For example, say you’re looking at a sweatshirt that has an original price of $40, but is advertised at 30% off. What’s the new price? Well, just as with calculating tips in the last article, start by finding 10% of $40. Moving the decimal point one place to the left in $40.00, we find that 10% of $40.00 is $4.00. So, 30% of $40 must be three times as large since 30% = 3 x 10%. In other words, 30% of $40 is 3 x $4, which is $12.
So, what’s the final price? What do we do with this $12? Well, since we’re talking about a $12 discount here, the final price had better be less than the initial price. So, to get the final price, just subtract the savings, $12, from the original price: $40 - $12 = $28.
How to Round Numbers to Make Estimating Savings Easier
Okay, that’s easy enough. But before we get too excited and run off on a celebratory shopping spree, let’s think about one more problem. This time you’re interested in a shirt on sale for 40% off its normal price of $28. What’s the final price after applying the 40% discount? You could start, as usual, by finding 10% of the initial price—which would be $2.80—and then proceed to calculating the full 40% discount by multiplying this 10% discount by 4. And, if you need a precise answer, that’s a great thing to do. In this case, 4 x $2.80 = $11.20, so the precise final price is $28.00 - $11.20 = $16.80.
But, to be honest, that’s a bit more work than I prefer since I’m usually perfectly content to know only approximately how much the shirt is going to cost me. So, let’s instead choose to work smarter and save ourselves some of the unnecessary effort. After all, unlike many areas of life, doing less work in math isn’t a sign of laziness, but is instead a sign of clever thinking! So, here’s the quick and dirty tip: Let’s pretend the shirt in question isn’t really selling for $28, but is instead selling for $30. In other words, let’s round the price up to the nearest ten dollars.
How does that help? Well, it helps because calculating 40% of $30 (10% of $30 is $3, so 40% of $30 is 4 x $3 = $12) is much faster to do in your head than calculating 40% of $28 (which we did earlier). So back to the initial question: What’s the final discounted price? Well, it’s the initial price minus the discount: $30 - $12 = $18, right? No, not exactly since this was just an estimate. Remember, the actual final price we calculated before was $16.80. But our quick and dirty estimate of $18 isn’t off by much—and it’s a lot faster too. Just remember to keep in mind whether you’re dealing with precise or estimated values to make sure you’re not surprised at the register!
Brain-Teaser Problem
Next time, we’re going to briefly depart from the world of fractions and percentages to take a peak at the surprisingly beautiful world of mathematical sequences. In particular, we’ll be talking about the famous and fascinating Fibonacci sequence.
Until then, here’s a problem dealing with a quirky aspect of percentages for you to ponder:
Your favorite clothing store starts offering a 20% discount on a shirt you’ve been eyeing. The next week, they announce they’ll be offering a second 20% discount off this discounted price. Upon hearing this, the main competitor of your favorite store announces they’ll be selling the same shirt at a discount of 40% off your favorite store’s original non-sale price. Is one store giving you a better deal than the other?
Think about it, and then look for the explanation in this week’s Math Dude Video Extra! episode on YouTube and Facebook.
Wrap Up
That’s all the math we have time for today. Thanks again to our sponsor this week, Go To Meeting. Visit GoToMeeting.com/podcast and sign up for a free 45 day trial of their online conferencing service.
Please email your math questions and comments to...............get updates about the show and my day-to-day musings about math, science, and life in general by following me on Twitter, and join our growing community of social networking math fans by becoming a fan of the Math Dude on Facebook—it’s a great place to ask questions and chat with other math enthusiasts.
If you like what you’ve read and have a few minutes to spare, I’d greatly appreciate your review on iTunes. 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!
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