Converting Between Mixed Numbers and Improper FractionsDate: 04/08/99 at 18:31:46 From: Linday Stahl Subject: Undoing improper fractions I get mixed up doing and undoing improper and mixed numbers. Date: 04/08/99 at 23:16:02 From: Doctor Peterson Subject: Re: Undoing improper fractions Hi, Linday. Let's take a simple example: What is 1 1/2 as an improper fraction? We can picture it as a box and half a box: +-------+ +-------+ | | | | | | +-------+ | | +-------+ If we turn the whole into halves, there are two halves there, plus the extra half makes 3: +-------+ +-------+ | | | | +-------+ +-------+ | | +-------+ What we've just done is to rewrite 1 as 2/2, then add 2/2 + 1/2 to get 3/2. In general, you multiply the whole part by the denominator, then add the numerator of the fraction part. One way to think of this is that you start at the "bottom" and move clockwise around the mixed number, multiplying by the whole, then adding the numerator: +--------+ | | | + 1 +-> 2 x 1 + 1 = 3 | 1 --- --- | x 2 ----------------> 2 | | | +----+ To go the other way, let's start with the 3/2. How many wholes can we make out of 3 halves? Just divide the 3 by 2, because it takes 2 halves to make each whole; we get 1 with a remainder of 1. That means there is one whole, and 1 half left over: +--------------+ | | | __1_rem 1 | 2 ) 3 --- | -2 2 <--+ So you just use the denominator (divisor) as the denominator with the remainder as the numerator. If you have any specific problems you need help with, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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