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• # Division of Fractions Explanation

Posted by on November 11, 2019 at 8:09 am

I need some help with division of fractions. So we have been modelling that 3 divided by 1/2 would equal 6 because you would have 6 groups of 1/2. Now I need help explaining why when you would divide 2 1/2 by 1/3 you end up with 15/2 or 7 1/2. I get where the 15 comes from because when you take 5 one-half pieces and break those one-half pieces into thirds, you would have 15 one-third pieces, but why then do you put them into groups of 2? Or if you divide 2 1/2 by 2/3, why do you put them into groups of 4?

3 Members · 4 Replies
• 4 Replies
• ### Kyle Pearce

November 18, 2019 at 10:09 pm

This is a great discussion!

First off, have you explored anything around the two types of division?

I can’t wait to dig into this deeper with you and the community!

• This reply was modified 3 years, 4 months ago by  Kyle Pearce.
• ### Ryan Foley

Member
February 4, 2020 at 11:53 pm

This is a tape diagram of that problem. As a visual learner, this helps me understand. You can see the 7 groups of 1/3 and the half of a group left over. Thus 7 1/2

• ### Kyle Pearce

February 5, 2020 at 9:39 pm

@Ryan-Foley

I agree that using concrete and visual models is so important to make sense of mathematics.

It looks like you’ve attacked this “naked” division of fractions problem quotatively (i.e.: determining how many groups of 1/3 are in 2 1/3)

I wonder if anyone out there is interested in trying to tackle this partitively?

The two types of division are shared here: http://mathisvisual.com/division/

• This reply was modified 3 years, 1 month ago by  Kyle Pearce.
• ### Ryan Foley

Member
February 5, 2020 at 10:38 pm

I took a stab at using partitive division (how much is in each group). It was more challenging for me to think of it this way. I wonder if that is the case for most of us or our students? It wasn’t until recently, I had even thought about division as two different questions. Here’s my attempt….

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