Comments on Dividing Fractions
Date: 03/15/2007 at 18:55:16 From: Tiffany Subject: Is there a much simpler term in dividing fractions? I was reading your posts on how to divide fractions and it took me a while to understand. It's basically multiplying and find the reciprocal right? My teacher told me you can use the KCF to help. KCF stands for "Keep it. Change it. Flip it." ex. 4/5 divided by 1/5 K C F 4/5 / 1/5 4/5 x 5/1 = 4 We can still use that too, right?
Date: 03/15/2007 at 20:09:01 From: Doctor Peterson Subject: Re: Is there a much simpler term in dividing fractions? Hi, Tiffany. You didn't say which page(s) you read; sometimes we explain things the long way in order to talk about why we do something, rather than just tell you quickly what to do. We usually avoid just giving mnemonics like your KCF, but there's nothing wrong with it. It's merely a very short way to say the same thing we say. My own "quick version", which is more in line with the way mathematicians like to think, is this: "division is defined as multiplication by the reciprocal". That is, a / b = a * 1/b So, to divide a by b, we multiply a by the reciprocal of b, which means exactly what your teacher says: we "change" the operation from multiplication to division, and we "flip" the divisor to use its reciprocal. Similarly, I've heard subtraction explained as KCC, or "Keep Change Change", meaning that you change the subtraction to an addition, and change the sign of the second number (the subtrahend). The mathematician's version of that one is that subtraction is defined as addition of the negative (additive inverse). That is, a - b = a + -b So really, subtraction and division are just addition and multiplication with the second operand "inverted" in an appropriate way. I rarely hear anyone point out the similarity of the two rules (or definitions), but I think it's very useful to see it. If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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