Comments on: Mental Math Shortcuts http://betterexplained.com/articles/mental-math-shortcuts/ Learning shouldn't hurt. Let's share the insights that made difficult ideas click. Wed, 08 Sep 2010 10:32:31 +0000 http://wordpress.org/?v=2.8.4 hourly 1 By: jay http://betterexplained.com/articles/mental-math-shortcuts/#comment-308533 jay Mon, 23 Aug 2010 11:16:34 +0000 http://betterexplained.com/articles/mental-math-shortcuts/#comment-308533 very nice!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! very nice!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

]]> By: Anonymous http://betterexplained.com/articles/mental-math-shortcuts/#comment-307947 Anonymous Mon, 09 Aug 2010 00:29:39 +0000 http://betterexplained.com/articles/mental-math-shortcuts/#comment-307947 hai hai

]]> By: Mitch http://betterexplained.com/articles/mental-math-shortcuts/#comment-306382 Mitch Fri, 18 Jun 2010 08:12:29 +0000 http://betterexplained.com/articles/mental-math-shortcuts/#comment-306382 Just thought of something else, sorry, I'm new here. Over the years, i always wondered how 1 square foot equaled 144 square inches. I realized not only were the measurements squared, but so were their proportions. This lead to a discovery of "dimensional scaling" i call it. -If one square has half the width AND height of another, its area is (1/2 * 1/2)= (1/2)^2= 1/4 the area of the other, yet a cube with half dimensions would be (1/2 * 1/2 * 1/2)= (1/2)^3= 1/8 the volume. Notice the pattern? The space occupied (area, volume, etc.) of a relative object is the (space occupation of the reference object) * (scale^dimensions). -This works for circles and spheres when you consider the dimensional occupation of the object first (circles: dimensions=2). -It can also apply to varying scales: a cube with width/2, height/3, depth/4 equals (whd)(1/2)(1/3)(1/4). I really hopes this helps, it allowed me to answer an ACT question faster and easier. Just thought of something else, sorry, I’m new here. Over the years, i always wondered how 1 square foot equaled 144 square inches. I realized not only were the measurements squared, but so were their proportions. This lead to a discovery of “dimensional scaling” i call it.

-If one square has half the width AND height of another, its area is (1/2 * 1/2)= (1/2)^2= 1/4 the area of the other, yet a cube with half dimensions would be (1/2 * 1/2 * 1/2)= (1/2)^3= 1/8 the volume. Notice the pattern? The space occupied (area, volume, etc.) of a relative object is the (space occupation of the reference object) * (scale^dimensions).
-This works for circles and spheres when you consider the dimensional occupation of the object first (circles: dimensions=2).
-It can also apply to varying scales: a cube with width/2, height/3, depth/4 equals (whd)(1/2)(1/3)(1/4).

I really hopes this helps, it allowed me to answer an ACT question faster and easier.

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