Easy multiplication

[kirennia]

I know this is a bit of a boooooring thread but bare with me because I just found something I've found quite interesting.

Personally I don't have problems with multiplying without a calculator but for any of you who do, maybe this could help you in the future.

Take 2 numbers...any number you want, they can be in the billions if you want but it'll take you a while but it DOES still work.

For the purpose of this exercise, I'm going to use 32 x 150. You write them down, one next to the other and you start off by Halving the first number. It generally works best if you have the smaller number first When you halve the number, you IGNORE any decimal point...it doesn't matter if it is 5.5, get rid of that half. So you have this:

32
16
8
4
2
1

You note that you have halved the number 5 times so with the other number, you DOUBLE it 5 times.

You will then have:

32 150
16 300
8 600
4 1200
2 2400
1 4800

From this point, you then have to cross out and ignore any of the lines by which the number on the left hand side is EVEN so you're simply left with

1 4800.

Ignore the number on the left, you add all of the numbers on the right side which are still remaining but this case has been made very simple as there's only one number.

The answer is 4800

What a spinner.....

 

[Drege]

Nice;P. Is this the kind of stuff you think about on your spare time?=) Except playing daoc that is=).

 

[Jupitus]

For the purpose of this exercise, I'm going to use 33 x 150. You write them down, one next to the other and you start off by Halving the first number. It generally works best if you have the smaller number first When you halve the number, you IGNORE any decimal point...it doesn't matter if it is 5.5, get rid of that half. So you have this:

33
16.5 ---> 16
8
4
2
1

You note that you have halved the number 5 times so with the other number, you DOUBLE it 5 times.

You will then have:

33 150
16 300
8 600
4 1200
2 2400
1 4800

From this point, you then have to cross out and ignore any of the lines by which the number on the left hand side is EVEN so you're simply left with

1 4800.


So... 32x150 = 33x150

=> 32 = 33

Hmmm... something seems a bit wrong

Edit: I hope Ezteq didn't read this before her maths exam!!!!

 

[Healer McHeal]

For the purpose of this exercise, I'm going to use 33 x 150. You write them down, one next to the other and you start off by Halving the first number. It generally works best if you have the smaller number first When you halve the number, you IGNORE any decimal point...it doesn't matter if it is 5.5, get rid of that half. So you have this:

33
16.5 ---> 16
8
4
2
1

You note that you have halved the number 5 times so with the other number, you DOUBLE it 5 times.

You will then have:

33 150
16 300
8 600
4 1200
2 2400
1 4800

From this point, you then have to cross out and ignore any of the lines by which the number on the left hand side is EVEN so you're simply left with

1 4800.


So... 32x150 = 33x150

=> 32 = 33

Hmmm... something seems a bit wrong

Edit: I hope Ezteq didn't read this before her maths exam!!!!

actually, 33x150 is 4950 , 32x150 is 4800, or so a calculator says

 

[kirennia]

actually, 33x150 is 4950 , 32x150 is 4800, or so a calculator says

Aye, still don't think it's a rule which can be broken Just something strange I was told one day.

 

[tookha]

Jupitus > thread

McHeal is the bringer of the obvious ^^

 

[Outlander]

calculator and/or normal multiplication totally prawns your Easy Multiplication imo

 

[tris-]

what if your stranded on a desert island with no calculator and you need to work
0.2345E-12 x 657.5 E46
?

 

[Kronic]

This is the best way of doing it:
example 1
33*150

...........100..........50
30........3000 + 1500 = 4500
3...........300 + 150 = 450
..................................+
...................................=4950

i.e
100*30=3000
50*30= 1500
100*3= 300
50*3= 150
...........=4950


example 2

562* 658
..............600........50............8
500.......300000 + 25000 + 4000.......=329000
.60.........12000 + 3000 + 480..........=15480
...2..........1200 + 100 + 16.............=1316
....................................................+
....................................................=345796



Tris write the full line up of numbers to 0.2345E-12 x 657.5 E46 and i see what i can come up with.


Kronic

 

[tris-]

lol, why dont you write it kronic? there is too much room for error writing numbers that big and small.

i can tell you the answer though, is

1.5418375E36

good luck!

 

[Jeriraa]

Aye, still don't think it's a rule which can be broken Just something strange I was told one day.

What you are doing is almost binary multiplication. Its flawed thou.

Correctly you do it like this: You turn a multiplication into a number of smaller multiplications by powers of 2 and add these up.

Example

7 x 10 = 70

Decimal we do this:
4 x 10 = 40
2 x 10 = 20
1 x 10 = 10

40 + 20 + 10 = 70

As you can see we simply split the 7 into powers of 2 (1 + 2 + 4 = 7), then multiplied the bits with 10 and added them up again.


Now binary: A multiplication by 2 is done by shifting left. (Take the most left number off and add a 0 to the right.)

So we want to do 00000111 x 00001010.
You do it by taking the 2nd operator and for each bit set in the 1st operator you shift it left according to the position of the set bit. (Sounds complicated - really isnt.)

00000111 -> shift left twice (yeah its the 3rd bit but you count them from 0-7)

00000111 -> 00101000
00000111 -> 00010100
00000111 -> 00001010

Then we add them up and we are done: 01000110

 

[Wyst]

For the purpose of this exercise, I'm going to use 33 x 150. You write them down, one next to the other and you start off by Halving the first number. It generally works best if you have the smaller number first When you halve the number, you IGNORE any decimal point...it doesn't matter if it is 5.5, get rid of that half. So you have this:

33
16.5 ---> 16
8
4
2
1

You note that you have halved the number 5 times so with the other number, you DOUBLE it 5 times.

You will then have:

33 150
16 300
8 600
4 1200
2 2400
1 4800

From this point, you then have to cross out and ignore any of the lines by which the number on the left hand side is EVEN so you're simply left with

1 4800.


So... 32x150 = 33x150

=> 32 = 33

Hmmm... something seems a bit wrong

Edit: I hope Ezteq didn't read this before her maths exam!!!!

Actually this does work as you forgot to add in the first line where 33 is not an even number so 150 + 4800 = 4950 which is correct, so the flaw in your example to disprove the theory is actually in your reading and understanding of the rules. Sorry <hides from the backlash of smartass replies>

 

[evzy]

Surely everyone on this thread is using a PC to post...and don't they have an inbuilt calcumelator anyway? And anyone who trolls O-T is never gonna be more than 2 foot from their pc at any given moment of teh day.

 

[Meduza]

What you are doing is almost binary multiplication. Its flawed thou.

Correctly you do it like this: You turn a multiplication into a number of smaller multiplications by powers of 2 and add these up.

Example

7 x 10 = 70

Decimal we do this:
4 x 10 = 40
2 x 10 = 20
1 x 10 = 10

40 + 20 + 10 = 70

As you can see we simply split the 7 into powers of 2 (1 + 2 + 4 = 7), then multiplied the bits with 10 and added them up again.


Now binary: A multiplication by 2 is done by shifting left. (Take the most left number off and add a 0 to the right.)

So we want to do 00000111 x 00001010.
You do it by taking the 2nd operator and for each bit set in the 1st operator you shift it left according to the position of the set bit. (Sounds complicated - really isnt.)

00000111 -> shift left twice (yeah its the 3rd bit but you count them from 0-7)

00000111 -> 00101000
00000111 -> 00010100
00000111 -> 00001010

Then we add them up and we are done: 01000110

In the early days i was programming assembler on the C64... there was no command for multiplication, so if u needed that, u actually had to make a procedure urself... ur example just brought back those old and long forgotten memories, ty (easier now on x86... ie its just: MOV AL, 10 | MOV DL, 7 | MUL DL | Result: AX = 70)

man, the countless hours ive spend making a procedure for division on C64... argghhh

 

[Jeriraa]

man, the countless hours ive spend making a procedure for division on C64... argghhh

At university I once had the task to construct a basic cpu... hardcoding the multiplication was evul. But the solution I came up with was the fastest of all given by the class.

 

[Meduza]

At university I once had the task to construct a basic cpu... hardcoding the multiplication was evul. But the solution I came up with was the fastest of all given by the class.

U also tried making a division one? I found the multiplcation part tricky... but the division one was waaay harder and surely have shorten my life by severel years due to frustration

 

[Ezteq]

rofl im soo glad i didnt see this thread before my exam it would have sent me running, but its really good stuff i just am a bit doubtful as to weather or not i could do it lol.

 

[Rhori]

For the purpose of this exercise, I'm going to use 33 x 150. You write them down, one next to the other and you start off by Halving the first number. It generally works best if you have the smaller number first When you halve the number, you IGNORE any decimal point...it doesn't matter if it is 5.5, get rid of that half. So you have this:

33
16.5 ---> 16
8
4
2
1

You note that you have halved the number 5 times so with the other number, you DOUBLE it 5 times.

You will then have:

33 150
16 300
8 600
4 1200
2 2400
1 4800

From this point, you then have to cross out and ignore any of the lines by which the number on the left hand side is EVEN so you're simply left with

1 4800.


So... 32x150 = 33x150

=> 32 = 33

Hmmm... something seems a bit wrong

Edit: I hope Ezteq didn't read this before her maths exam!!!!

from 5.5 to 5.9 will be shortened to 6, 5.4 to 5.1 to 5
so then it'll be 17 not 16

 

[Jeriraa]

U also tried making a division one? I found the multiplcation part tricky... but the division one was waaay harder and surely have shorten my life by severel years due to frustration

Nah, we had only 30 hours in total so they spared us that one.

 

[DrunkSkunk]

from 5.5 to 5.9 will be shortened to 6, 5.4 to 5.1 to 5
so then it'll be 17 not 16

When you halve the number, you IGNORE any decimal point...it doesn't matter if it is 5.5, get rid of that half.

ignore, not shorten!

 

[Straef]

what if your stranded on a desert island with no calculator and you need to work
0.2345E-12 x 657.5 E46
?

You could draw the numbers in the sand, then whipe away the bottom half of the numbers, and if you can manage to read the top half, there's the answer!

 

[Rhori]

When you halve the number, you IGNORE any decimal point...it doesn't matter if it is 5.5, get rid of that half.

ignore, not shorten!

doh missed that

[edit]

what if your stranded on a desert island with no calculator and you need to work
0.2345E-12 x 657.5 E46
?

quite easy since you have to ignore the decimal, it'll be: 0E-12 x 657 E46= 0 xD

 

[tris-]

lol that sucks, missing the decimal can kiss my ass. the answer isnt 0. so this method isnt altogether perfect.

more like 1.5E36

 

[Gogge^^]

fook, this treads make no sense to me ::eek2:

 

[Ilienwyn]

Why do all that? Multiplying would be much faster than that

 

[tris-]

it doesnt matter, if you ignore halfs on the origional number then i think this method can be flung into the furnace.

you cant even get estimate something if you throw away the half. lol.

 

[kirennia]

It's for whole number multiplication I think. I'm pretty sure it can be easily adapted though so it'll work for numbers with decimal values

I don't know exactly whether this'd work but when you start, if there is a decimalled number, multiply the number by a multiple of 10 enough times until it is a whole number. Note the number you had to multiply your decimalled number by. Then after doing the multiplication, simply knock the decimal point back however many times you had to multiply the initial numbers by 10.

Test:

0.001 x 45 The answer is of course 0.045 but lets try with the above method.

0.001 = 1x1000. So you note down a thousand.
1x45 = 45.
Then you have to knock the decimal point back 3 places to get 0.045


Test2:

0.365x7.940
The first number will have to be x1000 and the second number by 100. Multiply these and you've got 100000. So push the decimal point back 5 places
365 794
182 1588
91 3176
45 6352
22 12704
11 25408
5 50816
2 101632
1 203264

Work it out as before using only the odd number lines

365 794
91 3176
45 6352
11 25408
5 50816
1 203264

Add up the right numbers...blergh, wont use a calculator I promise

289810 if I've added them up right. Then push the decimal back 5 places and you've got 2.89810.

/em checks calculator

It's right Okay so it isn't exactly the easiest of ways to multiply something but it's not open to much human error as long as you're confident with adding up. Tsk tsk to non-beleivers!

 

[Rhori]

For the purpose of this exercise, I'm going to use 33 x 150. You write them down, one next to the other and you start off by Halving the first number. It generally works best if you have the smaller number first When you halve the number, you IGNORE any decimal point...it doesn't matter if it is 5.5, get rid of that half. So you have this:

33
16.5 ---> 16
8
4
2
1

You note that you have halved the number 5 times so with the other number, you DOUBLE it 5 times.

You will then have:

33 150
16 300
8 600
4 1200
2 2400
1 4800

From this point, you then have to cross out and ignore any of the lines by which the number on the left hand side is EVEN so you're simply left with

1 4800.


So... 32x150 = 33x150

=> 32 = 33

Hmmm... something seems a bit wrong

Edit: I hope Ezteq didn't read this before her maths exam!!!!

found what you did wrong

let's use the same numbers

33 150
16 300
8 600
4 1200
2 2400
1 4800

From this point, you then have to cross out and ignore any of the lines by which the number on the left hand side is EVEN so you're simply left with

33 150
1 4800

which makes 4950

 

[Jupitus]

Doh!

Oh yeah!!!

 

[Meduza]

Tsk tsk to non-beleivers!

Its not becuz we r non-believers... Its becuz ur a girl...

If a dude posted it, we all would have said: Wow! - and not questioned it