Cool math shortcuts
 

While teaching some boring Algebra stuff today (FOIL and factoring) I came up with a math shortcut that I thought was kind of cool. Anyway, one problem was to expand (x-2)(x+2) (it is x^2 - 2x + 2x - 4, or x^2 - 4). My brain started to wander and I was thinking that means x^2 = (x-2)(x+2) + 4. So, if you wanted to square a number like 98, you could do 100*96, then add 4 to get 9604. In fact, you could generalize the formula:

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

So, if you wanted to square 94, you could make a = 6 and do 100*88 + 36 = 8836.

Anyway, does anyone know of any other shortcuts like this or of a book I could get to learn how to solve problems more quicky in my head. It doesn't really serve any purpose other than to entertain myself, but I'm curious if there is something like this out there.

Re: Cool math shortcuts
 

That's fairly cool, actually.

Re: Cool math shortcuts
 

[ QUOTE ]
While teaching some boring Algebra stuff today (FOIL and factoring) I came up with a math shortcut that I thought was kind of cool. Anyway, one problem was to expand (x-2)(x+2) (it is x^2 - 2x + 2x - 4, or x^2 - 4). My brain started to wander and I was thinking that means x^2 = (x-2)(x+2) + 4. So, if you wanted to square a number like 98, you could do 100*96, then add 4 to get 9604. In fact, you could generalize the formula:

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

So, if you wanted to square 94, you could make a = 6 and do 100*88 + 36 = 8836.

Anyway, does anyone know of any other shortcuts like this or of a book I could get to learn how to solve problems more quicky in my head. It doesn't really serve any purpose other than to entertain myself, but I'm curious if there is something like this out there.

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square 37 for me using your shortcut

Re: Cool math shortcuts
 

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While teaching some boring Algebra stuff today (FOIL and factoring) I came up with a math shortcut that I thought was kind of cool. Anyway, one problem was to expand (x-2)(x+2) (it is x^2 - 2x + 2x - 4, or x^2 - 4). My brain started to wander and I was thinking that means x^2 = (x-2)(x+2) + 4. So, if you wanted to square a number like 98, you could do 100*96, then add 4 to get 9604. In fact, you could generalize the formula:

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

So, if you wanted to square 94, you could make a = 6 and do 100*88 + 36 = 8836.

Anyway, does anyone know of any other shortcuts like this or of a book I could get to learn how to solve problems more quicky in my head. It doesn't really serve any purpose other than to entertain myself, but I'm curious if there is something like this out there.

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square 37 for me using your shortcut

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Was waiting for this.

Re: Cool math shortcuts
 

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[ QUOTE ]
While teaching some boring Algebra stuff today (FOIL and factoring) I came up with a math shortcut that I thought was kind of cool. Anyway, one problem was to expand (x-2)(x+2) (it is x^2 - 2x + 2x - 4, or x^2 - 4). My brain started to wander and I was thinking that means x^2 = (x-2)(x+2) + 4. So, if you wanted to square a number like 98, you could do 100*96, then add 4 to get 9604. In fact, you could generalize the formula:

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

So, if you wanted to square 94, you could make a = 6 and do 100*88 + 36 = 8836.

Anyway, does anyone know of any other shortcuts like this or of a book I could get to learn how to solve problems more quicky in my head. It doesn't really serve any purpose other than to entertain myself, but I'm curious if there is something like this out there.

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square 37 for me using your shortcut

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40*34 + 9 equals I think 1369. I guess your point is that it doesn't always make things much easier and you're right. It just got me thinking about possible shortcuts of which I am unaware.

Re: Cool math shortcuts
 

Unless I'm missing something>

I'd make a = 3 to square 37, so 34*40 + 9 = 1369.

Thanks Homer!

edit: Homer responded the same time I did, but I think that 34*40 + 9 (basically 34*4 + 9) is easier to do quickly in your head than 37*37.

Re: Cool math shortcuts
 

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square 37 for me using your shortcut

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a = 3. 40 x 34 = 340 x 4 = 1360. 1360 + 9 = 1369.

GoT

Re: Cool math shortcuts
 

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While teaching some boring Algebra stuff today (FOIL and factoring) I came up with a math shortcut that I thought was kind of cool. Anyway, one problem was to expand (x-2)(x+2) (it is x^2 - 2x + 2x - 4, or x^2 - 4). My brain started to wander and I was thinking that means x^2 = (x-2)(x+2) + 4. So, if you wanted to square a number like 98, you could do 100*96, then add 4 to get 9604. In fact, you could generalize the formula:

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

So, if you wanted to square 94, you could make a = 6 and do 100*88 + 36 = 8836.

Anyway, does anyone know of any other shortcuts like this or of a book I could get to learn how to solve problems more quicky in my head. It doesn't really serve any purpose other than to entertain myself, but I'm curious if there is something like this out there.

[/ QUOTE ]
square 37 for me using your shortcut

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Was waiting for this.

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It still works and serves its purpose of making it such easier to do in your head. Normally if I had to do this in my head I'd do 900 + 210 + 259, but Homer's way is much faster and simpler.

GoT

Re: Cool math shortcuts
 

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square 37 for me using your shortcut

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use a = 13

50*24 + 169 = 1369

EDIT: i picked 13 because 50*24 is instantaneous whereas i'd have to think a little about 40*34

Re: Cool math shortcuts
 

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Anyway, does anyone know of any other shortcuts like this or of a book I could get to learn how to solve problems more quicky in my head. It doesn't really serve any purpose other than to entertain myself, but I'm curious if there is something like this out there.

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I want a book also or a website that has examples of math systems. Years ago I knew a cool system using visual place holders ect. it was simple but had it's uses. I will try to find it when I have more time.