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5 Easy to Remember Mathematical Tricks You Can’t Live Without

Math Feature

As grade schoolers we all dreamed of the day when math would no longer be apart of our lives.  More than twenty years later, we’re haunted by practical situations with no use for the quadratic equation.  Thankfully there are a few tricks to mastering every day math that you’ll have down in no time.

By Jeff Barnett

Perfect information is great, but usually takes too much time and effort to calculate. Reasonably good information that you can calculate very quickly is often priceless. In this article I will skim the top of numerous areas of life to show you tricks I’ve learned to make many common mathematical tasks quicker and easier.

1. Use the Distributive Property to Multiply Awkward Numbers

This is simply a review of a mathematical property we all learned in grade school. What’s 24 * 10? Easy, right: 240. What’s 24 * 2? Also easy: 48. What’s 24 * 12? Whoa! Not so easy, huh? Actually, yes it is. Break the 12 into (10 + 2).

24 * 12 = (24 * 10) + (24 * 2) = 240 + 48 = 288

Whenever you’re presented with two awkward numbers to multiply, try to simplify one of them into 10 plus something. 27 * 14 becomes (27 * 10) + (27 * 4). The number multiplied by 10 is almost trivial, so spend a few seconds on the latter portion and then add it to 270. You can even take this further. For instance, I would actually further reduce 27 * 4 into (25 * 4) + (2 * 4) because 25 * 4 = 100. Now I’ve got three things to add, but they’re all very comfortable numbers: 270 + 100 + 8 = 378.

This may sound like more trouble than digging out a calculator, but you can become quite fast with it. While it may take several minutes to type this or to read it, you can think it in mere seconds. You can also use subtraction instead of addition.

2. Tire Size

The numbering on your tires’ sidewalls may be the most commonly misunderstood characters this side of the Rosetta Stone.

The numbering will read something like this:

P205/55/R16

I’ve met way too many shade tree mechanics that think the tire width is a function of the second number (55). They think that “50s are wider than 55s.” That is often true, but not always true, and that number really has nothing to do with tire width.

Here’s what each section means:

P: passenger vehicle

205: width of the tire in millimeters

55: aspect ratio

R: radial construction

16: diameter of wheel in inches

Aspect ratio is a percentage that allows you to calculate sidewall height. To get sidewall height multiple the width by the aspect ratio (205 * 55% = ~113mm). Then total tire diameter is (wheel diameter + [2 * sidewall height]). To get the final tire height in a single set of units we’ll need the next section.

3. Common English to Metric Conversions

1 inch = 2.54 centimeters

1 kilogram = 2.2 pounds

1 meter = 3.3 feet

This may seem pretty basic, but you really need to know some of the most common metric conversion factors to function in our crazy mixed-unit world.

To complete our tire diameter example we have [ (16 in * 2.54 cm/in * 10 mm/cm) + (2 * 113 mm)] = ~632 mm = ~24.9 in. No, I wasn’t able to use the mental distributive property on that one.

As a practical example, yesterday I had to deal with two 25 kilogram weights at the gym mixed with other weights denominated in pounds. I knew that for each kilogram I was adding 2.2 pounds, so I used the distributive property to find that (50 * 2) + (50 * 0.2) = 110 lb.

4. Salary

You can easily estimate annual salary from hourly rate.

$20/hour * 2000 hours/year = $40,000 / year

Practically, just double hourly rate, add three zeros, and you’re done. This stems from the fact that there are 2080 work hours in a calendar year, assuming a 40-hour work week. The estimate is actually a little low, but it’s good enough for estimation. If you’re anal retentive you can add a little to the annual salary figure after calculating it, or use the distributive property with the correct number of 2080 hours.

5. Used Car Depreciation

You can roughly project your used car’s future value by estimating that it depreciates 2% per month. This is obviously a very rough estimate, and is only valid for vehicles that have already absorbed the first year of depreciation, which can be much higher. It also may be too aggressive in some cases, but it’s a conservative estimate.

Example depreciation schedule for a used car worth $4000 at the beginning of January:

Feb: $4000 * 0.98 = $3920

Mar: $3920 * 0.98 = $3842

Apr: $3842 * 0.98 = $3765

Obviously, this isn’t useful for finding your used car’s current value because websites like Kelly Blue Book can give you the most accurate value in seconds. However, it’s a handy equation for using a spreadsheet to estimate future value.

Read more at Jeff’s blog, The Midnight Hour.

 
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  • http://mintz.hushedcasket.com Matt S.

    Hey Jeff, good article. I just wanted to say that in Tip #1, you break down the distributive property like so:

    24 * 12 = (24 * 10) + (24 * 2) = 240 + 48 = 288

    While that’s easy to understand for those of us who are mathematically inclined, you might miss your target audience with that explanation. It might be easier to explain it with:

    24 x 12 = 288
    24 x 10 = 240
    24 x 2 = 48
    240 + 48 = 288

  • http://midnight.hushedcasket.com Jeff Barnett

    Thanks, Matt. I’m always up for different presentations for different learners.

  • http://jdlong.blogspot.com JD Long

    More handy shortcuts I learned living in Belgium 4 years:

    1.) 5 miles is almost exactly equal to 8 kilometers. So 55mph is 88 kph. Going 50 miles is 80 klicks.

    2.) To approximate temperature conversions, take your celcius temperature, double it, and add 32. If the temperature is 20 C, double it (40) and add 32, which makes it 72 degrees F. However, this does NOT work if the temperature is below freezing.

    ~~JD~~

  • Reg

    Rounding and metric advantages. The guy at the register was away at the phone when I plonked the bananas on his scales and found they weighed 700 grams. I glanced over at the price on the rack and they were $2.99 @ kg. That’s a 1000 grams if you’re not sure. Round up to $3.00 a thousand and 3 x 7 = 21 so they cost $2.21. Even the Chinese guy was amazed.

  • http://www.appliedcolors.com Applied Colors

    Yes! Practical math. I have bookmarked and social bookmarked this page.

  • Doug

    One thing I found amazing a few years ago was my ex gf and her mom didn’t know the short hand way of figuring out discounts in your head. For example: 30% off of something that is listed as $37, round to $40, move the decimal place over ($4.00) and the multiplying by 3. Otherwise meaning 40*.1*3 = roughly $12 off.

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