时间:2018-12-07 作者:英语课 分类:数学英语


英语课

 




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by Jason Marshall


Today we're turning our attention to using everything we've learned so far to help you solve math problems faster than you ever thought was possible. In this article you’ll learn two tips to help you add quickly…all in your head!

Tip #1: Find Pairs of Numbers that Add to 10

Here is perhaps the single most useful quick and dirty tip to help you calculate quickly: When adding a list of numbers, look for pairs of numbers that add to ten. Here’s what I mean:

1 + 9,

2 + 8,

3 + 7,

4 + 6,

5 + 5.

All of those pairs add to ten.

So, when you’re adding groups of numbers, look for these special pairs. If you’ve got one or more pairs, it’s easy to add them up—as easy as 10 + 10 = 20.

How to Do It

Here’s an example: Let’s say you need to add the numbers 1, 3, 5, 7, and 9. You could run through the numbers in order, adding them up one-by-one; something like:

1 + 3 = 4, then

4 + 5 = 9, then

9 + 7 = 16, and finally

16 + 9 = 25.

But that’s a lot to keep track of. Instead, if you start by pairing up numbers that add to ten—in this case 3 and 7, and 9 and 1—that leaves you with an easy problem. You just have to add the two 10s to the remaining number 5 that didn’t pair with anything:


10 + 10 + 5 = 25

Tip #2: Find Groups of Numbers that Add to 10

The second tip is really an addendum 1 to the first. Say you need to add a series of numbers like 47, 14, 21, and 32. Let’s look for pairs of numbers in the ones place that add up to 10. That's the 7 from 47, the 4 from 14, the 1 from 21, and the 2 from 32. Hmm, no two numbers here add up to 10. Are we out of luck?

No, look at the numbers again: 7, 4, 1, and 2. Three of those numbers do add up to ten:


7 + 1 + 2 = 10


That brings us to the second quick and dirty tip: Don’t restrict yourself to grouping pairs of numbers—sometimes looking at groups of three (or even more) can help.

How to Do It

Let’s look at how to solve the example problem from before in a little more detail: 47 + 14 + 21 + 32. First, notice that each term in the problem can be written as:

47 = 40 + 7,

14 = 10 + 4,

21 = 20 + 1, and

32 = 30 + 2.

Then, let’s use this to rewrite the original problem:(见图一)


Now, as we discussed during the episode 2 on the commutative property of addition, you can add these numbers in any order you like. So, let’s gather the numbers that add up to 10 and rearrange the terms as:(见图二)


The three numbers in the first term add to 10 and the four numbers in the second term add to 100, so the problem becomes:(见图三)


Believe it or not, eventually—after a bit of practice—you’ll be able to do all this in your head.

Wrap Up




You can find several practice problems below to help you sharpen your skills. Remember, try to work them out in your head if you can. Next week we'll combine these two tips with a couple of other tricks, and continue your transformation 3 into a calculating machine. Then, get ready, because the week after that we’re going to begin our foray into the world of fractions, decimals 4, and percentages.

And, throughout the month of March, we’re going to be giving away one copy of the fantastic book “The Number Devil” each week to a lucky Math Dude fan on Facebook. So please join the community there and become a fan of the Math Dude. It's a great place to ask questions and chat with other math enthusiasts 5. 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 addendum
n.补充,附录
  • This is an addendum to the book.这是本书的附录。
  • Six parts and one addendum are separated in the paper.论文由六章和一个附录组成。
2 episode
n.(作品的一段)情节,插曲,系列事件中之一
  • The episode was a huge embarrassment for all concerned.这段小插曲令所有有关人员都感到非常尴尬。
  • This episode remains sharply engraved on my mind.这段经历至今仍深深地铭刻在我的心中。
3 transformation
n.变化;改造;转变
  • Going to college brought about a dramatic transformation in her outlook.上大学使她的观念发生了巨大的变化。
  • He was struggling to make the transformation from single man to responsible husband.他正在努力使自己由单身汉变为可靠的丈夫。
4 decimals
n.小数( decimal的名词复数 )
  • 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
5 enthusiasts
n.热心人,热衷者( enthusiast的名词复数 )
  • 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
学英语单词
Abdel
acceleration of ripening
additional advance
anecdotically
antiriot ammunition
apical bud
arecaceaes
augelli
average repair
Bankia spengler
bankruptcy administrator
basic lead sulphate
bilge logs
booster inoculation
bored shitless
boringly
chain and sprocket drive
Chalkedon
checking off symbol
CLMW
course-stability
cross rod
Curley
damper segment
declaratory judgments
deflection calculation
delivered free to destination
dietary-supplement
dress in
dust crops with an insecticide
emince
enterouterine anus
equitangential
faralatrioside
farbs
finely divided scale
folia vermis
heavy work
helius (helius) minusculus
Hose Connectors
hyperhomocysteinemic
intermolecular respiration
lava column
lead number
lends out
lenticel(le)
lywallzyme
macnee
magnitude spectrum
master screw
max sth out
mellower
memory error report analysis
movable appendage
naked-flame mine
nickel-vanadium steel
nominal ocular hazard area
oculometry
one pack
ordinary wheel
organizational climate index
over-grateful
over-indulged
overtowered
pattern representation
phenoxathin
phenylphosphine
pick-up attachment
pilot flame burner
pipeline stopcock
plash
pot-holder
preservative substance
pressure admission chamber
pressure of blast
Prohepes
pseudodiploidy
r.d
ramming up
rankine thermometric scale
riborg
righi-leduc effect
roricon
sclenchyma
self-illuminating sight
selfcontradictory
sniper
sousant
Subhanallah
sukhooei
Swap Curve
tahsildars
thermo anelasticity
three stages fluidized-bed dryer
toner concentration
unkissing
unvote
upright drill
visual agnosia
Wiener schnitzel
with a swing in it
worldless