Fun With Math

Here's a nice trick for helping you calculate your gas mileage. Since it's easier for most people to multiply rather than divide, this technique transforms the problem into one of remembering a simple table and performing one multiplication. It can therefore be performed quickly in your head, without pencil and paper.

The technique is to memorize a handful of numbers that divide 100, then mutliply the appropriate number by the "number of hundreds" of miles you drove since the last fill-up.

Steps:

1. When you fill up your gas tank, note the number of gallons of fuel. Let's call that 'f'.
2. Check your odometer to note the number of miles travelled since your last fill-up. Call that 'm'.
3. Look up the number of times f divides 100, or compute (100/f). Call this number N. This is the key step and I'll give more information about it later. Think of this value as "miles per gallon per hundred miles".
4. Now multiply 'N' by ('m'/100). That's your mileage in miles per gallon.


Wow, this looks hard. But it's actually easier than dividing m/f directly. Here are the techniques that make it easy:

1. Remember a few key divisions of 100, those that result in numbers that are typical of the number of gallons you normally purchase when you fill up your tank. For example, 100/8 = 12.5. I often put between 10 and 15 gallons of fuel into my tank. Here's the table I use:

15 divides 100 6 times (remember 15 gals -> 6)
14 divides 100 7.1 times (remember 14 gals -> 7+)
13 divides 100 7.7 times (remember 13 gals -> 8-)
12.5 divides 100 8 times (remember 12.5 gals -> 8)
11.1 divides 100 9 times (remember 11.1 gals -> 9)
10 divides 100 10 times (you better know this already!)

I've memorized these divisions of 100 and a few more that are convenient.

2. It's very simple to divide a large number by 100; just move the decimal two places to the left. For example, 345/100 = 3.45


Sample Problem
Today I filled up my tank with 12.5 gallons. The odometer read 269. You could divide 269 by 12.5 directly, or you can use this method:

Step by Step Answer
1. I know that 12.5 goes into 100 8 times. I note the number 8.
2. 269 is about 270, so I round up to 270 and move the decimal two places to the left to divide by 100 and get 2.7.
3. I multiply 8 x 2.7 to get 21.6 mpg.

Even the last multiplication can be made easier by breaking it into parts:

8 x 2.7 = (8 x 2) + (8 x .7)
= 16 + 5.6
= 21.6 mpg Hmmm, mileage not too good...