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:
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.
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.