Fractions Continued Divide and Conquer -Week 4

Last week's math class was a continuation from Week 3. In week 3 we learned the proper way to add and subtract fractions using various manipulative's. This past week we continued the fabulous journey of fractions and learned the appropriate way to divide them. Back in elementary and high school I was taught to invert the fractions and multiply, this was the only way we were taught. Now, being a young student who didn't like math to begin with or really understand it, this was extremely confusing to me. Fast forward to several years later to my teacher's college J/I math class. I have now learned that this is totally the WRONG way to teach kids how to divide fractions. Not only is this way wrong but it is also extremely complicated. PSA: dividing fractions does not have to be complicated, I'll show you below.

When dividing fractions we can remember that dividing is the same as multiplying. We must remember to just divide across the fractions as we would multiply across the fractions. We do not need the reciprocal anymore, there is no need to invert the second fraction and multiple!

MathChat. How to Divide Fractions From Annoying to Fun! (November 19 2008). Math, [Online Image]. Retrieved From https://mathchat.me/2008/11/19/dividing-fractions-from-annoying-to-fun/

For example: 6/12 divided by 2/3
Solution: divide the numerators by each other: 6 divided by 2 and divide the denominators by each other: 12 divided by 3.
Answer: 3/4

Division Problem Example: Kate divided a fraction less than one by another fraction less than one and came to an answer of 3/4. What might her fractions have been?
9/16 divided by 3/4 = 3/4
Thus, you simply divided the numerators by one another and the denominators by one another.

HOW SIMPLE WAS THAT!

Furthermore, another key aspect that I was taught in elementary and high school was that you are not allowed to create a common denominator when dividing fractions. Why? Because my teacher said so. Now, in teacher's college my teacher is stating that you CAN use common denominators to divide fractions.

Heitin, Liana. Education Week. With Fractions, Common-Core Training Goes Beyond 'Invert and Multiply' (August 12 2014). Math, [Online Image]. Retrieved From http://blogs.edweek.org/edweek/curriculum/2014/08/fractions-common-core-invert-and-multiply.html

For example: 5/6 divided by 1/3 -find the common denominator: 18 is a common denominator.
HOW did we get that you might ask? Well both 6 and 3 can be multiplied by each other to get 18. Thus, whatever you do to the denominators you must do to the numerators.
So, 5/6: 5x3=15 and 6x3=18. Now our fraction becomes 15/18.
So, 1/3: 1x6=6 and 3x6=18. Now our fraction becomes 6/18.
So, 15/18 divided by 6/18= 15/6/1 a three part fraction which = 15/6/1 because both denominators being 18 can be divided by each other, equalling 1. We drop the 1 and this fraction, 15/6 can be simplified by dividing both the numerator and denominator by 3. Thus, giving us 5/2 as the simplified answer.

One more example using the common denominator method:
4 divided by 2/3... How can we solve this? - We must find a common denominator. I choose 3.
Therefore, whatever we do to the bottom we must do to the top. So I multiply the numerator 4, by 3 = 12. Thus, my equation becomes: 12/3 divided by 2/3 = 6/1. This can be simplified to 6.

Wiki How. How to Divide Fractions by a Whole Number. Math, [Online Image] Retrieved From http://www.wikihow.com/Divide-Fractions-by-a-Whole-Number

HALLELUJAH!!! IT'S A MIRACLE

I find doing numerous examples helps me to remember the process for solving problems. Therefore, making me more successful when answering math questions. For me it's all about repetition.

Here is a fun link that I learned about from my math lesson, the object of the game is to answer the questions using your fraction skills to make several smoothie recipes.

http://www.learnalberta.ca/content/mejhm/index.html?l=0&ID1=AB.MATH.JR.NUMB&ID2=AB.MATH.JR.NUMB.FRA&lesson=html/object_interactives/fractions/use_it.html

Rules to take away from this lesson:
-Yes you can divide fractions without inverting them. Just simply divide across.
-Yes you can use a common denominator to divide fractions- why the hell not?
-When creating a problem make sure it has a wide base= scenario where everyone can get started
-When creating a problem make sure it has a high ceiling= lots of choice in between, students can add onto the problem.

As a future teacher it is important to remember the, 6 Fail Safe Ways for Opening Problems:
1. Begin with the answer.
2. Ask for similarities and differences- How is multiplying fractions like dividing fractions? How are they different?
3. Leave certain information out of the problem. Ie. omit number's.
4. Provide several numbers and math words so the student can create a sentence using all of them.
5. Use soft language, Ie. Two fractions are almost but not quite equal, what could they be? Example: 3/4 and 8/9.
6. Ask to prove if an idea is true or false.

This past week we learned a lot in our math class. We learned the PROPER way to divide fractions by dividing across the fractions as well as, finding common denominators to divide the fractions. These are the appropriate methods that I will use when teaching my students to divide fractions. It is important to remember the take home rules and the 6 Fail Safe Ways for Opening Problems for your students.

Till next time,
Cheers, Courtney