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I am listening, for the second time today, to Jonathan Kozol’s absolutely brilliant speech on Alternative Radio on National Public Radio (NPR). If you care about education in America at all, you should know about the work of this exceptional man. The thrust of the speech is that apartheid is more alive and well than any time [...] A few posts ago, I offered some tips about how to check large division problems without having to multiply huge divisors and quotients to get even huger dividends. One of the drawbacks to using the “crunch” method, which I described, is that it is not 100% accurate. Often, people who need to defend the status [...] This has nothing to do with math, per se, but I think some readers will still find it useful. As a member of the Macintosh Users Group of Oneonta, NY (MUGONE.com), I notice that even some savvy computer users are a little shaky on some of the basics. So once in awhile I’d like to put [...] We’ve been talking about using factors to make long-division problems easier, sometimes being able to turn them into a manageable sequence of short-division problems, in which no paper and pencil (and certainly no calculators!) are needed. Want to try another one? How about 962/52 ? Well, they’re both even, so that’s going to [...] In the last post we looked at the problem of 926/18, and we simplified it to 463/9, so we could make it a short division problem. What if the problem had been 927/18? If you know how to factor (if you [...] (Is that title an oxymoron?) Imagine you have to do this division: 926/18 How would you do it? Would you rewrite it with that funny division symbol (“division bracket,” or “right parenthesis followed by a vinculum over the dividend”)? Would you use a calculator? (Please say “no” to that!) After you rewrote it, would you start by trying to figure out how many times 18 would go into 92? If you did, you would be doing it the way most people learned in school, and you would be wasting a lot of time and effort. They way we are usually taught to check division problems in school is unnecessarily complex. There is a better way. I always wondered why, after thousands of years of mathematics, schools generally haven’t figured that out. But I’d rather try solving the Riemann zeta-hypothesis than figure out why schools teach the way they do. [...] Someone wrote in to ask: 40 * 53 is 125. Why isn’t it 0? On the Math.Com website, problems such as 4 to the zero power times 5 to the third power have an answer of 125 as correct. Shouldn’t the answer be zero. If not, why? Thank you! Professor Homunculus’ response: The answer actually should not be zero, and here’s why: Because 4 to the 0 power is 1, not 0. So 40 * 53 would be 1 x 53 which is 125. Any integer raised to the zero power equals 1. That is hard for most people to believe, so I wrote a little piece to explain why it makes sense. Here it is: “Why do I need to know fractions? Square roots? Algebra or geometry? I mean, why do we ever even need them in real life? I am never going to be a mathematician, and I hate math. So why do I have to learn this?” I was just fooling around with some numbers, and realized that 13^2 (which gives you 169) is the reverse of 31^2 (which gives you 961 – which is the reverse of 169). Is there any name for a number, the reverse of which, when squared, will also yield the reverse of the original number’s square? Here’s another one: 12^2=144 Do [...] |
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