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Ratios & Percentages:

Play the Percentages


Today's Snack: Have a baked potato with some minced ham, sour cream, a sprinkle of shredded cheddar, and a little minced chives or green onion. With many foods, you can't eat 100% -- no apple seeds or stems, no carrot tops with the carrot, no orange rind - but with a potato, the skin is the healthiest part, so you can eat 100% of it and be happy. Add a glass of milk to be 1,000% happy!





Scratch paper and pencil


Here are some examples of ways that understanding percentages can help you in everyday life. Follow along with your scratch paper and pencil so that you understand these tricks of percentages and can avoid being on the losing end of them in the future:


Government statistics. It's important to know what is included in statistics so that you can understand their significance. One year, the federal government reported that a whole lot more people had jobs than the year before, and everybody was happy. That seemed to mean that the economy was doing better. But oops - what few people realized is that the government had decided that year to count members of the U.S. military among the employed people, which they hadn't done before. Similarly, one year the statistics about people with AIDS took a huge jump, and it looked like the epidemic was getting worse, but all that happened is that a whole new group of AIDS patients - people from Haiti - was included in the American statistics, making it look like there was a big increase in the disease, but there really wasn't.



Polls. It is very important that you know how many people were included in a particular poll. If you saw an ad that said "67% of those surveyed favored our brand of salsa over all others," that's impressive - but what if you found out that only THREE people were surveyed? That means only two people added up to 67% as claimed in the ad. That's a LOT less impressive than what you were thinking, right?



Utility price increases. If you receive a notice that your water bill is going up by 6%, you probably wouldn't squawk. But what if the notice pointed out that the water utility was increasing its spending by $91 million, and that's why they need the rate increase? Of course, you'd be mad. But percentages can be used to conceal the truth just as much as they can be used to reveal it.



Converting fractions to percentages. Let's say that you know that 1/4 of the world's population is Chinese, and 1/5 of the remainder is East Indian. So what percentage of the world's population is East Indian? Multiply .20 x .75 = .15, or 15%. You do this because .20 is the same as one-fifth, and .75 is the three-fourths of the world who are not Chinese.



Shopping. If you don't understand how percentages work, you can lose money, or cheat yourself when you think you're getting a good deal in a store. For example, a pair of jeans whose price has been increased by 50% and then reduced by 50% does not cost the same as it did before - it actually had a NET price reduction of only 25%. You have to re-figure the percentage after each change in the price in order to understand the deal.


Let's compute it: say the jeans cost the store $30. The store marks the price up to $45 to try to sell the jeans. They don't sell. The store reduces the price by 50% to put the jeans on sale. Multiply $45.00 x .50 and you get $22.50, so that's how much the jeans will cost. But $22.50 is nowhere near 50% of the original $30. See the trick? You have to know the actual cost to evaluate how much a sales price really saves you.


Next time you see a piece of clothing that has been "slashed" in price by 40%, and then another 40%, keep in mind that it hasn't really been cut in price by 80% -- it's been cut a lot less than that. Let's figure it: let's say the original price of the shirt was $20. If it went on sale at 40% off, it was marked down to $12.00 ($20.00 x .40 = $8, and $20 - $8 = $12). If they mark it down 40% again, though, it's not $8 that's being reduced, but 40% of the $12.00, which is just $3 ($12.00 x .40 = $3). So the sales price is now $9 ($12 - $3 = $9). Now, $9 compared to the original price of $20 is pretty good, but it's a 55% reduction, not the 80% reduction that two 40%-off stickers might have you believing.



By Susan Darst Williams Math 2010

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