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英语煎蛋小学堂视频百科105:如何通过加法做减法(MP3+中英双语)

cocotang 于2015-05-31发布 l 已有人浏览
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英语视频:煎蛋小学堂105:如何通过加法做减法,以幽默诙谐的方式为你解答那些那些你意想不到的科学小知识,含有中英双语字幕视频,mp3下载。
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Suppose you want to know how long it was between the Norman invasion of England and Columbus's arrival in the Caribbean;that is,what's 1492 minus 1066 but you hate long subtraction with its borrowing and such.Well,we can subtract by adding:first we just need to replace each digit of the smaller number with 9 minus that digit,except the final digit gets replaced with 10 minus that digit,so 1066 becomes nine minus 1,nine minus 0,nine minus six,ten minus 6.

假设你想知道 诺曼底登陆和哥伦比亚抵达加勒比海之间 相隔多久;答案是1429减去1066 但你又讨厌多位数减去的借位等麻烦步骤。那么 我们可以通过加法来进行减法运算:首先我们需要用9减去每个数位上的数字 得到一个较小的数字来代替它,最后一位数用10来减,那么1066就是 9减1 9减0,9减6 10减6.

Adding that to 1492 gives 10426,and if we ignore the first digit,we get the answer:1492 minus 1066 is 426.You can check just to be sure.Coincidentally,it's roughly 426 times farther from Portugal to the West Indies and back than from France to England.

将得到的数值加上1429等于10426,然后去掉首位,我们就得到了1429减1066的答案426.不信 你可以计算验证一下。巧的是 从葡萄牙到到西印度群岛的距离 大约是从法国到英国距离的426倍。

But anyway,the subtraction-by-adding trick works for any positive numbers! 8 minus 6,or 2 is the same as 9 plus 4,ignoring the first digit.100 minus 1? is 100 plus 999,which is 99,ignoring the first digit.And 424,242 minus 333,333 is 424,242 plus666,667 or,90,909 ignoring the first digit.I'll let you check that one.

总之 通过加法做减法的技巧 对一切正数都管用!8减6 得2.这根8加4 忽略首位的结果是一样的。100减1? 相当于100加999.略去首位 就是99.424242减333333 相当于424242加666667等于90909再略去首位。再试试这个。

This trick might seem useless,but suppose you built a machine that can add numbers together,and you wanted to make it subtract?Well,in that case it might be easier to make it subtract by adding:and matter of fact,my friend Hank Green took apart an adding machine and that's exactly how it subtracts-by adding!

这个计算技巧看起来似乎没什么用,但是假设你制造了一台可以进行加法计算的机器,可你却想用它做减法?在这种情况下 用加法做减法运算就很好用了:事实上 我朋友Hank Green拆解了加法机器 而这正是做减法的办法————通过相加!

Basically,the machine adds numbers by rotating numbered wheels,but there aren't infinitely many wheels so if you add up past the maximum possible number,you get back to zero-this is called"overflow"in computing and modular arithmetic in mathematics.But most importantly getting back to zero by adding means it's possible to have positive negative numbers,since,for example,negative three is just what you add to three to get zero,and on Hank's adding machine if you add 3 plus 9,997.00,you get zero,so 9,997is literally negative three!

基本上 机器通过转动数字齿轮进行加法运算,问题是齿轮是有限的 因此 一旦相加的数值超过上限,你得到的数值就是0 计算机里称之为“溢出”数学运算中称之为“模运算”。最重要的是通过加法得到0 意味着 这可能是加了一个负数的结果,例如 负3加3就等于0,使用Hank的加法机器 3加9997等于0,也就是说9997相当于负3!

Unfortunately,there are an infinite number of numbers when you're doing regular arithmetic,so you might think that negative three is just negative three.But if you're willing to fudge a little,you can just take the adding machine's version of negative three,add a bunch of 9s out in front,and when you add that to stuff it's basically the same as subtracting three,as long as you don't look too far.

不幸的是 在你进行常规计算时 存在着无数多的数字,所以你会觉得负3就只是负3.但是如果你愿意胡思乱想一番,那么负3就可以变成加法机器意义上的负3,在前面加上一大串的9,然后与某个数值相加 结果就相当于这个数值减3,就跟少几个9的时候一样。

Because,you know,nine gadgillion nine hundred and ninety bajillion nine hundred and ninety seven plus three,is zero.By the way,this method of subtracting by adding is how computers subtract as well,they just do it in binary which makes it a lot easier.It's called "subtracting using the two's complement,"if you want to look it up,"subtracting using the two's complement"

因为 你瞧99999.。。。。。99997加3 等于0.顺便说一句。计算机就是 通过这种加法 进行减法运算,只不过计算机在二进制下计算 会更简单些。

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