163 TMD 5 Tips for Faster Mental Division (Part 1)

沃尔玛极速配送最快一小时就能把你要的东西送到家。

Walmart Express delivery can get what you need delivered in as fast as an hour.

不管是最后一勺婴儿奶粉、宠物粮快见底、遥控器没电，还是临时要送的礼物，都能搞定。

Whether it's baby formula when you're down to the last scoop, pet food before the bowl runs empty, batteries for a dead remote, or a last minute gift, It is handled.

今天就试试沃尔玛极速配送，使用优惠码 express 即可享受免费配送。

Try Walmart Express delivery today and get free delivery with promo code express.

本优惠仅限首次使用极速配送订单，且订单满50元方可使用。

Promotion valid for first express delivery order, $50 minimum.

商品库存有限，送完即止。

Subject to availability.

具体条款详见说明。

Restrictions apply.

嘿，

Hey,

数学爱好者们。

math fans.

我是数学达人杰森·马歇尔，每周为你带来快速实用的数学小技巧，让数学更简单。

Jason Marshall, math dude here with your weekly dose of quick and dirty tips to make math easier.

如果你跟我一样，不太喜欢做长除法，那我完全理解——所以我能躲就躲。

If you're anything like me, you don't exactly love doing long division, which is exactly why I avoid it as much as I can.

当然，避开纸笔算除法的一个办法就是用计算器。

Of course, one way to avoid doing division the old fashioned way with paper and pen is by using a calculator.

大多数时候，我确实就这么干。

Most of the time, that's exactly what I do.

但说实话，有时候计算器或手机里的计算器用起来不方便，你可能得当场在脑子里算除法。

But the truth is that sometimes calculators or phones with calculators are inconvenient, and sometimes you need to do division right there on the spot in your head.

那该怎么算呢？

How can you do it?

继续听下去，我会教你五个简单方法，帮你大幅提升心算除法的能力。

Keep on listening to learn five simple things that you can do to take your mental division skills to the next level.

好了，不多说了，下面就是帮你更快心算除法的几个技巧。

And now without further ado, here are your tips for faster mental division.

第一招，能估算就先估算。

Tip one, approximate if you can.

加快心算除法的第一步，是停下来想想，你到底需要多精确的结果。

The first thing you can do to speed up a lot of the mental division problems you'll encounter is to stop and think about just how accurate you need the answer to be.

有时候你确实需要精确答案，或者要精确到小数点后两位、三位，或者其他具体要求。

Sometimes you need an exact answer or perhaps an answer that's accurate to two decimal places or three decimal places or something else specific like that.

但很多时候，你其实只需要一个大概的数就行。

But a lot of the time, you really just need a ballpark estimate.

如果只是要个大概，就别浪费时间去算精确值了。

In those cases where you only need an approximate answer, don't waste your time by figuring out the exact answer.

直接做个快速估算就好。

Instead, make a quick and dirty estimate.

怎么做呢？

How?

比如你在一个咖啡店工作，想算算顾客平均每人花多少钱。

Well, let's say you work in a coffee shop and you want to figure out the average amount spent by your customers.

到目前为止，你从26个人那里收了164美元。

So far, you've collected 164 from 26 people.

那平均每人消费是多少呢？更准确地说，是均值是多少？

What's the average or more technically the mean bill?

164美元差不多是150美元，26个人也接近25个人。

Well, $164 is pretty close to $150 and 26 people is pretty close to 25 people.

所以别直接算164除以26，先算个差不多的数试试。

So instead of calculating $164 divided by 26 people, let's start by calculating something that's close to that.

用150除以25。

$150 divided by 25 people.

这样算简单多了，结果大约是每人6美元。

That's a much easier problem to solve, and it says that the answer is roughly $6 per person.

不对。

No.

这方法算出来的不是精确值。

This technique doesn't give exact values.

这取决于你的估算是否准确。

It's only as good as your estimates.

但如果你估算得当，就能得到接近的结果，而且省下不少功夫。

But if you estimate wisely, it'll give you answers that are pretty close and with only a fraction of the work.

沃尔玛即时配送最快一小时就能把你要的东西送到。

Walmart Express delivery can get what you need delivered in as fast as an hour.

不管是奶粉只剩最后一勺、宠物粮快见底、遥控器没电，还是临时要送礼物，都能搞定。

Whether it's baby formula when you're down to the last scoop, pet food before the bowl runs empty, batteries for a dead remote, or a last minute gift, it is handled.

今天就试试沃尔玛即时配送，使用优惠码 express 即可享受免费配送。

Try Walmart Express delivery today and get free delivery with promo code express.

优惠仅限首次使用即时配送订单，且订单满50元方可使用。

Promotion valid for first express delivery order, $50 minimum.

商品库存有限，恕不保证。

Subject to availability.

具体条款详见说明。

Restrictions apply.

第二个技巧：开始之前先简化。

Tip two, simplify before you start.

今天剩下的这些技巧，都是在近似答案不够用的时候可以派上用场的。

The rest of today's tips are all things that you could do when an approximate answer just isn't good enough.

遇到这种问题，第一步应该先看看能不能在动手算除法之前把问题简化。

When faced with such problems, the first thing you should do is check if you can simplify the problem before you start doing any division.

特别是，如果你要除的数（被除数）和除你的数（除数）都是偶数，那就先都除以二。

In particular, if the number you're dividing into, also known as the dividend, and the number you're dividing by, also known as the divisor, are both even, you should start by dividing both by two.

比如算164除以26，先同时把分子和分母都除以二，变成82除以13，问题更简单了，但结果完全一样。

For example, in the problem 164 divided by 26, start by dividing both the top and bottom by two to obtain the simplified, but otherwise identical problem, 82 divided by 13.

这有什么好处呢？

Why is that helpful?

因为数字越小，算起来通常就越轻松。

Simply because it's almost always easier to work with smaller numbers.

不过，简化除法问题的方法可不止这一种。

But that's not the only way a division problem can be simplified.

像93除以27这样的题，被除数和除数都不是偶数，所以没法直接都除以2来简化。

In a problem like 93 divided by 27, the dividend and divisor are not both even numbers, so we can't simplify the problem by dividing both by two.

但它们都能被3整除。

But both are divisible by three.

也就是说，3是93和27的公因数，这时候我们可以把被除数和除数都除以3，得到简化后的算式：31除以9。

In other words, three is a factor of both ninety three and twenty seven, which means that in this case, we can divide both the dividend and divisor by three to obtain the simplified problem 31 divided by nine.

这里的小技巧是：先找被除数和除数的公因数，然后在做任何运算之前，先把两者都除以这些公因数。

The quick and dirty tip here is to always look for factors common to both the dividend and the divisor, and then to divide both by each common factor before you do anything else.

第三点：先乘再除。生活中有些时候，做跟该做的事相反的事是错的，但也有时候，这么做反而特别好。

Tip three Multiply before dividing There are times in life when doing the opposite of what you should be doing is bad, but there are other times when it's actually very, very good.

这正是其中一个例子，因为在心算除法时，有时候改用乘法反而更有效。

This is one of those times because when it comes to mental division, it turns out that it's often helpful to multiply instead.

和很多心算技巧一样，这个方法的基础是：除以10、100，或者任何10的幂次，都特别简单。

Like many mental math tricks before it, this one relies upon the fact that dividing by 10 or 100 or any other power of 10 is easy.

只需要把小数点往左移一位，对应每一个10的幂次就行。

Just move the decimal point one position to the left for each power of 10.

因为除以10的幂次特别简单，所以我们应该尽量多用这种方法，哪怕本来是要除以5的时候。

And since it's so easy to divide by powers of 10, we should strive to do it as often as possible, even when we're supposed to be doing something like dividing a number by five.

那该怎么做到呢？

How can we possibly do that?

关键在于，5其实就是10除以2。

By using the fact that five is equal to 10 divided by two.

比如，想象你又回到咖啡店工作，想算算自己一周五个工作日每天平均赚多少钱。

For example, let's imagine you're back working in your coffee shop and you've decided to calculate the average amount of money you make each day of a five day work week.

也就是说，你需要把这五天的总收入——比如说1677美元——除以5。

In other words, you need to divide the total amount of money you bring in over those five days, let's say it's $1,677, by five.

但别直接算1677除以5，我们可以利用5等于10除以2这个关系，把问题变成16.77除以（10除以2）。

But instead of calculating 1,677 divided by five, let's use the fact that five is equal to 10 divided by two to turn this problem into $16.77 divided by the quantity 10 divided by two.

根据我们学过的分数除法——记住，除以一个分数等于乘以它的倒数——这其实就等于16.77乘以2，再除以10。

Using what we've learned about how to divide fractions remember invert and multiply we see that this is the same as sixteen seventy seven times two all divided by 10.

换句话说，我们把原本难算的除以5，变成了两个特别简单的步骤。

In other words, we've managed to turn a hard problem of mentally dividing by five into two simple problems.

首先，把16.77美元乘以2，得到3354美元，再把结果除以10，就能算出每天的平均收入是3354除以10，也就是335美元40美分。

First, multiply $16.77 dollars by two to get $3,354 and second, divide the result by 10 to find that the average income for each day of the week is $3,354 divided by ten or three hundred thirty five dollars and forty cents.

这个技巧只适用于除以5吗？

Does this trick only work for division by five?

当然不是。

Absolutely not.

你可以自己试试，同样的方法也能把除以20变成先乘5再除以100，把除以25变成先乘4再除以100，还有很多其他情况都能用。

As you should check for yourself, you can use the same idea to turn division by 20 into multiplication by five followed by division by 100 or division by 25 into multiplication by four followed by division by 100, and lots and lots of other things too.

如果再结合今天第一个关于估算的技巧，这个方法就更强大了。

And when combined with today's first tip about making approximations, this trick becomes even more powerful.

记住，动手之前先停一下想一想，很多时候你会发现，其实有简单得多的解法。

Just remember to stop and think before you start working on a problem, and you'll often see that there's a much easier way to the solution.

明白了。

Okay.

今天关于数学的内容就到这里了。

That's all the math we have time for today.

当然，这些只是我五大快速心算除法技巧中的三个，记得下次回来学习最后两个最厉害的技巧。

Of course, those are only three of my top five tips for faster mental division, so be sure to check back next time to learn the last most powerful pair of tips.

如果你想了解更多心算技巧，不妨听听之前《数学达人的》相关节目。

If you want to learn more mental math techniques, be sure to check out some of the earlier Math Dude episodes on this topic.

里面还包括如何快速心算加减乘，以及如何迅速计算百分比。

Among other things, you'll find shows on how to perform quick mental addition, subtraction, and multiplication, as well as how to perform lightning fast percentage calculations.

所有这些节目和其他资源的链接，你都可以在 mathdude.quickanddirtytips.com 找到。

You can find links to all of these shows and more at mathdude.quickanddirtytips.com.

另外，我的心算有声书《数学达人的五大心算技巧》也在 Audible 上架了，别忘了去看看。

Also, be sure to check out my mental math audiobook called the math dudes five tips to mastering mental math available from audible.com.

还想更过瘾？我的《数学达人的代数速成指南》这本书也推荐你读一读。

And for even more math fun, be sure to check out my book, the math dudes quick and dirty guide to algebra.

别忘了在 Facebook 上关注《数学达人》，搜索 facebook.com/themathdude 就行。

And remember, become a fan of the math dude on Facebook at facebook.com/themathdude.

好了，这期就到这里，我是杰森·马歇尔，为您带来《数学达人的快速实用技巧》。

Until next time, this is Jason Marshall with the math dude's quick and dirty tips to make math easier.

谢谢收听，数学爱好者们。

Thanks for listening, math fans.

沃尔玛极速配送最快一小时就能把你要的东西送到家。

Walmart Express delivery can get what you need delivered in as fast as an hour.

不管是奶粉只剩最后一罐、宠物粮快见底、遥控器没电了，还是临时要送礼物，都能搞定。

Whether it's baby formula when you're down to the last scoop, pet food before the bowl runs empty, batteries for a dead remote, or a last minute gift, It is handled.

今天就试试沃尔玛极速配送，使用优惠码 express 即可享受免费配送。

Try Walmart Express delivery today and get free delivery with promo code express.

此优惠仅限首次使用极速配送服务。

Promotion valid for first express delivery order.

订单满50元起适用。

$50 minimum.

商品库存有限，送完即止。

Subject to availability.

其他条款细则请见官网。

Restrictions apply.