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05-21-2008, 08:18 AM
How do you personally multiply these two numbers together in your head? You know, the step by step process that you use to come to your conclusion.

365 + 365

Easy enough I suppose, but I'm no savant. I had to work it out in my head for about 8 seconds.

What intrigued me about it, was when I later reviewed how I came to the correct answer (yes, for no good reason at all).

I took 365, and brought it down as far as I could to a 100 base (if you can call it that). So... 300+300 = 600.

I then took 65 x 2 and thought to myself "what do I have left over after 100?" 15. Okay, so 15x2 is 30. Result 600+100+30 = 730

Does anybody else do this, and how can I improve on getting the answer in a simpler way?

05-21-2008, 08:23 AM
Multiply?

Švejk
05-21-2008, 08:26 AM
for multiplying i'd use a calculator here. :) To add them, I calculate 2*(350 + 15) = 2*350 + 2*15 = 700 + 30 = 730.

ultrafilter
05-21-2008, 08:27 AM
It's easier for me to calculate 360 + 370, so that's what I do.

The Chao Goes Mu
05-21-2008, 08:27 AM
I use the pretty much the same method as you do Parental Advisory. Smaller two digit numbers I can just multiply.

Hampshire
05-21-2008, 08:38 AM
I guess I did it the long way.
5 + 5 = 10 carry the one.
_ _ 0

6 + 6 + 1 = 13 carry the one.

_ 3 0

3 + 3 + 1 = 7

7 3 0

NinetyWt
05-21-2008, 09:12 AM
Knead to Know is right, that's ain't multiplyin' ! :p

I say 65x2 = 130 and 300x2 = 600. Then 600+130 = 730.

Trunk
05-21-2008, 09:17 AM
When I see that, I know that 65 + 65 is going to be over 100, and I know that 300 + 300 is 600, so BOOM, I'm in the 700s.

Then, anything like 65+65 or 85+85 is just "in there".

I still need to process it, though. Some people just fire it off.

Yorikke
05-21-2008, 09:26 AM
I took 365, and brought it down as far as I could to a 100 base (if you can call it that). So... 300+300 = 600.

I then took 65 x 2 and thought to myself "what do I have left over after 100?" 15. Okay, so 15x2 is 30. Result 600+100+30 = 730

I do it pretty much like this, although the method changes (I think) with different numbers.

Joe

One And Only Wanderers
05-21-2008, 09:31 AM
I do ((2 * 36) * 10) + 10, but then, I'm odd

Amblydoper
05-21-2008, 09:34 AM
Lets multiply, just for kicks...
Multiplying a number by itself is pretty easy, even for large numbers. Just as you can factor 365+365 into 2*300 + 2*60 + 2*5 (or any other method described here) You can factor the product as well
365*365
= (300+60+5)*(300+60+5)
= 300*300 + 60*60 + 5*5 + 2*(300*60) + 2*(300*5) + 2*(60*5)
= 90000+3600+25+36000+3000+600=133225

Amblydoper
05-21-2008, 09:42 AM
Missed the Edit Window...
Let me explain more if its not clear how to do this in your head...
You are multiplying each digit of the first number by each digit in the second number, adding the appropriate number of zeros, then adding up the results. The first three terms are easy, because you are just squaring 3, 6, and 5. Then you double each combination possible, 3*6, 3*5, and 6*5. Keeping track of the zeros is the hard part, then you have to add 6 numbers together, but they are all nice, neat numbers with lots of zeros.

Gary "Wombat" Robson
05-21-2008, 09:44 AM
365 + 365I look at closest round number (350), and double the two parts I get: 350x2=700 and the remaining 15x2=30, hence 730.

If the problem were something like 392+392, I'd round up (400x2=800) and then subtract what's left (8x2=16), coming up with 784.

OtakuLoki
05-21-2008, 10:04 AM
I use radcon math - I will round the initial numbers to something I find convenient to manipulate: In this case 375. Which works out to 300 + 300 + 150 = 750. Then just subtract the amount I rounded by - 20, to get 730.

Of course, that's only because I needed an exact answer. For most uses, I'd find 750 useful enough for rough calculations.

Mangetout
05-21-2008, 10:08 AM
Twice 36 is 72, so twice 360 is 720

5+5 is 10

720+10 = 730

Gordon Urquhart
05-21-2008, 10:08 AM
I look at closest round number (350), and double the two parts I get: 350x2=700 and the remaining 15x2=30, hence 730.

If the problem were something like 392+392, I'd round up (400x2=800) and then subtract what's left (8x2=16), coming up with 784.

I did something very similar to InvisibleWombat's first solution, although I rounded each instance of 365 up to 400, added them together (or multiplied 400x2, which gets the same result when using numbers of equal value) to get 800, then doubled 35 (400-365) to get 70, which I then subtracted from 800 to get 730.

I've said it before (although not in this arena): you want to learn how to do math quickly in your head, you work at a high school concessions counter. There's no pressure like the kind experienced when a high school football fan orders three hot dogs, two Butterfingers and a large Coke, and he wants exact change back from his \$10 bill.

TokyoBayer
05-21-2008, 10:55 AM
Doubling numbers is easy, so twice 36 is 72, which gives you 720, plus 10.

Thudlow Boink
05-21-2008, 11:45 AM
Twice 36 is 72, so twice 360 is 720

5+5 is 10

720+10 = 730This is the way I did it in my head.

Antinor01
05-21-2008, 12:10 PM
300 + 300 = 600
60 + 60 = 120
5 + 5 = 10

600+120+10=730

gigi
05-21-2008, 12:14 PM
If we're talking addition, put me down for

360+360 = 720
5+5=10
730

beanpod
05-21-2008, 12:21 PM
Like gigi, but I break it up according to each place and then add the totals together.

300+300 (or 300x2, depending on my mood) = 600
60+60 = 120
5+5 = 10

730

Similar structure for multiplication and adding large numbers. My mom tried to teach me this back in 4th grade or so, but it just didn't stick. I realized long about 11th grade what she was talking about and went to her excitedly, saying, "Hey, I understand it now!" "What?" she asked. "Addng in my head!" I say. "Well, it took you long enough." Oh mom, where would I be without your encouragement?

(disclaimer: She actually was quite encouraging. She's just also kinda mean in a lovable mom sort of way.)

panache45
05-21-2008, 12:23 PM
If we're talking addition, put me down for

360+360 = 720
5+5=10
730
That's what I do, but it happens so fast, I just basically look at the numbers and know the answer.

Nancarrow
05-21-2008, 12:27 PM
I do ((2 * 36) * 10) + 10, but then, I'm odd

Not odd at all judging by many of the other posts. Including the one I'd write if it weren't made redundant by this post.

Nars Glinley
05-21-2008, 12:46 PM
3 + 3 = 6
6 + 6 = 12
6(0) + 12 = 72
5 + 5 = 10
72(0) + 10 = 730.
Qed

ShelliBean
05-21-2008, 12:51 PM
I guess I did it the long way.
5 + 5 = 10 carry the one.
_ _ 0

6 + 6 + 1 = 13 carry the one.

_ 3 0

3 + 3 + 1 = 7

7 3 0

That's what I do but in my head it looks something like a slot machine, or maybe Connect Four but with numbers instead of little red disks.
It didn't take a terribly long time. Does that make sense?

Shodan
05-21-2008, 12:51 PM
I used logarithms, which I find childishly easy.

Regards,
Shodan

Valgard
05-21-2008, 01:14 PM
If you actually meant multiply, not add, here's how I did it in my head:

365*365 = (300+65)*(300+65)
=300^2 + 65^2 + 2*300*65

300^2 and (2*300*65) are simple mentally. I then had to do 65^2 in my head which you can apply a similar breakdown to:

65*65 = (60+5)*(60+5)
=60*60+5*5+2*5*60
=3600+25+600
=4225

And that's the only hard term in the original question.

Now I returned to the original terms which are "simpler" and kept a running total: 300*300 = 90,000
2*300*65 = 300*130 = 39,000 (total 129,000)

Finally add in the funny number (that's how I think of it), 4225 and you get 133,225.

Got it right the first time, took a minute or three in my head. I'm pretty good with multiplying two digit numbers mentally. I generally find it easier to express them as (a+b) rather than (a-b) because in the former case, all of your operations are addition whereas in the latter you have some addition and some subtraction, I find that I start making mistakes adding when I should have been subtracting, or vice versa.

DLuxN8R-13
05-21-2008, 04:17 PM
How do you personally multiply these two numbers together in your head? You know, the step by step process that you use to come to your conclusion.

365 + 365

Whaat? Do you think most people can multiply 3-didjit numbers in their heads? Are folks in general expected to be able to do that kind of multiplication in their heads?

Because there is just no fucking way I can do that, not to save my ass from a firing squad or to win a zillion dollars tax-free. It wouldn't be a matter of just getting the answer wrong, either; manipulating that many numbers mentally without dicking it out in pencil is flat out impossible for me. I thought it was only real math whizzes who could do shit like that.

Easy enough I suppose, but I'm no savant. I had to work it out in my head for about 8 seconds.

"Easy enough", s/he says. "8 seconds."

I knew I was just a half-step up from a practical innumerate already (hell, I can't count past ten if I've got shoes on ;) ) but the inference that intelligent people do sums like that in their heads every day as a matter of course, tells me maybe I oughtta just put on this nice pointy paper hat....and climb up on this five-foot stool back here in the corner...and whimper to myself, very quietly, for the rest of the day .

What intrigued me about it, was when I later reviewed how I came to the correct answer (yes, for no good reason at all).

I took 365, and brought it down as far as I could to a 100 base (if you can call it that). So... 300+300 = 600.

I then took 65 x 2 and thought to myself "what do I have left over after 100?" 15. Okay, so 15x2 is 30. Result 600+100+30 = 730

Now that just literally makes my head hurt trying to follow it.

how can I improve on getting the answer in a simpler way?

The only way I know to find 365 times 365 is with a pencil on scrap paper, and I'd probably need the better part of a minute to dope it out.

I'm not trying to mess with you, OP, it just slays me that you, and the folks you aimed your query to, can figure that out in your mind in just seconds, like it was nothing, while I would have to sweat it out like a dog shitting peach pits.

05-21-2008, 05:14 PM
Whaat? Do you think most people can multiply 3-didjit numbers in their heads?

...

I'm not trying to mess with you, OP, it just slays me that you, and the folks you aimed your query to, can figure that out in your mind in just seconds, like it was nothing, while I would have to sweat it out like a dog shitting peach pits.

Would it help if I told you I screwed up my post? I meant Add the two together.

As far as multiplying two numbers nearing 100, check this out:

Belrix
05-21-2008, 05:40 PM
I do it in powers of ten: 365+365=(300+300)+(60+60)+(5+5)=600+120+10=730.

<Tom Lehrer> 'cause addition is commutative, right!<TL>

redtail23
05-21-2008, 05:51 PM
300x2 = 600 +
60x2 = 120
= 720 +
5x2 = 10
=730

eleanorigby
05-21-2008, 05:53 PM
Multiply? It says "+".

I know it's been years since I had any formal math, and almost none of it stuck, but I do believe that is not multiplying you have there.

If I was to add those 2 numbers in my head (and that I can do--but no way could I multiply them), I would do 300+300=600. 65+65=130. 600+130=730.

Or I might ask one of my offspring. What are children good for, if not for small errands and stray math problems?

rocking chair
05-21-2008, 05:59 PM
good grief, it gives me a headache just thinking about it. i can not juggle that many numbers in my head and have them land properly.

were i to attempt such a thing without a calculator i would...figure on it being about 2 years.

if that didn't fly. it would be 5+5=0 carry a 1... 6+6=12+1=3 carry a 1... 3+3=6+1=7 so that will be seven three zero.

if i were multiplying them you may as well sit down for 2 years... here we go:

5 time 5 is 5 carry a 2. 5 times 6 is 0 +2=2 carry a 3, 5 times 3 is 15+3=18 so first line is 1835

onward to the second line... six times 5 is 0 carry a 3, six times six is 6 plus 3=9 carry a 3, six times 3 is 18 +3= 21 so second line is 2190

and still we juggle... 3 time 5 is 5 carry a 1, 3 times 6 is 8 +1=9 carry a one 3 time 3 is 9 plus one is 10 so third line is 1095

at this point my brain shuts down because i am now juggling 3 set of 4 numbers and have forgotten the first set completly and def. need paper or a calculator and start over.

i am in utter awe of people who can make numbers dance to their tune. complete and utter awe.

samclem
05-21-2008, 07:09 PM
It just magically appears in my head that it's 730. :)

And, my 15 year old daughter's. Not so, my 17 year old and 21 year old son.

If I were tortured to explain in detail, I guess I might say something like
36 +36 is 72, add the half + half, you get 73.

But it's more instantaneous than that.

lobotomyboy63
05-21-2008, 07:42 PM
2=10/5

You could multply by 10 and divide by 5.

365x10=3650/5=730

Or reverse the operations: 365/5=73 x 10=730.

Yeah, it's often harder but sometimes people can get /5 by imagining the number of nickels.

Khampelf
05-21-2008, 07:44 PM
I use 90wt's method, only I did the 300s first. plus the internal dialogue is like "Two three hundreds is six hundred plus two 65s, 130. Uhh what was the first number, oh yeah 600 plus those two 65s again, 130..730. OK, yeah....."

I use 'round up and subtract the difference' When the number is close to an ordinal. (That the right term?)

elfkin477
05-21-2008, 09:34 PM
600 + (65x2=130) = 730

Now that just literally makes my head hurt trying to follow it. That's what people say when I explain how I do averages in my head.

Say you want to average 65, 72, and 85:
first, subtract 65 from the higher numbers (so all the numbers are the same, you see) = 7, 20
then add those numbers together = 27
now divide by three (since you now have 3 65s off over there)= 9
last add that 9 to 65 = 74 so that's the average. 74.

This works for me with up to 5 or 6 numbers before I get confused by what I'm keeping track of in the second step.

SCSimmons
05-21-2008, 09:52 PM
Well, first I convert to binary: 101101101 + 101101101. Then, I load the rightmost digit into my A register ... Well, the rest should be pretty obvious, right?

ToeJam
05-21-2008, 10:06 PM
Doh!
Here I was thinking I was quite clever as all I did was:

365*2

Northern Thalia
05-21-2008, 10:39 PM
As a former roulette dealer, I've learned/was taught to add the 100's first, then 10's, then 1's. It is something that you REALLY need to do in order not to lose things in the muck that is your thoughts. And now, I just apply that to everything, which is awesome, because my Arts degree brain is a zillion times faster at basic math than my Science PhD boyfriend's. :D

However, you stick some X's, Y's, Z's... or any other symbol, and he wins, hands down!

Amblydoper
05-21-2008, 11:05 PM
...my Arts degree brain is a zillion times faster at basic math than my Science PhD boyfriend's. :D

That is because he is integrating the function y=365, and evaluating the result at 2. ;)

CanvasShoes
05-21-2008, 11:19 PM
I multiply the 2 300s, then the 2 65s. If it's an odd number like 367 and 379, I'd need to break it down further.

I'd separate out the 600 (2*300), Then add the 6 and 7 together (13) and set that aside in my head and then finally the 9 and 7 (16). then to add the 13 and 16, either 29 will just pop into my head, or I may need to break it down further depending upon the number, 10+10= 20+6 and 3 is 9, all in is 29. (right? I could still be wrong, this is why I have to "break it down" at all, I'm not that great at math in my head).

Bottom line, for odd or unusual numbers I usually have to break them apart into numbers ending in 0 or 5, or down to just single digits, and than add the parts back together.

This is why God gave us the great equalizers, calculators and Excel!! :D

Boozahol Squid, P.I.
05-22-2008, 12:15 AM
3 + 3 = 6
6 + 6 = 12
6(0) + 12 = 72
5 + 5 = 10
72(0) + 10 = 730.
Qed

Me too

lizardling
05-22-2008, 02:11 AM
That's what I do but in my head it looks something like a slot machine, or maybe Connect Four but with numbers instead of little red disks.
It didn't take a terribly long time. Does that make sense?

Me too. It's a visual combination of numbered gear wheels and scratching out and carrying the ones on that cheap blue lined paper from elementary school.

I'm going to have to remember the breaking down trick. (300 + 300, 60 + 60, 5+5)

DLuxN8R-13
05-22-2008, 02:31 AM
Would it help if I told you I screwed up my post? I meant Add the two together..

Oh! ThatI can do! I'd bust it down to 350+350 is 700 and 15+15 is 30 and so it adds up to 730. I didn't think I could do it the proper way like we were taught in gradeschool in my head, where you havet to carry the numbers over to the next column. if i can have a couple of minutes, rhree alone with a scratch pad, pencil and at least one cigarette.

As far as multiplying two numbers nearing 100, check this out:

uuuhhh ooooh...am i in n-nu-numbermovie trouble now? i'm sorry pleeeze!

Help@!Help

Indian
05-22-2008, 02:47 AM
My way

360 x 2= 720

5x2=10

adding both = 730 .. pretty quick just some seconds..

Nava
05-22-2008, 03:21 AM
Those two numbers are easy, I don't need to add them. I've seen so many "years" tables it's just in automatic, see.

Now, if you're talking 366+366, then it's "365+1+365+1, so 730+2, so 732"

LouisB
05-22-2008, 05:25 AM
How do you personally multiply these two numbers together in your head? You know, the step by step process that you use to come to your conclusion.

365 + 365

Easy enough I suppose, but I'm no savant. I had to work it out in my head for about 8 seconds.

What intrigued me about it, was when I later reviewed how I came to the correct answer (yes, for no good reason at all).

I took 365, and brought it down as far as I could to a 100 base (if you can call it that). So... 300+300 = 600.

I then took 65 x 2 and thought to myself "what do I have left over after 100?" 15. Okay, so 15x2 is 30. Result 600+100+30 = 730

Does anybody else do this, and how can I improve on getting the answer in a simpler way?IIRC, this is the method we were taught in a distributive education class my senior year in high school. (1958)

Colophon
05-22-2008, 06:12 AM
Twice 36 is 72, so twice 360 is 720

5+5 is 10

720+10 = 730
Like this, pretty much. I say "36 and 36 is 72, so it's 720 plus the two fives which makes 730."

If you wanted me to multiply 365 x 365 in my head, I'd say

365 x 3 = 730 + 365 = 1095 gives me 109500

365 x 6 = double the above, so 2190 gives me 21900

365 x 5 would be 1095 + 730 = 1825.

Add them up and you have 131400 + 1825 = 133225.
I hope that's right.

Colophon
05-22-2008, 06:19 AM
The part I find tricky with multiplying three figure numbers like the above, though, is remembering the intermediate results while calculating the next bit.

Amblydoper
05-22-2008, 06:57 AM
If you wanted me to multiply 365 x 365 in my head, I'd say
...
Add them up and you have 131400 + 1825 = 133225.
I hope that's right.
You are right, and that is a clever system, better then mine. The only problem I see is if one of the digits is 7, although I have a fear of the number 7, so I might be biased.

Engineer Dude
05-22-2008, 07:27 AM
In my head, I said 350 = 3.5 hundred, so:

(350+350) + (15+15) = 700 + 30 = 730

Valgard
05-22-2008, 11:15 AM
The part I find tricky with multiplying three figure numbers like the above, though, is remembering the intermediate results while calculating the next bit.

That's why I try and break it down a little differently so that I've got some very simple terms that I can handle at the end and the more complex bits get handled in one slug. Then I can just add the simple parts (in my example, stuff like 300*300) to finish.

Leaffan
05-22-2008, 11:48 AM
I just looked at it and thought "730." I didn't need to do anything.

Dolores Reborn
05-22-2008, 11:52 AM
I rounded up to 400, x 2 = 800. Then 35 x 2 = 70; 800 - 70 = 730.

05-23-2008, 01:39 AM
I just looked at it and thought "730." I didn't need to do anything.

Did you learn how to do this, or is it just natural for you?

Valgard
05-23-2008, 12:24 PM
My dad has an old set of books called something like "The history of mathematics" and there's a section I remember reading as a kid, about mathematical prodigies including lightning calculators - people who can extract 20th roots of 15 digit numbers in their head, that kind of thing. They asked a very similar question as the OP, how one particular calculator squared a 12 digit number mentally in about 60 seconds. He said that it was the same as doing long multiplication on paper, he was just capable of running the numbers in his head very quickly without losing his place.

So to do 365*365 he'd mentally add up:

300*300+300*65+300*5+65*300+65*60+65*5+5*300+5*60+5*5

Nothing amazing about the method, it's just the sheer speed and ability to store the parts of the solution without getting them confused that are incredible. It wasn't "I don't know, the answer just comes to me".

Bearflag70
05-23-2008, 12:38 PM
I just work the numbers from left to right.

1. 300 + 300 = 600

2. 60 + 60 is more than 100, so the result will be 700-something

3. 60 + 60 = 120, so the answer will be 720-ish

4. 5 + 5 = 10, so the answer is 730

Same process for something like 842 + 576:

1. 8 + 5 = 13, so the answer will be 1300-ish

2. 7 + 4 = greater than 10, so the answer is 1400-something

3. 7 + 4 = 11, so the answer is 1410-ish

4. 6 + 2 = 8, so the answer is 1418