数学英语 05 How To Add Quickly, Part 2

 

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by Jason Marshall

Continuing our quest¹ towards turning you into a quick-calculating machine, today we’re building upon last week’s tips with one additional very important tip that will help you to perform lightning-quick mental-addition.
The Traditional Adding Method: Working From Right-to-Left
Let’s kick things off by looking at the problem $132 + $8 + $58 + $29. Perhaps you’re doing some shopping and want to get a quick total before heading to the register to make your purchases. Let's first do the problem using the method everybody learns in school: that is, right-to-left style. Start by writing the problem down with the ones column lined up vertically:（见图一）

I’m actually going to ignore the dollar signs for now to save some writing. Just remember, the addition problem works the same whether we’re talking about adding dollars, euros, potatoes, hiccups², or anything else. In other words, the problem is the same as:（见图二）

Continuing to solve the problem via the traditional right-to-left method, let’s add the numbers in the ones column:
2 + 8 = 10, then
10 + 8 = 18, and finally
18 + 9 = 27.
Now, write the 7 below the ones column, then carry the 2 and write it above the tens column. In other words, take the total of 27 from the ones column and break it into 20 + 7, leaving the 7 in the ones column, and putting the 2 above the tens column where it represents 20:（见图三）

Next add the numbers in the tens column:
2 + 3 = 5, then
5 + 5 = 10, and finally
10 + 2 = 12.
Of course, since this was the tens column, the sum of 12 actually represents 12 tens, which is 120. So, break this 120 into 100 + 20, write the two—which represents 20—below the tens column, then carry the one—which represents 100—and write it above the hundreds column:（见图四）
Finally, add the numbers in the hundreds column—that’s the 100 that we carried plus the 100 from 132—to get the final answer: 227, or $227, in this case.（见图五）

The Quicker Adding Method: Working From Left-to-Right

Okay, that worked great, right? So, what's wrong with adding from right-to-left? Well, nothing is wrong with it. It does work; but it's slow. So here's a quick and dirty tip to speed things up: It's much faster to add large numbers from left-to-right than from right-to-left. Here's what I mean.
Instead of starting at the ones column on the right, start at the hundreds column on the left. So first: How many hundreds are there in this problem?.（见图六）

There’s just one from $132. So we've got one 100 (think of it as a single $100 bill), and the total to keep in your head is $100.（见图七）

Now, move from left-to-right to the tens column. How many tens do we have? There are 3 from $132, 5 from $58, and 2 from $29. So there are 3 + 5 + 2 = 10 tens (think of this as ten $10 bills), for a total of 10 times 10 or $100. The running total in your head is now $100 + $100 = $200.（见图八）

Finally, move further from left-to-right to the ones column. What's the total there? Well, the ones column contains 2 from $132, 8 from...well...$8, another 8 from $58, and 9 from $29. So the total is 2 + 8 + 8 + 9 = 27. And the grand total for the whole problem is therefore $200 + $27 = $227.（见图九）

Of course, this is the same answer we got before when we worked from right-to-left. But the beauty of working left-to-right is that it’s much easier to do the work in your head without needing to carry digits³ and do lots of bookkeeping. Give it a bit of time and practice, and I bet you'll find it’s much faster.
Wrap Up
And on that note, you’ll find several practice problems below to help you sharpen your skills. Remember, try to work them out in your head if you can. Check out the “videos” section of the Math Dude’s Facebook page or YouTube to see a video walkthrough demonstrating how to solve the practice problems. Okay, that’s all the math we have time for today, but start getting excited because next week we’re going to begin tackling⁴ the wonderful world of fractions, decimals⁵, and percentages!
And, throughout the month of March, we’re giving away one free book each week to lucky Math Dude Twitter followers⁶ and Facebook fans. So please join our growing community of social networking math fans, ask questions, and chat with other math enthusiasts⁷. Check it out and see how you can win a free book!

Until next time, this is Jason Marshall with The Math Dude’s Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!

 

1 quest   

n.寻求，搜索，追求

参考例句：

• Man will suffer many disappointments in his quest for truth.人类在探索真理过程中必然会遭受挫折。
• His quest for perfection is relentless.他不断追求完美。

2 hiccups   

n.嗝( hiccup的名词复数 )；连续地打嗝；暂时性的小问题；短暂的停顿v.嗝( hiccup的第三人称单数 )；连续地打嗝；暂时性的小问题；短暂的停顿

参考例句：

• I cannot find a rhyme to "hiccups". 我不能找到和hiccups同韵的词。 来自《简明英汉词典》
• Can we rhyme 'hiccups'with 'pick-ups'? 我们能把‘hiccups’同‘pick－ups’放在一起押韵吗？ 来自辞典例句

3 digits   

n.数字( digit的名词复数 )；手指，足趾

参考例句：

• The number 1000 contains four digits. 1000是四位数。 来自《简明英汉词典》
• The number 410 contains three digits. 数字 410 中包括三个数目字。 来自《现代英汉综合大词典》

4 tackling   

n. 扭住, 抱住, 卷起

参考例句：

• a bottom-up approach to tackling the problem 处理这个问题的自下而上的方法
• There are three essentially different ways of tackling the problem. 解决这个问题有三种根本不同的方法。

5 decimals   

n.小数( decimal的名词复数 )

参考例句：

• His first small calculator could perform certain computations to eight decimals. 他制造的第一台小型计算器能进行八位数的某些运算。 来自互联网
• T: Who can divide the repeating decimals into two groups? Why? 师：谁能再将上题中的循环小数分成两类？为什么？ 来自互联网

6 followers   

追随者( follower的名词复数 )； 用户； 契据的附面； 从动件

参考例句：

• the followers of Mahatma Gandhi 圣雄甘地的拥护者
• The reformer soon gathered a band of followers round him. 改革者很快就获得一群追随者支持他。

7 enthusiasts   

n.热心人，热衷者( enthusiast的名词复数 )

参考例句：

• A group of enthusiasts have undertaken the reconstruction of a steam locomotive. 一群火车迷已担负起重造蒸汽机车的任务。 来自《简明英汉词典》
• Now a group of enthusiasts are going to have the plane restored. 一群热心人计划修复这架飞机。 来自新概念英语第二册