Converting a Long Decimal to a FractionDate: 04/11/2002 at 12:22:02 From: Linda Popovich Subject: Converting long decimal to fraction If I have 74/13 and I want to reduce it to a mixed number, I know that when I divide 74 by 13 I get a long mixed decimal, 5.6923076. My answer book says that the answer is 5 9/13. How do I get from 5.6923076 to 5 9/13? Thanks. Date: 04/11/2002 at 13:09:54 From: Doctor Peterson Subject: Re: Converting long decimal to fraction Hi, Linda. It's better to avoid the decimals if you are just converting to a mixed number. Instead of dividing to get a decimal answer, divide to get a whole quotient and remainder: ___5_r_9 13 ) 74 65 -- 9 The remainder is the number of extra 13ths that don't form a whole, so the answer is 5 9/13. Now, if you are doing this with a calculator, you have to use decimals, because most calculators don't know about fractions. To get the remainder, just multiply the decimal part by the denominator: 13 * .6923076 = 9 (Your calculator may give a number very close to 9 because it's missing digits, and you will have to round to the nearest whole number.) This tells you how many 13ths there are in .6923076. This is a special kind of decimal-to-fraction conversion that you can use when you know the denominator you want. On my Windows calculator in Scientific mode, there is a "mod" key which finds the remainder. If I press "74 mod 13" I get 9, which is the numerator for the fractional part. For more on converting improper fractions to mixed numbers, see our archives: Fractions - Elementary Level http://mathforum.org/library/drmath/sets/elem_fractions.html - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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