tag:blogger.com,1999:blog-30226356.post1903729877763924544..comments2024-02-16T23:32:12.073-08:00Comments on The Exponential Curve: Common Denominator DivisionDan Wekselgreenehttp://www.blogger.com/profile/08696028020767073620noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-30226356.post-29140461624796127272007-08-05T11:27:00.000-07:002007-08-05T11:27:00.000-07:00It looks to me like "invert and multiply" is reall...It looks to me like "invert and multiply" is really the same thing as CDD using the product of the denominators as the common denominator.<BR/><BR/>(a/b) / (c/d) = (ad/bd) / (bc/bd) = ad/bc<BR/><BR/>I suppose the advantage of "invert and multiply" is that it introduces the idea that division is the same as multiplying by the inverse.Adamhttps://www.blogger.com/profile/13524952709453904676noreply@blogger.comtag:blogger.com,1999:blog-30226356.post-83836805798317010732007-07-26T07:22:00.000-07:002007-07-26T07:22:00.000-07:00CDD was how I learned it when I was in 6th grade (...CDD was how I learned it when I was in 6th grade (1960-1961). The text used was "Arithmetic We Need" by Buswell, Brownell and Sauble, copyright 1955. After learning that, we went to invert and multiply and then did both for a while before abandoning CDD. Invert and multiply was introduced as a consequence of seeing the "pattern" of invert and multiply in other problems. Cutting 8 oranges into halves yields 16 halves, or 8 divided by 1/2 = 8 x 2. 8 divided by 2 is the same as 8 x 1/2. Dividing a half into two yields two quarters so 1/2 divided by 2 = 1/2 x 1/2. With the pattern established they ask the students to make the leap.Barry Garelickhttps://www.blogger.com/profile/01281266848110087415noreply@blogger.comtag:blogger.com,1999:blog-30226356.post-16671735957274427772007-07-19T11:22:00.000-07:002007-07-19T11:22:00.000-07:00I've always wondered why fraction division is not ...I've always wondered why fraction division is not taught using CDD approach - it is such a natural follow-through from fraction multiplication --> simply the inverse! <BR/><BR/>Granted, when the denominators are the same (or when the divisor is a factor of the dividend), it is a lot easier to do. The challenge becomes what happens when the denominators (or the numerators) are not divisible. <BR/><BR/>One thought I had is that you could multiply one (or both) of the fractions by a form of one (as you would with adding or subtracting fractions) and then divide.<BR/><BR/>For example 1/2 divided by 1/3. If I multiply the first fraction by 3/3, I get 3/6 divided by 1/3. Dividing across now, I get 3/2, which is the same result as if I had inverted and multiplied, but without that magic trick.<BR/><BR/>I fully support CDD!!!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-30226356.post-63848940831600367812007-07-04T08:55:00.000-07:002007-07-04T08:55:00.000-07:00Why not teach them the how and the why of multiply...Why not teach them the how and the why of multiplying by the reciproal?<BR/><BR/>Today we are going to talk about identity. If you multiply or divide any number by one, then what do you have? And you are off to the races...Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-30226356.post-86421485372662929622007-06-30T12:14:00.000-07:002007-06-30T12:14:00.000-07:00It actually has some points going for it. Student...It actually has some points going for it. Students already know how to find a common denominator (in theory) because they did it for addition and subtraction, and it's consistent with multiplication of fractions. <BR/><BR/>There's a good argument to be made that it's smart to teach this way, and then go to "invert and multiply" later.Darrenhttps://www.blogger.com/profile/15730642770935985796noreply@blogger.com