Monday, January 9, 2012

Fractions - LCF

I'm new to blogging and I'm doing more posting. I got a Bamboo tablet for Christmas and I'm trying to learn how to use it.  After I get the hang of it, I want to start doing videos in the  future.

Today, I'm starting with the easiest of fractions. Which one is that you say? Well, division of fractions of course.  I'm always trying to find fun ways to teach students. Hopefully this will be new to you and you can try it with your students. I wish you much success!

Have you ever had students blurt out something that you taught them during the year such as, "Oh Yeah!.....Mrs. So and So said do this." This usually happens when they are taking a test. I love when this happens. This means that you have got them to a point that they remember things and hopefully will be able to apply that knowledge to anything they are given.

So, with division of fractions, I'm going to teach my students to follow these three letters: LCF. What is that suppose to mean? Well, let me tell you. The "L" stands for: leave the first fraction alone. "C" stands for change the sign from division to multiplication (multiplication you would cross simplify). Please see the steps below.  Finally the "F" stands for flip (reciprocal of) the second fraction.

Now here is an example of what that would look like and the process you do to complete the math problem. 
Step 1: This is the division of fractions problem.

Step 2: This is the problem again and now we are going to apply the letters- LCF- which mean leave alone, change, and flip. This means that we leave the first fraction alone (3/4). We change the division symbol to a multiplication symbol. Finally we flip the second fraction (1/2 becomes 2/1).

 Step 3:  You've applied LCF (see above) and you are now going to cross simplify your multiplication. You can simplify the 2 and 4, but you can't simplify the 3 and 1.  The 2 can go into itself and 4, thus simplifying the 2 to a 1 and the 4 to a 2.

Step 4: Now you take your problem and multiply straight across. So 3 x 1 = 3. 2 x 1 = 2. So the fraction is now 3/2 (An improper fraction).

Step 5: You are almost done. As you can see we have an improper fraction and it must be simplified. To solve an improper fraction, you take the bottom number (2) and divide into the top number (3). This will give you 1 with a remainder of 1. The  denominator will be the same. The answer is 1 1/2.

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