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Actually, a helper ... Finding a Fraction of Something?
I don't know if anyone knows about this. But I thought up this method of finding a fraction of something in a simple way.
Say you want to find 3/7 of 84. Well, it's 36.
I'll tell you a quick and easy way, the way I do it, and it's like this:
You take the base number, which is 84 in this case. Then, you divide it by the denominator, which is 7. This actually gives you ONE-seventh of the base. Then, you multiply that answer (84/7 = 12, BTW) by the numerator, which is 3 in this case. That gives you THREE-sevenths of the base.
And the base/denominator doesn't have to divide evenly. You'll get the same decimal number you would if you worked it any other way.
I just thought I'd share this. And I am not calling anyone stupid. I just wanted to share this with everyone, and maybe someone will find it easier.
And yes, I will choose a "Best Answer" for this post. LoL. =)
5 Answers
- 2 decades agoFavorite Answer
Makes sense. Formally, 3 sevenths is 3 * (multiplicative inverse of 7). 84 = 7 * 12 so 3/7 * 84 = (3 * 7^(-1)) * (7 * 12) = 3 * (7^(-1) * 7) * 12 = 3 * 1 * 12 = 3 * 12 = 36.
That's why those multiplication rules for fractions of integers work.
a/b * c/d = a*b^(-1)*c*d^(-1) = a*c*(b^(-1)*d^(-1)) = a*c*(d*b)^(-1) = (a*c)/(b*d)
You can verify others as well with this definition. (See commutative groups, commutative rings, and fields for general abstractions.)
- 2 decades ago
it's almost the same thing. what you did was like this: (3X84)/7 then you divided the 84 by 7 first then multiplied it. what's great is that you made multiplying and dividing easier because of the small number you get from dividing 84 by 7. nice technique. good job!
- 2 decades ago
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....
...So...best answer? :D
^_^
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