The last few days I have been able to attend CAMT (Conference for the Advancement of Mathematics Teaching) also know as "Nerdfest". It is three days full of learning how to be a better math teacher. It is awesome.
Today I learned something that was a real "aha" moment. I learned how to divide fractions WITHOUT taking the inverse of the second fraction and then multiplying. Let me share!
No one questions when you multiply fractions like this. It is what you were taught to do.
But when we teach division of fractions it HAS to be done this way (it is law!) where you invert or flip the second fraction and then multiply as shown above.
So, is that really law?? What happens if we do like we did for multiplication above?
"Ok, so it JUST happened to work for these two numbers", you say. Let me show you another one.
"There is no way that works EVERYTIME! What about when the numbers don't divide all nice like the ones just shown.", you say. (You didn't know I could read your mind, did you?)
When they numbers don't divide nicely that is where common denominators come in. Notice, I didn't say least common denominator, just a common one will work. Let me show you.
Check it the way you were taught. You still get 6, right? Want to see another one? This one requires that both fractions be changed to a common denominator.
It even works with mixed numbers, but first you have to convert them to improper. You have to do that for multiplication as well, so that is nothing new. Here is an example.
At first, it may seem like more work, but I wrote down every single step. Once you get use to it you can do some of these in your head. Sometimes though, it does seem faster to just flip and multiply and it may be depending on the problem.
This new method will flow more naturally to someone who never learned the flip and multiply way. But the fact that I never ever thought to try it is what blows my mind.
I plan on showing this to my 7th and 8th graders and having them do many many problems so it becomes more natural to them. They are going to have SO MUCH fun!
If you have questions or see any mistakes please let me know!
Until later, divide on!
Oh and I still have Orlando/Georgia to blog about, I didn't forget them!