Dividing a Fraction by a Fraction
Date: 08/11/97 at 23:18:44 From: Chris Tafoya Subject: Dividing a fraction by a fraction Dr. Math, The cookie scenario below is an excellent example to visualize why dividing a whole number by a fraction causes the answer to be larger than the original whole number. But what about dividing a fraction by a fraction? The scenario becomes incomprehensible when the "5 cookies" become a half a cookie. Do you have another example/scenario that can help students visualize a problem such as: 1/3 / 1/2 = 2/3 The abstract concepts have been explained tremendously. Is there a concrete way? If I have a third of a pie, and I want to divide that third of a pie by 1/2, why does the answer become 2/3 of the pie?? Thanks, Chris "from the old school" Tafoya
Date: 03/21/97 at 04:19:54 From: Doctor Mitteldorf Subject: Re: Divide by a Fraction Dear Tim, Lots of people find this confusing. If you divide 5 by 2, the answer is 2.5. If you divide 5 by 1/2, do you expect the same thing as dividing by 2? If you divide by a number bigger than 1, it always reduces the number. If you divide by 1, it doesn't change anything. Does that make you think that dividing by a fraction less than 1 should INCREASE the number? How many kids can you serve with 5 cookies if each kid gets 2 cookies? You can serve 2 kids (with enough left over for 1/2 a kid). How many kids can you serve with 5 cookies if each kid gets 1/2 a cookie? That's 5 divided by 1/2. -Doctor Mitteldorf, The Math Forum Check out our web site!
Date: 08/12/97 at 04:27:50 From: Doctor Mike Subject: Re: Dividing a fraction by a fraction >1/3 / 1/2 = 2/3 Maybe you could think about it this way. For the 5/2 = 2.5 you could think of how many 2-cookie servings you can make out of 5 cookies. You get two full 2-cookie servings plus half of a 2-cookie serving. For the 5/half = 10 you could think of how many half-cookie servings you could get out of 5 cookies. For the (1/3)/(1/2) = 2/3 it's probably clearer to write it as (2/6)/(3/6) = 2/3 and ask how times you could get a (3/6)-cookie serving out of 2/6 of a cookie. You can't! You get **zero** (3/6)-cookie servings. But you can get PART OF A (3/6)-cookie serving. In fact you get exactly "two thirds of a (3/6)-cookie serving. I'll leave it up to you to decide whether what I just said is incomprehensible. It may be clearer to keep it (1/3)/(1/2) = 2/3. Then say, "how many cookie-halves can you get out of a third of a cookie?" The answer would then be, "You can't get ANY cookie- halves out of a third of a cookie, BUT you CAN get two thirds of a cookie-half from a third of a cookie. WE NEED MORE COOKIES! -Doctor Mike, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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