Cool math shortcuts

[Homer]

Heh, that's pretty cool. I never read that post since it was the last in the thread.

<font color="white">Alright, that's a lie. The minute I saw your post I decided to wait 3 months and claim the idea as my own to ascend to my rightful throne as lord of the OOT math nerds.</font>

[tbach24]

That triangle with all the numbers is pretty cool. Pretty useful too

[lu_hawk]

you can take a common way to solve squares and go one step further and make it easy to multiply numbers that aren't the same but are close to each other using an anchor. for example, to square 47 you square 50 to get 2500, subtract 3*100, and then add 9. so you get 2209. and you used the formula:

x^2 = a^2 + (x-a)(2a) - (x-a)^2

'a' can be anything but you pick a multiple of 10 to make it easy to do in your head. someone else referred to the way feynman described how to do squares near 50 in your head and this is feynman's way, but describing it in this formula shows that the number doesn't need to be near 50. so for example, to get the square of 38 in your head:

40^2=1600
subtract 2*80=160 and you get 1440
add 2^2=4 and you get 1444

but the formula above is specific to squares you can go back a step and make it easy to multiply numbers that are close but not the same. so if you want to multiply x times y, and 'a' is your anchor number:

x*y = a^2 + (x-a)*a + (y-a)*a + (x-a)(y-a)

yes this seems complicated but it's the same as feyman's way of squaring but you just add 2 steps. so to multiply 48*45 in your head:

50^2=2500
subtract 2*50=100 and get 2400
subtract 5*50=250 and get 2150
add 2*5=10 and get 2160.

it might take some practice but this is the best way i have found, and after awhile you don't have to think about it too much.

[mmbt0ne]

Mulitply any 2-digit number ab by 11 and it's a(b+a)b

Example:

12*11 = 1(1+2)2 = 132
17*11 = 1(1+7)7 = 187
39*11 = 3(3+9)9 = 429

[Luzion]

Heres an easy way to add up a sequence of numbers. For example, lets say from 1 to 100.
1 + 2 + 3 + 4 + 5 + 6 ..... + 100 = ?

The sum of the first and last number, which is 1 + 100 = 101.
The sum of the second and second to last number, which is 2 + 99 = 101.
The sum of the third and third to last number, which is 3 + 98 = 101.

Get the pattern? Summation of two numbers that equal 101 occurs 50x in this sequence. 1+100, or 2+99, or 3+98, or 4+97, or 5+96...

1 + 2 + 3 + 4 + 5 + 6 + 7 .... + 100 = 101 x 50 = 5050

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 11 x 5 = 55

Summation of

1 to 1000 = 1001 x 500 = 50050
17 to 9862 = 9879 x 4923 = 48,634,317

Its a neat idea, and could be fairly useful...

[Jazza]

most of you know the shortcuts for figuring out if a whole number is divisible by:

2 - if it's even
3 - if the sum of the digits is divisble by 3
4 - if the last two digits are divisible by 4
5 - if the last digit is 0 or 5
6 - if it's divisible by 2 and 3 (duh)
8 - if the last 3 digits are divisible by 8
9 - if the sum of the digits is divisible by 9

but no one ever told me one for 7, and i thought that was bullshit, so i found it myself:

write the number in question backwards

under this number write the number 132645132645132645...

now multiply each digit with the number below it, then add them all together

if this number is divisible by 7, then the original is

so, lets say you wanted to know if 27351223 was divisible by 7, well...

2*1+7*3+3*2+5*6+1*4+2*5+2*1+3*3=84, and 84 is divisible by 7, so 27351223 is divisible by 7

also not that you can't figure out if your new number is divisible by 7, repeat the procss:

4*1+8*3=28 which is divisible by 7, so 84 is too

this methods kinda blows though, it's not as easy as the other ones, which is probably why they don't teach it

[jason_t]

[ QUOTE ]
Heres an easy way to add up a sequence of numbers. For example, lets say from 1 to 100.
1 + 2 + 3 + 4 + 5 + 6 ..... + 100 = ?

The sum of the first and last number, which is 1 + 100 = 101.
The sum of the second and second to last number, which is 2 + 99 = 101.
The sum of the third and third to last number, which is 3 + 98 = 101.

Get the pattern? Summation of two numbers that equal 101 occurs 50x in this sequence. 1+100, or 2+99, or 3+98, or 4+97, or 5+96...

1 + 2 + 3 + 4 + 5 + 6 + 7 .... + 100 = 101 x 50 = 5050

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 11 x 5 = 55

Summation of

1 to 1000 = 1001 x 500 = 50050
17 to 9862 = 9879 x 4923 = 48,634,317

Its a neat idea, and could be fairly useful...

[/ QUOTE ]

Good job Gauss.

[Luzion]

[ QUOTE ]
[ QUOTE ]
Heres an easy way to add up a sequence of numbers. For example, lets say from 1 to 100.
1 + 2 + 3 + 4 + 5 + 6 ..... + 100 = ?

The sum of the first and last number, which is 1 + 100 = 101.
The sum of the second and second to last number, which is 2 + 99 = 101.
The sum of the third and third to last number, which is 3 + 98 = 101.

Get the pattern? Summation of two numbers that equal 101 occurs 50x in this sequence. 1+100, or 2+99, or 3+98, or 4+97, or 5+96...

1 + 2 + 3 + 4 + 5 + 6 + 7 .... + 100 = 101 x 50 = 5050

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 11 x 5 = 55

Summation of

1 to 1000 = 1001 x 500 = 50050
17 to 9862 = 9879 x 4923 = 48,634,317

Its a neat idea, and could be fairly useful...

[/ QUOTE ]

Good job Gauss.

[/ QUOTE ]

well hey, no one ever said it was an original shortcut... [img]/images/graemlins/grin.gif[/img]

[jason_t]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
Heres an easy way to add up a sequence of numbers. For example, lets say from 1 to 100.
1 + 2 + 3 + 4 + 5 + 6 ..... + 100 = ?

The sum of the first and last number, which is 1 + 100 = 101.
The sum of the second and second to last number, which is 2 + 99 = 101.
The sum of the third and third to last number, which is 3 + 98 = 101.

Get the pattern? Summation of two numbers that equal 101 occurs 50x in this sequence. 1+100, or 2+99, or 3+98, or 4+97, or 5+96...

1 + 2 + 3 + 4 + 5 + 6 + 7 .... + 100 = 101 x 50 = 5050

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 11 x 5 = 55

Summation of

1 to 1000 = 1001 x 500 = 50050
17 to 9862 = 9879 x 4923 = 48,634,317

Its a neat idea, and could be fairly useful...

[/ QUOTE ]

Good job Gauss.

[/ QUOTE ]

well hey, no one ever said it was an original shortcut... [img]/images/graemlins/grin.gif[/img]

[/ QUOTE ]

Gauss came up with it when he was five.

[gumpzilla]

[ QUOTE ]

Gauss came up with it when he was five.

[/ QUOTE ]

I wonder if this story is apocryphal or not. But at any rate, if this is the old Gauss learns his teacher good, he was ten, I believe.