Today, the addendum is a departure from standard blog fare. It has come to my attention (once again) that many adults still have trouble with fractions. I’m going to choose the two [fractions] that I find give the most difficulty and show you the tactics I’ve invented to solve them. Wish somebody had helped me with this back when.
This is the town hall from PHC. Prairie Home Companion is the radio link I listen to most often and I think you should too. Toast or tea tastes better when somebody else makes it, and thus with radio stations, I'll set the dial for you. I prefer PHC to some ho-hum oldie station in the background. Give it a whirl, they have great musical guests. (I advise listening to several full shows to get into it.)
I took time off (an hour) to study electronic switches. That’s a small science in itself. The mechanical switch types don’t interest me because they are, well, mechanical—and damn expensive. But the duplication of this behavior electronically really has my attention. Most interesting are the latching switches. You turn it on, the switch springs back, but the current keeps on flowing. This is not at all as straightforward as most of us assume. Every aspect has to be taken account of in the electronic version, even the amount of time before and speed at which the switch returns to position. Fascinating to me.
Here’s more trivia, the kind that we don’t have time to look up for ourselves. Now that eBay has trampled all competition, they are about to hike their commissions. A lot of the anti-trust laws are difficult to apply to cyber-business, so eBay can get away with price fixing that would doom a competitive operation. On the same day, NATO announced it will condone drone strikes against hackers (there are two types of hackers, we assume NATO means the bad ones). While these two stories are unrelated, it might serve as a warning to eBay.
What do I have against eBay? Paypal, that’s what. I won’t go into a lot of detail, but one of the greatest promises of Internet shopping was originally that it would be anonymous. There were plenty of proto-companies that would allow you to charge up an account under a code name. Only a party to whom you sent an encrypted key could withdraw payment. This is the ideal “cash” transaction. This meant the cashier holding the money never knew the identity of either party. They didn’t need to be sticking their noses in there.
Along comes eBay, which buys Paypal, and now uses it to monitor and record identities. Is this wrong? Yes, in the sense that it crowded out the cash companies. There is now no real choice, it is Paypal or nothing. I still believe there are billions to be made by anybody who can devise a way to spend cash on-line. I believe people willingly obey good laws and break bad ones. Think of Prohibition. Right now you cannot spend cash on the Internet even if you want to. Thanks to eBay.
I had two outings today. Coffee this morning with DeeDee and a mini-date this afternoon. The latter will not be repeated. Have you ever dated someone who is a total follower? They form clinging dependencies if you don’t apply a constant back-pressure of prevention. (Ma’am, you are going to have to do that kind of thing the same way you did before we met.) They resent that you are not “nice” enough to be their next mark. Is there a name for the type who are constantly thinking about how you could help them out instead of helping themselves? What? Very funny, I didn’t mean that name. Besides, the guy still owes me $1,600.
One has to notice the new media take on white supremacists, this time in Texas. Without any changes in the law, supremacists have gone from political organizations to “gangs”. This came about after a prison official was killed, the 35th such attack on criminal justice bureaucrats in about two years. If I didn’t know better, I’d say that represents a highly organized and sustained assault (some say revolt) by American citizens who have a different view on “justice” than the one they were handed. The supremacists are shooting back, which is nowadays the same as fighting to the death. That’s something we haven’t seen in a while.
ADDENDUM
Fractions. There’s your classic love-hate relationship. Solving fractions doesn’t require any advanced math. Yet it seems very few of us were ever taught any methods to help figure out where the numbers go, at least I know that I never got a lick of help. I’m only going to cover simple fractions here, that is only fractions with the small number over the big number, as in 5/9 or 11/16.
This may help only one reader in a hundred, but learning electronics reminds me of how difficult it was to find a teacher who made sense. So my approach is to show a method that works for me because it is the easiest to understand without getting into theory. Read my lips—THE IMPORTANT NUMBER IS THE BIGGER NUMBER ON THE BOTTOM OF THE FRACTION. I often scribble this number, called the denominator, in the page margin before I start.
Here are two rules I developed when I run into a difficult fraction.
Rule #1: when you see the word “of”, it means to solve this problem, realize you are going to have to divide by the big number on the bottom. Avoid the temptation to always leave division to the last. It may not be obvious where you have to divide just yet, but make a mental note of that bigger number. You will need it sooner or later.
Examples: 1/6 of a dozen. 1/3 of the population. 4/5 of a ton. In each case, you see the word “of” and that means you will have to divide by the bigger number on the bottom of the fraction. You still have to figure out where to divide, but you’ve just won half the battle. (If this seems too simple an example, wait a moment, we'll go places with it.)
Rule #2: ratios are NOT the same as fractions, you have to calculate the bigger number. If you have the ratio 3:5, this is not the same as the fraction 3/5. When I see the colon, I right away add the two numbers. 3+5=8. Thus, a ratio of 3:5 means TWO fractions, namely 3/8 and 5/8. I always pick the "least" fraction, in this case, 3/8 because small numbers are easier to work with. From this point on, just use Rule #1 again.
Example: the ratio of trucks to cars is 4:11. If there are 77 vehicles on the lot, how many are cars? First add 4+11=15. Okay, it means 4 out of every 15 of the vehicles are trucks, and the other 11/15 are cars. (Aha, there’s that word “of”.) And, if I calculate 4/15 of 77 I get 28. Now I don’t need to figure out 11/15 because I just subtract 28 from 77. There are 28 trucks and 49 cars, and I only had to calculate one fraction.
Now, about that raise . . .
I’m not going to cover multiplying or dividing fractions because in real life, that happens so rarely I’ll look it up if I ever need it. But, we are having so much fun, here’s one more trick of the trade I’ve developed. Here's Rule #1 in a different disguise.
Say you need to know 17/63 of 15,309. The fraction from hell! Well, not really. Rule #1 says I have to divide by 63 anyway, so let’s do that first. 15,309 / 63 = 243. Ah-ha, if I know that 1/63rd equals 243, then 17/63rds must be 17 times as much as 243. As long as you get the right answer, demand full marks.
For the record, math has always been my worst subject.