How do you do multiplication in your head?

[cjsketchy]

Originally posted by: SOSTrooper
I do it the Hong Kong way...

Lets say it's 26x34

....26 .......I drop the 0 down below the 6 and 4
..X34 .......Then I multiply 3 to 26 to get 780
-------
..780 .......Now I multiply 4 to 26 to get 104
+104 .......Finally I add 780 to 104
-------
..884

Hmm... I was trying to figure out how to do that one a bit easier in my head. I rounded them both to 30, so 30x30 = 900, then you would subtract 4x4=16 so the answer would be 884. Does this work for all problems?

Gonna try it myself...
48x32 = 1536
round to 50x30 = 1500
subtract 2x2 = 4
...nope 🙂

/scrambles back to his corner

 

[cjsketchy]

Originally posted by: DrPizza

Originally posted by: PipBoy

Originally posted by: DrPizza

Something like 15*17, I would do 16 squared minus 1. = 256-1 = 255.

(it's from the form (x-1)(x+1)= x^2 -1 )

You're a maniac for even considering that.

Nah, not a maniac, just way better than most people at mental arithmetic. It only takes practice though. The more you rely on a calculator, the weaker your ability to do mental math becomes. It's fun to beat people who are using a calculator... especially sales clerks. Or better, to get out the exact change long before they're done adding up the prices and calculating the sales tax.

Another way to do things mentally, say for something like 26 * 47 would be to also reduce it to an algebra problem
(20 + 6)(40 + 7) use FOIL
I would: 20*40 = 800
40*6 = 240, running total is 800...900...1000...1040
20*7 = 140, running total 1040...1140...1180
6*7=42, running total 1180...1220...1222 Done.

Yet another way to do 26*47 would be
26*47..... 13*94
940 + 3*94
940 + 300 -18
1222

Either way, takes about 2-3 seconds mentally. (for me)

yup... I would do that the second way.... I always like to cut the smaller number in half then double the other, or do it by a factor of 3, etc.

 

[DrPizza]

cj, it will always work if you round one number up and round the other number down the same amount *to the same number*
i.e. 57 * 43 = 50*50 = 2500 - 7*7 = 2451

 

[dighn]

intersting methods of mental multiplication. very usefull stuff 🙂

i use the calculator too much...

 

[DrPizza]

yup... I would do that the second way.... I always like to cut the smaller number in half then double the other, or do it by a factor of 3, etc.

That works great a lot of the time, but it's not as useful for 19*12. You just have to develop a large bag of tricks and recognize problems right away for what they are.

 

[EugeneChien]

There's also ways to do squares quicker, Such as:

Squares that ends with 5:

For example, 35^2

the answer will always end with a 25, so you put that down
now to determine the remaining digits, you times it by n(n+1), where n in this case is 3. So it will be 3 x 4 which is 12, plus 25, which is 1225.

Squares that ends in 1, 4, 6, 9 ( Works best using this method ):

Say if it's 46 square you are finding :

you take 45 square, which is 2025 (Using the method above), and you double 45 + 1, then you add that to the total, and you will get 2116.

Same if want to take 44 square, except you minus 1, so it's would be 89 from 2025, which is 1936.

Now if you want to do 47 square, you get 2025, then you add 91 for 46 square, and you add another 91 + 2 for 47 square, which is 2209.

Just some intresting things I found out while looking at stuff.. 😉

 

[amcdonald]

just glancing at 19x12 its natural for me to reason in this order: (9x12)+(10x12)=228

 

[microAmp]

Originally posted by: WinkOsmosis
19x12? I would do 20x12, which is 240, then subtract 12. 228.

I do the samething myself.....

 

[cjsketchy]

Originally posted by: DrPizza
cj, it will always work if you round one number up and round the other number down the same amount *to the same number*
i.e. 57 * 43 = 50*50 = 2500 - 7*7 = 2451

Ahhh, I see. Thanks for the info 😀
/adds to his miniature sized bag of tricks

 

[Yax]

Originally posted by: DrPizza
I do it a variety of ways, depending on the problem..... but, I agree with wink on that one.

Something like 15*17, I would do 16 squared minus 1. = 256-1 = 255.

(it's from the form (x-1)(x+1)= x^2 -1 )

Computing the square makes it harder, duhhh.

 

[MeanMeosh]

i do foil

 

[Mark R]

Maybe I'm weird but I just did it: 19x12 = 12x12 + 7x12. But then, I know my multiplication tables very well.

For higher numbers I usually just use addition.

For special cases like 64x128 I might do something like: ln2(64) = 6; ln2(128)=7; 2^(6+7) = 8192

 

[J1600B]

Who the hell does "2x9 = 18,carry the 1" in their head??? Thats for paper, fredless.

 

[tcsenter]

I mastered all permutations of the first 20 numbers when I was a kid. The school required us to master the first 12 but I did 20 for some reason. So I don't do any multiplication if both numbers are 20 or less. Its just memory/associative recall.

Like 8x8=64, nobody actually does 'sixteen, twenty four, thirty two, fourty......sixty four!' in their head. They've memorized 8x8=64. Well, I've done that all the way up to 20.

After that, it gets pretty messy when i have to do it in my head. Messy indeed.