What a FABULOUS tutorial. I've been struggling to REALLY understand what it means to divide fractions. Your explanation is clear, foundational, memorable. A thousand thanks for taking the time to make and post this.
what do you think about also showing 1/3 as a ratio of 1 things to 3 things while you are introducing division and fractions and that way they can "see" another way that 1/3 can look like?
I like that idea! The video was so long already I had to leave some things out. But I’ll try to work that in to the next one. How would you show division by a ratio?
Great how you explain about neuroscience and why conceptual understanding, which is about making connections to other knowledge and to applications in the real world, makes sure that your brain does not "throw out" isolated knowledge when it is not connected because your brain will continuously weed out knowledge you don't use/need. I like it that when you divide by a unit fraction is the same as multiplying by that denominator. I then like to explain that when we divide by a multiple of these unit fractions, we have to divide our original answer by that multiple. So this "explains" the algorithm (but no need to even use the algorithm if you truly understand). I also like to show division by a fraction through finding equivalent fractions of both fractions first with a common denominator, and then see that we can just divide the numerators.
Thanks, Suzanne! That's a great point about dividing by non-unit fractions. We can always "unstack" the divisor, divide by the unit fraction, then divide by the numerator (4/7 ÷ 2/5 becomes 4/7 ÷ 1/5 ÷ 2)
![Understand Fraction Division w/ Pictures and Models - [6-2-11]](/img/n.gif)
What a FABULOUS tutorial. I've been struggling to REALLY understand what it means to divide fractions. Your explanation is clear, foundational, memorable. A thousand thanks for taking the time to make and post this.
I finally found a clear way to understand WHY we have to multiply fractions when we divide them. Thank you.
what do you think about also showing 1/3 as a ratio of 1 things to 3 things while you are introducing division and fractions and that way they can "see" another way that 1/3 can look like?
I like that idea! The video was so long already I had to leave some things out. But I’ll try to work that in to the next one. How would you show division by a ratio?
Great how you explain about neuroscience and why conceptual understanding, which is about making connections to other knowledge and to applications in the real world, makes sure that your brain does not "throw out" isolated knowledge when it is not connected because your brain will continuously weed out knowledge you don't use/need. I like it that when you divide by a unit fraction is the same as multiplying by that denominator. I then like to explain that when we divide by a multiple of these unit fractions, we have to divide our original answer by that multiple. So this "explains" the algorithm (but no need to even use the algorithm if you truly understand). I also like to show division by a fraction through finding equivalent fractions of both fractions first with a common denominator, and then see that we can just divide the numerators.
Thanks, Suzanne! That's a great point about dividing by non-unit fractions. We can always "unstack" the divisor, divide by the unit fraction, then divide by the numerator (4/7 ÷ 2/5 becomes 4/7 ÷ 1/5 ÷ 2)