TL;DR It is very useful in many financial and construction situations, saves heaps of time and you don't even have to actually memorize all twelve numbers. Also, just random day to day arithmetic problems.
First off, I should let you know exactly why. After memorizing less than 12 simple numbers you will instantly be able to calculate, to as many decimal places problems you wish, things like:
How much per month is $500/year? Or $70. Or $8,000 or any other similar amount. Down to the penny. In your head.
The inverse is true too: you'll recognize decimal twelfths when you hear them and immediately know just how much a year that would mean to your budget.
What is the accurate number of square feet given something like 5'-3" X 17'-5" and a calculator (hint: it's how to enter 5 inches and 3 inches properly).
It's just that twelfths happen so often in Western culture that they are worth bothering about. Twelfths pop up here and there randomly too.
Is $8 for a package containing three X 400 gram chubs of hamburger a good deal? This is actually the real-world reason from the other day that made me bother to write this post. 3 X 400 grams = 1200 grams. Twelve Hundred. Twelve. Now it's a question of $8/12 or 67 cents per 100 grams. Simple and instant. Just slop the decimal point around until it makes sense.
Next, let's be clear about what we're talking about. This is the decimal version of 1/12, 2/12, 3/12 and so on up to 12/12:
|1/12||=||0.083333 *||2/12||=||0.166667 *|
|7/12||=||0.583333 *||8/12||=||0.666667 *|
The above table was conveniently copy/pasted just for this post. Thanks very much http://www.sciencemadesimple.com/fractions-decimals.html! I just knew someone had already done it and found them! :-)
O.K., let's get rid of the obvious first. The ones you DON'T need to memorize. You already have them.
12/12 =1 You knew that already. That one's gone. Now we're down to memorizing only 11 numbers.
Now, we can think of just regular North American money. 25 cents is 1/4 of a dollar or $0.25. Three inches is 1/4 of a foot, because 4 X 3 is 12.
What is a 'quarter' a 'half' or 'three quarters'? .25 .50 and .75 -- you already knew that. So, for example 3 mos goes into 12 four times and a quarter of twelve (3/12) is 0.25
So that covers off 3,6,9 and 12 that you don't need to learn, because you've already memorized them (0.25, 0.50, 0.75, 1.00). That leaves 1, 2, 4, 5, 7, 8, 10 and 11 -- which seems like a lot. Nope.
1/12 and 10/12 are just the same except for the decimal, so just memorize .083333333..... (the repeating decimals and subsequent rounding is why you can be so accurate)
4/12 is 0.3333333333 (because 3X4=12) so
8/12 must be 0.66666666
So really, the only "work" for memorizing anything is in 5, 7 and 11.
5/12 = .416666...
7/12 = .583333...
11/12 = .916666...
I've found this slight bit of memory work to be a huge time-saver over the years. It comes in very handy when shopping in grocery stores, negotiating a loan or payment plan of some kind -- all kinds of things. However, I don't think I've made the case very well. I'm going to ask Kalid at Better Explained about it. Perhaps it's only me who finds it useful or (more likely) it's simply NOT better explained by me... :-(