Putting Fractions in OrderDate: 01/24/2001 at 22:32:09 From: Mat Subject: Ordering fractions Dear Dr. Math, I am trying to order fractions from least to greatest, but am having no luck. Could you please give me a hand? Your friend, Mat Date: 01/25/2001 at 08:29:35 From: Doctor Rick Subject: Re: Ordering fractions Hi, Mat. Which is greater, two quarters or four dimes? You solve this by converting each to cents: two quarters are 50 cents, and four dimes are 40 cents, so two quarters are greater. You compare fractions the same way: convert each fraction to a common denominator. The thing that makes it a little harder than comparing money is that, with money, you always know you can choose a common denominator (or denomination) of 1 cent (1/100 dollar). With fractions, you first need to decide what denominator you can use. Which is greater, 4/5 or 3/4? You can choose a common denominator of 20, the product of the two denominators (5*4). This will always work, though it may not be the LEAST common denominator, so you may have bigger numbers to work with than necessary. Convert 4/5 to 20ths: the denominator 20 is four times the denominator 5, so you multiply the numerator 4 by 4, as well: 4/5 = (4*4)/(5*4) = 16/20 Convert 3/4 to 20ths: the denominator 20 is 5 times the denominator 4, so you multiply the numerator 3 by 5, as well: 3/4 = (3*5)/(4*5) = 15/20 Now, which is greater: 16/20 or 15/20? You just have to compare numerators, since the denominators are the same. Since 16 > 15, you know that 16/20 > 15/20, so 4/5 > 2/3. (In case you haven't seen it before, > means "is greater than.") If you need to order three or more fractions, you can either put them all over a common denominator, or compare two at a time. If you choose the first approach, you will probably want to work with LEAST common denominators, because otherwise you could end up with some really big numbers. If you have a particular problem you'd like us to walk through with you, we'd be happy to do so. - Doctor Rick, The Math Forum http://mathforum.org/dr.math/ |
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