>people about this same topic. My concern dealt with the teaching of >multiplication and division of fractions. I teach 6th grade and highly >question the need for this. As an adult, I can do these types of problems, >but in real life, I don't...ever. I know one might say it is needed, for >example, in cooking. What if a recipe calls for 1/4 cup of flour and I only >want a half recipe? I know that 1/2 of 1/4 is 1/8. However in reality, I >simply fill the 1/4 cup measure 1/2 full.
Strictly speaking, you _do_ have to do these problems in the real world, since you teach math! (Logically this isn't a real argument, I know, since it would justify the teaching of any subject, but I couldn't pass it up.)
Personally, I am glad to see you asking a question like this, since a) if there is a good reason fro you to teach it, you should know it b) even if you weren't asking it, you can bet your students are wondering, and (in my opinion) they have not only the right to know but a definite need. For both a) and b), knowing where the skills/knowledge can be applied is worthwhile because it will (or at least should) make better teachers as well as learners--instead of "just doing it" it will be preparation for life.
Here are a few things that I can think of where muliplication/division of fractions comes into everyday life.
1) Not getting ripped off at the grocery store. A lot of companies sell the same item in various sizes of packages. Usually, the largest quantity is the best buy. Not so with tuna, soft drinks (3 liters often cost more per liter than 2 liters!), and various other products that either cost more in the bigger packages or the same amount. I frequently use division of fractions to make these calculations easier. Suppose I could get 5.5 oz of canned road kill for 24 cents or 7 oz for 32. You could see which cost fewer cents per oz by calculating 24/(5.5) and 7/(32), or you could calculate (5l5)/24 and 7/32 and compare, choosing the one with the most oz per cent paid. The second way is pretty easy if you say $.24 is about a fourth of a dollar, so you're getting about 4*5.5 (which I would calculate as 4*(11)/2=22, if I thought of it)oz/dollar, inthe other case, $.32 is around a third fo a dollar, so you're getting around 21 oz per dollar. They appear to be comparable deals depending on how accurate you want it. If you want to know about how accurate, you can often get a rough idea of your error with estimates like that, too. This is not just something I cooked up--I really do this every time I have to divide anything that looks like it could be in cimpler form as a fraction. 35 cents is 7/20 of a dollar, for example. It might be easier to do a calculation with that than with .35. If you look around for stuff like this, it comes up everywhere.
2) (Out of time so I have to be brief). In sixth grade I had no idea I was going to be a mathematician. Good thing I learned how to do it there, or I might not have had this opportunity. Where do you use it? In my case, for doing algebra that enables me to do calculus is the first things that comes to mind. Who has to do calculus? Chemists, physicists, engineers, mathematicians, etc. Not learning how to do fundamental mathematics can cut you off from some of the most lucrative and/or rewarding careers available (note the "or" in there!).
3) I have no experience in this, but don't carpenters do a lot of fraction work? How about ad layout people that put together newspapers and magazines?