Fractions in Simplest Form - When?Date: 11/29/2001 at 12:07:27 From: Krista Subject: Fractions Should fractions always be reduced to their simplest form? Why or why not? Date: 11/29/2001 at 12:25:02 From: Doctor Ian Subject: Re: Fractions Hi Krista, Whether you should reduce a fraction to its simplest form depends on what you want to do with it. For example, if you have a bunch of lengths, 1/2, 3/4, 6/16, 11/32 are they easier to compare if you reduce them, or if you convert them all to have a common denominator? 16/32, 24/32, 12/32, 11/32 You may have noticed that road signs often follow a sequence like this: 1/10 mile 2/10 mile 3/10 mile 4/10 mile 5/10 mile Would it be clearer if they read like this? 1/10 mile 1/5 mile 3/10 mile 2/5 mile 1/2 mile For the most part, there are two potential advantages to reducing fractions: 1. After you work with some common fractions a lot, you start to remember their decimal equivalents, e.g., 1/2 = 0.5 = 50% 1/3 = 0.333... ~ 33% 1/4 = 0.25 = 25% 1/5 = 0.20 = 20% 1/8 = 0.125 = 12.5% So if you end up reducing a fraction to something with one of these denominators, it may simplify later steps of whatever problem you're trying to solve. 2. If you're trying to compare answers with someone else (for example, a fellow student, a colleague, a teacher, an automatic grading machine), reducing fractions can help avoid miscommunications. There are infinitely many ways to express any fraction; but there is only one simplest form. But as we've seen, these advantages may not apply in a given situation. As with most things, there is no hard-and-fast rule that you can follow all the time. You have to use some judgment. Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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