Importance of Considering Units in Division Problems
Date: 01/27/2005 at 18:32:50 From: Liz (mom) Subject: What is the correct way to depict 12/ 4 equals three Bobby has 12 model cars. He puts them in cases. Each case holds 4 cars. How many cases does he fill? Draw a picture to show the problem then write a division sentence. My son drew 3 boxes with four dots in each and wrote 12/3 equals 4 and answered that Bobby filled 3 cases. My sons text book said that the division sentence should be 12/4 equals three. I thought 12/4 equals three meant 12 divided into four equal groups equals 3 where 12/3 meant 12 divided into 3 equal groups equals 4.
Date: 01/28/2005 at 12:13:55 From: Doctor Ian Subject: Re: What is the correct way to depict 12/ 4 equals three Hi Liz, Actually, all 12/4 means is '12 divided by 4'. What interpretation we place on that will vary from situation to situation. It might have nothing to do with 'equal groups'. For example, if I travel for 12 miles at 4 miles per hour, it takes me 12/4 = 3 hours to complete the trip. Nothing is being grouped there. Where you get into trouble is in losing track of what's being divided into what, and why. With units added, what your son wrote was this: 12 cars -------- = 4 cars per case 3 cases It's a perfectly correct statement, and it describes the situation from one perspective; but it happens not to be what was asked for, which is this: 12 cars ---------------- = 3 cases 4 cars per case Personally, whenever there are units attached to the numbers in a problem, I recommend keeping them in the problem for as long as possible. The problem with trying to decide between 12/4 = 3 or 12/3 = 4 is that you don't know: 3 of what? 4 of what? Keeping the units in play answers that question for you, and lets you know whether what you're calculating is what's being asked for, or something else entirely. Does this make sense? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/
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