Improper FractionsDate: 04/15/99 at 20:32:29 From: Priyana Kumar Subject: Fractions (Mixed number.....) Dear Dr. Math, I really need help on how to make an improper fraction into a mixed number. Date: 04/16/99 at 16:44:05 From: Doctor Peterson Subject: Re: Fractions (Mixed number.....) Hi, Priyana. Dr. Math to the rescue! Let's look at an improper fraction this way: I'll give you 53 blocks of wood, and tell you that each piece is 1/6 of a board. How many boards did I use to make them? +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ | 1 | | 7 | | 13| | 19| | 25| | 31| | 37| | 43| | 49| +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ | 2 | | 8 | | 14| | 20| | 26| | 32| | 38| | 44| | 50| +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ | 3 | | 9 | | 15| | 21| | 27| | 33| | 39| | 45| | 51| +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ | 4 | | 10| | 16| | 22| | 28| | 34| | 40| | 46| | 52| +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ | 5 | | 11| | 17| | 23| | 29| | 35| | 41| | 47| | 53| +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ | 6 | | 12| | 18| | 24| | 30| | 36| | 42| | 48| +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ I can divide 53 by 6 to find out how many boards I can make by putting the blocks back together in groups of 6: ___8_ 6 ) 53 48 -- 5 This says I can make 8 whole boards, using 8x6 = 48 of the pieces, and I'll have 5 blocks left. Since each block is 1/6 of a board, that means I've made 8 5/6 boards: +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ | | | | | | | | | | | | | | | | | | +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ | | | | | | | | | | | | | | | | | | +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ | | | | | | | | | | | | | | | | | | +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ | | | | | | | | | | | | | | | | | | +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ | | | | | | | | | | | | | | | | | | +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ | | | | | | | | | | | | | | | | +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ \_____________________________________________/ \___/ 8 boards = 48/6 5/6 The rule for changing an improper fraction into a mixed number is to divide the numerator by the denominator; the whole-number quotient is the whole number part of the answer, and the remainder is the numerator of the fraction part: +------------------------+ | | | 5 <--+ | | ___8_----> 8 --- | | 6 ) 53 6 <--|---+ 48 | -- | 5 --------------+ Another way to say it is that we find the largest multiple of 6 that is less than 53 (that's what dividing means), and change that part into a whole number: 53 48+5 48 5 5 -- = ---- = -- + --- = 8 --- 6 6 6 6 6 I hope that helps you make sense of mixed numbers. Here are some other explanations in our archives if you need more help: Fractions, Improper Fractions, Mixed Numbers http://mathforum.org/library/drmath/view/58069.html Converting Fractions to/from Mixed Numbers http://mathforum.org/library/drmath/view/58875.html Improper Fractions and Mixed Numbers http://mathforum.org/library/drmath/view/58936.html - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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