tag:blogger.com,1999:blog-7718462793516968883.post8849002690941508759..comments2021-04-10T08:19:35.051-04:00Comments on MadMath: Why Is Distribution Prioritized Over Combining?Deltahttp://www.blogger.com/profile/00705402326320853684noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-7718462793516968883.post-66011516104722013762015-09-30T03:51:40.673-04:002015-09-30T03:51:40.673-04:00I suggest you think more carefully about the namin...I suggest you think more carefully about the <i>naming</i> question. When the transformation is from right-to-left, it doesn't match the natural language definition of "to distribute" ("to divide and give out in shares/to scatter or spread out"). And in fact, we do have a standard existing phrase, "combine like terms", used to describe that distinct transformation (with numerical coefficients). So arguably that distinct usage and name should be presented first. Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-58312118623058162112015-09-28T19:57:54.759-04:002015-09-28T19:57:54.759-04:00I don't think I understand your point.
The di...I don't think I understand your point.<br /><br />The distributive law merely asserts that the two sides of the equation are equal. It makes no difference which is on the left and which is on the right.<br /><br />Perhaps your difficulty is coming from thinking of the "=" as an operation to perform, rather than as a symmetric statement of equality. (This is a common mistake for students to make.)<br /><br />Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-91867557335421514202015-09-28T10:26:54.733-04:002015-09-28T10:26:54.733-04:00Thanks for the correction!Thanks for the correction!Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-43522841074730326622015-09-28T06:06:16.724-04:002015-09-28T06:06:16.724-04:00I think the reason for this choice has to do with ...I think the reason for this choice has to do with geometric intuition. It is often helpful to visualize multiplication as computation of area. Being able to combine two rectangles with a common side length into one is just a very special case of combining two arbitrary rectangles, less interesting than splitting one rectangle into two.<br /><br />> (the transformation ax+bx=(a+b))<br /><br />Missing an x on the rhs.Don Rebahttps://www.blogger.com/profile/18015532040220223370noreply@blogger.com