Practical Uses

Given that mathematics is used in every conceivable area of modern life, it almost seems silly to me that I should feel compelled to include a section on the "practical" uses of mathematics. However, as a teacher, I know that many students and much of the general public is unaware of the immense impact that mathematics has on their daily lives. I mostly blame the public schools for this, for their historically dismal record in mathematics education, but ultimately we have ourselves to blame. We created this mess. So here I will give a necessarily very sketchy sample of some of the practical uses of mathematics.

Much of the mathematics used in the modern world is used by specialists and takes place behind the scenes, hidden from view. The obvious ones are the scientists, engineers, and technicians of our technological age. But math is also used by doctors, architects, builders, realtors, insurers, banks, lawyers, merchants, contractors, and retailers. But the usefulness of math goes even farther than this. To be an educated citizen in a complicated modern world requires an understanding of basic mathematics and mathematical ideas. Mathematics is too powerful and dangerous a tool to leave only in the hands of specialists.

I'm going to start with some of the ways mathematics has helped me in my daily life. In general, math gives me the power to look at the world in a different way, a more precise way. I'm going to include some examples that might not seem too important in a “practical” sense, but I included them because they deepened my understanding of the world in some way. To me, understanding the world is the most useful thing of all.

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I recently bought a home and took out a 30 year mortgage but I wanted to pay off the house in 15 years instead of the original 30. I knew this would save me tens of thousands of dollars over the years. Using math and a spreadsheet program, I was able to make an “amortization schedule” of the mortgage on my house, set for fifteen years. This told me how much the monthly payment would have to be to pay it off in 15 years. So all I have to do now is pay the extra amount each month and I’ll own my house 15 years early and save a lot of money. By the way, it only cost me about a hundred dollars extra each month to do this. And the mortgage company wanted twenty five dollars to prepare the amortization table!

I use the concept of “unit price” to shop by comparison when I go to a supermarket. The unit price, rather than the price itself, tells you how much a standard quantity of goods will cost you and is therefore a much more useful number than price alone. This standard quantity depends on the type of goods. If you are buying liquids, it will usually be price per quart. Disposable shavers might be price per 100. It makes sense to compare similar products by the unit price if quality is not an issue. For example, paper plates get used once then tossed. Why not get the cheapest ones? Toothpaste might be another matter, but paper towels? If quality is an issue, such as with breakfast cereals, use the unit price to compare different sizes of the same product. Most people would assume that the larger sizes would be more economical, meaning that the unit price would be lower, but this is not always true. Sometimes the larger box of Corn Flakes costs more per pound than the smaller box. You have to check.

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The force of a car crash depends on it’s speed, so you might think that the force at 60 mph is double the force at 30 mph. However, it’s much more. The force would be four times as great! This is not a consequence of anything mathematical. Nature just works that way. The math in this case is a consequence of nature. It is a mathematical description of natural phenomena which can be written in words or more concisely, as a formula.

Here’s an often overlooked use for math: Doing math “puzzles”. This keeps your brain sharp. Try this “simple” one. If it takes 15 minutes to cut a log into two pieces, how long will it take to cut it into four pieces? Many people will say 30 minutes because there are twice as many pieces, but if you think about it, you’ll see that it’s wrong.

Sometimes people have difficulty figuring the tip at a restaurant. Assuming a tip of 20%, here’s a simple way to do it. Take the check amount and move the decimal point one place to the left. Double this amount. For example, say the check is $26.58. Move the decimal one place to the left to get $2.658. If you double this you get approximately $5.30 which is 20% of the check. I would add this to the check and round off to the nearest dollar $26.58 + $5.30 = $32.00 total.

Here's a simple and fairly accurate way to measure your gas mileage. Fill up your tank without "topping off". Just fill it until the pump stops automatically. Remember which pump you used because you'll have to use it one more time. Write down the odometer reading. Drive around normally until the tank is almost empty and then fill it up again at the same pump, again without topping off. Note the number of gallons used to fill the tank. Record the odometer reading a second time. The difference (subtract) between the two odometer readings is the number of miles. Divide the number of miles by the number of gallons. For example, say the two odometer readings were 97668.4 and 97993.2 and the number of gallons was 14.375. Subtract 97668.4 from 97993.2 to get 324.8 miles. Now divide 324.8 miles by 14.375 gallons to get 22 miles per gallon.

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