Rounding Fractions to the Nearest Half or WholeDate: 01/10/2003 at 01:04:01 From: Michelle Subject: Rounding fractions to the nearest half or whole? How do you round fractions to the nearest half or whole? I don't understand how you can tell what the fraction needs to be rounded to. What do you look for to know whether it goes up or down? 9 1/4 6 2/15 11/15 The example shown was 9/16 rounds to 1/2. Why? 1/14 rounds to 0. Why? Date: 01/10/2003 at 08:55:07 From: Doctor Peterson Subject: Re: Rounding fractions to the nearest half or whole? Hi, Michelle. Here is a number line containing 9/16: |<-+------------------->| | | | 0 1/2 | 1 +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 I've indicated the fact that 8/16 is the same as 1/2, and I've located 9/16 on the line. Note that 9/16 is between 1/2 and 1, and is closer to 1/2 than to 1; so the nearest half is 1/2. Now, how could you determine that without drawing the number line? One way is to first consider how many 16ths is 1/2; that is 1/2 of 16, or 8 16ths. Now compare 9 with 8, and see that it is greater; so 9/16 is greater than 1/2. That puts it between 1/2 and the next whole, namely 1. Which is closer? Just compare the difference 9-8 = 1 with the difference 16-9 = 7. That is, 9/16-8/16 = 1/16, while 16/16 - 9/16 = 7/16. Since 1 < 7, 9/16 is closer to 1/2. You can do the same with each of your problems. 1/14 is between 0 and 7/14 = 1/2, and is closer to 0. When you have a mixed number, you can ignore the whole part while you are making this decision. When you have an odd denominator, 1/2 will not be a whole number of them; 1/2 is equal to 7 1/2 15ths, for example. But you can still do all the same work: 2/15 is less than 7 1/2 15ths, so 6 2/15 is between 6 and 6 1/2. Which is closer? The hard case is 9 1/4. You will find that 1/4 is exactly between 0 and 1/2, so it is a tossup whether to round up or down. I don't think there is a standard rule to decide this, as there is when rounding to a whole number, but you might as well follow a rule like the one usually taught in school, and always round up when you are exactly between. Then 9 1/4 will round up to 9 1/2. 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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