taking a math for elementary teachers class in uni right now and we are going over this using visual representations. I could not figure out how to do it visually. This made it perfectly clear and taught me why it works. thank you!
This is a powerful video, with the demonstration it shows the deep meaning of arithmetically basic math and why it is so important to human mind's development. Combining graphic and math grows the logic! And that is the fundamental concrete base of a great civilisation! Oh sir, thank you so much! I'm an adult audience but not until today has anyone shown me this kind of profound yet simple knowledge of math. If I had seen this when I was a kid, it might have changed my life. (It still changes my life now though...hahaha)
Oh please do! That's something that I'm rather obsessed about, how to do a visual explanation of complex fractions using the partitive method. It would make my month!
I am primary teaching intervention maths, and your video very clear explains division of fractions for students who learn more easily with visual supports. Thank you very much.
quite interesting to be honest. It's always been a question to me why invert and multiply, and I think even most math major will have a hard time explaining this concept on the spot. You did a fine job. Thanks you
Coolblueocean2001 not really, I was close to that but thanks to my college calculus teacher (he made me dislike math, it's either his way to solve a problem or no credit). So I changed to Chemistry, and it hasn't been too bad since then. I will admit there are quite a few thing I am still shaky in math. Are you doing a survey to see how many are math major? :)
I am not doing a survey. But I am always interested in people who watch my videos or people who are interested in math in general. Chemistry is a great discipline!
Excellent thing about mathematics is that in many cases it provides intuitive approach and visualisation of given concept (like pizza slices when working on fractions), HOWEVER, what about visualisation and finding REAL LIFE example for the rule: ''Invert and multiply''... I searched all around the internet and many books to find some good explanation for that. OK, I get why it works mathematically, I know the proofs, calculating this is not a problem, but understanding WHY it works in REALITY is simply beyond me! How can you find a good example to explain this strange phenomenon, that suddenly: 2/3 of one thing, divided by 4/5 (that is: what part of 4/5 of 2nd thing fits exactly in 2/3 of the first thing) is THE SAME as: 2/3 of one thing, multiplied by 5/4 (does it even make sense beyond mathematics?!) I really can't grasp this very basic concept in relation to the way nature works (after all mathematics is thelanguage of the universe... supposedly...)
+Coolblueocean2001 I know why it works mathematically, I fully get a/b divided by c/d equals a/b*d/c, I know mathematical justification but what I am struggling at... is finding good Analogy, intuitive understanding and some good examples in Real Life ( maybe some word problems) when trying to explain WHY it works in relation to real life, not only mathematical rules. So for example, when i have 2/3 litre of milk, and I want to know how many 4/5 litre bottles of milk would 'fit' in that 2/3, (since divisor is larger than dividend, only a part of 4/5 litre bottle will cover that 2/3 litre of milk) - I would write it down like this: 2/3 divided by 4/5 . Ok, it makes sense, but where i am starting to lose the understanding is: how is this problem the same as: 2/3 litre of milk multiplied by 5/4? I would love to be able to express that concept more clearly, but I just can't find right words to express it more accurately :(... if I were to write my main question: How does ''÷4/5'' become ''*5/4 '' and makes perfect sense in real world?
+Szpulenso I think I understand you better now. I will think about your problem. You do have a point. Makes a lot of sense. What level of math are you at? Are you as student, a teacher?
+Szpulenso How many times 1/3 goes into 1? The answer is 3 times. How many times 2/3 goes into 1? The answer is 1.5 times. Is that kind of what you asking for? The general case of this?
+Coolblueocean2001 Thank you for such quick answers: I am 2nd year college linguistics student, but really interested in mathematics - I only know basics though, no calculus, probability and anything beyond That's not what I am asking: I am asking for scenario from real life, when you operate mathematically on REAL objects - not only numbers. How do you comprehend that suddenly the case when one Object (like 2/3 litre of milk) divided by other object (bottles that can contain 4/5litre of milk) is the same as taking 2/3litre of milk and multiplying it by 5/4litre bottle - The second ''object'' [or whatever you wish to call it] is suddenly flipped upside down, but It still yields same answer: 5/6. I have no problems with taking'' invert and multiply'' rule for granted, just like any rule in card games or whatever and apply it in practice. BUT finding out WHY it works in real world, on real objects - that's real challange.
Very interesting, congratulation. Have you ever made the video on the partitive interpretation? Do you have some kind of paper/hand out on Division of fractions?
Thanks for the videos Coolblueocean2001! I taught secondary math in Los Angeles for 8 years and had never seen the measurement and partitive methods of division explained so clearly until now. I enjoy your videos very much. I have three questions, 1) Can the measurement method only be used when we are dividing two fractions that have the same units? The key step of identifying a whole that can be evenly divided by either denominator only makes sense if each fraction relates to the same unit if I am not mistaken. (eg Given $ as my unit, I can divide quarters by dimes. 5 quarters measured by 3 dimes can be written (5/4) / (3/10) and is equivalent to (50/40) / (12/40) which reduces to 4 + (1/6). Meaning that 4 and 1/6 groups of 3 dimes is the same amount of $ as 5 quarters) 2) Is the partitive method used when we are dividing fractions that have different units? In this case I can't identify a whole. (eg If (3/4) lb of lentils costs $ (7/5), then I can find the price per pound of lentils by dividing (7/5) / (3/4). To do this, I can write (7/5) as (21/15) to see that there is an equivalent ratio that shows how much the missing (1/4) costs: (7/5) / (3/4) = (21/15) / (3/4) = (7/15) / (1/4), and this means that the price is $(28/15) per 1 lb of lentils. 3) Correct me if I am wrong, but It seems as though this kind of partitive division is more of a ratio/rate problem than a fraction problem.
You asked some really good questions. My understanding is this... both partitive and measurement ideas can be used when a fraction is divided by another fraction. It depends on the context of the problem. Here is an example. Consider the following: 1/2 divided by 1/3. If you asked how many times 1/3 goes into ½, the answer is 1.5, and you are using the measurement model. Instead if you ask ½ is 1/3 of what number, the answer is 1.5), you are using the partitive model. Your model (partitive or measurement) is dictated by the context of the problem, not the type of fractions involved. Yes, I agree with you of partitive division is like a ratio/rate problem.
well - he did get to my questions, he just avoided the part about unitary measures. I still found the response informative and useful for GlassLab's work on Ratio Rancher. But Big Gargantuar if you have further questions or want to discuss this topic, I would be happy to, and Coolblueocean2001 might chime in to. Let us know!
If I get a chance, I will make a video. This might help. Visualize 1/4 divided by 3/4. You are asking how many times 3/4 goes into 1/4. The answer is only 1/3 times. I hope this gives you an idea.
![Understand Fraction Division w/ Pictures and Models - [6-2-11]](http://i.ytimg.com/vi/fMVOwML7zTY/mqdefault.jpg)
taking a math for elementary teachers class in uni right now and we are going over this using visual representations. I could not figure out how to do it visually. This made it perfectly clear and taught me why it works. thank you!
This is a powerful video, with the demonstration it shows the deep meaning of arithmetically basic math and why it is so important to human mind's development. Combining graphic and math grows the logic! And that is the fundamental concrete base of a great civilisation! Oh sir, thank you so much! I'm an adult audience but not until today has anyone shown me this kind of profound yet simple knowledge of math. If I had seen this when I was a kid, it might have changed my life. (It still changes my life now though...hahaha)
Thank you so much for your feedback. I really appreciate it.
Fr...that part where you said that visuals are very helpful when It come to understand maths..that true
Sir you just helped me a ton. I graduated in 05 and finally learning the whys to math.🌻🌹
Oh please do! That's something that I'm rather obsessed about, how to do a visual explanation of complex fractions using the partitive method. It would make my month!
I am primary teaching intervention maths, and your video very clear explains division of fractions for students who learn more easily with visual supports. Thank you very much.
Thank you so much. I appreciate feedback from other professionals like you.
Out of all the videos I have seen on youtube, this is the best!!!
Superb🔥
Thanks alot sir
You have made it so simple by your precised demonstration
I think finding a common partitioning ( measurement division) does prove invert/ multiply.
This what I was looking for! Great job!
Thank you!
Why are there no examples of improper fractions or division of the fractions by integers?
Very nicely explained
Thank you!
I am glad you liked the video. What do you teach?
Your videos are so interesting
Can you let me know the hardware/software you used to create this video? I'd like to give it a try.
quite interesting to be honest. It's always been a question to me why invert and multiply, and I think even most math major will have a hard time explaining this concept on the spot. You did a fine job. Thanks you
AkiraKeiKyo Thank you!
May I ask what your background in Math is? Are you a math major yourself?
Coolblueocean2001 not really, I was close to that but thanks to my college calculus teacher (he made me dislike math, it's either his way to solve a problem or no credit). So I changed to Chemistry, and it hasn't been too bad since then. I will admit there are quite a few thing I am still shaky in math. Are you doing a survey to see how many are math major? :)
I am not doing a survey. But I am always interested in people who watch my videos or people who are interested in math in general. Chemistry is a great discipline!
WOW !!! Words cant express how much you have helped me !
I really appreciate your feedback!
Excellent thing about mathematics is that in many cases it provides intuitive approach and visualisation of given concept (like pizza slices when working on fractions), HOWEVER, what about visualisation and finding REAL LIFE example for the rule: ''Invert and multiply''... I searched all around the internet and many books to find some good explanation for that. OK, I get why it works mathematically, I know the proofs, calculating this is not a problem, but understanding WHY it works in REALITY is simply beyond me! How can you find a good example to explain this strange phenomenon, that suddenly: 2/3 of one thing, divided by 4/5 (that is: what part of 4/5 of 2nd thing fits exactly in 2/3 of the first thing) is THE SAME as: 2/3 of one thing, multiplied by 5/4 (does it even make sense beyond mathematics?!)
I really can't grasp this very basic concept in relation to the way nature works (after all mathematics is thelanguage of the universe... supposedly...)
You do have a point. Are you asking why invert-and-multiply algorithm really works? It can be explained.
+Coolblueocean2001 I know why it works mathematically, I fully get a/b divided by c/d equals a/b*d/c, I know mathematical justification but what I am struggling at... is finding good Analogy, intuitive understanding and some good examples in Real Life ( maybe some word problems) when trying to explain WHY it works in relation to real life, not only mathematical rules.
So for example, when i have 2/3 litre of milk, and I want to know how many 4/5 litre bottles of milk would 'fit' in that 2/3, (since divisor is larger than dividend, only a part of 4/5 litre bottle will cover that 2/3 litre of milk) - I would write it down like this: 2/3 divided by 4/5 . Ok, it makes sense, but where i am starting to lose the understanding is: how is this problem the same as: 2/3 litre of milk multiplied by 5/4?
I would love to be able to express that concept more clearly, but I just can't find right words to express it more accurately :(... if I were to write my main question: How does ''÷4/5'' become ''*5/4 '' and makes perfect sense in real world?
+Szpulenso I think I understand you better now. I will think about your problem. You do have a point. Makes a lot of sense. What level of math are you at? Are you as student, a teacher?
+Szpulenso How many times 1/3 goes into 1? The answer is 3 times. How many times 2/3 goes into 1? The answer is 1.5 times. Is that kind of what you asking for? The general case of this?
+Coolblueocean2001 Thank you for such quick answers: I am 2nd year college linguistics student, but really interested in mathematics - I only know basics though, no calculus, probability and anything beyond
That's not what I am asking: I am asking for scenario from real life, when you operate mathematically on REAL objects - not only numbers. How do you comprehend that suddenly the case when one Object (like 2/3 litre of milk) divided by other object (bottles that can contain 4/5litre of milk) is the same as taking 2/3litre of milk and multiplying it by 5/4litre bottle - The second ''object'' [or whatever you wish to call it] is suddenly flipped upside down, but It still yields same answer: 5/6.
I have no problems with taking'' invert and multiply'' rule for granted, just like any rule in card games or whatever and apply it in practice. BUT finding out WHY it works in real world, on real objects - that's real challange.
Very interesting, congratulation. Have you ever made the video on the partitive interpretation? Do you have some kind of paper/hand out on Division of fractions?
I have a second video in division of fractions.
@@Coolblueocean2001 Thanks for the reply. I see now your ua-cam.com/video/yMEdEAFKSNQ/v-deo.html.
I finally understand this! Thank you for your amazing teaching skills!
Stacy Dumrauf Glad to hear that! It was worth doing the video.
Hoping this will help my ten year old who is struggling with the idea of modeling the question.
I hope so too!
Thanks for the video! Do you have an equally in depth explanation of division by fractions using the partitive method?
im wondering exactly the same...
Thank you for this visual.
Awesome explanation/demo.
Thank you so much! I appreciate it.
Thanks for the videos Coolblueocean2001! I taught secondary math in Los Angeles for 8 years and had never seen the measurement and partitive methods of division explained so clearly until now. I enjoy your videos very much. I have three questions,
1) Can the measurement method only be used when we are dividing two fractions that have the same units? The key step of identifying a whole that can be evenly divided by either denominator only makes sense if each fraction relates to the same unit if I am not mistaken. (eg Given $ as my unit, I can divide quarters by dimes. 5 quarters measured by 3 dimes can be written (5/4) / (3/10) and is equivalent to (50/40) / (12/40) which reduces to 4 + (1/6). Meaning that 4 and 1/6 groups of 3 dimes is the same amount of $ as 5 quarters)
2) Is the partitive method used when we are dividing fractions that have different units? In this case I can't identify a whole. (eg If (3/4) lb of lentils costs $ (7/5), then I can find the price per pound of lentils by dividing (7/5) / (3/4). To do this, I can write (7/5) as (21/15) to see that there is an equivalent ratio that shows how much the missing (1/4) costs: (7/5) / (3/4) = (21/15) / (3/4) = (7/15) / (1/4), and this means that the price is $(28/15) per 1 lb of lentils.
3) Correct me if I am wrong, but It seems as though this kind of partitive division is more of a ratio/rate problem than a fraction problem.
I will get to your questions soon. Sorry about the delay. I am glad to hear that you enjoy my videos.
You asked some really good questions. My understanding is this... both partitive and measurement ideas can be used when a fraction is divided by another fraction. It depends on the context of the problem. Here is an example. Consider the following: 1/2 divided by 1/3. If you asked how many times 1/3 goes into ½, the answer is 1.5, and you are using the measurement model. Instead if you ask ½ is 1/3 of what number, the answer is 1.5), you are using the partitive model. Your model (partitive or measurement) is dictated by the context of the problem, not the type of fractions involved.
Yes, I agree with you of partitive division is like a ratio/rate problem.
You never got to his questions and it was like 11 months!
well - he did get to my questions, he just avoided the part about unitary measures. I still found the response informative and useful for GlassLab's work on Ratio Rancher. But Big Gargantuar if you have further questions or want to discuss this topic, I would be happy to, and Coolblueocean2001 might chime in to. Let us know!
+Evan Rushton Measurement method seem meaningful to me when both fractions refer to the same physical quantity. But this is just my opinion.
This guy rocks he is like the math superhero😄😃😃😆☺😊
Thank you so much!
This was very helpful
How can you visually represent when the divisor is smaller then the dividend.?
What software are you using to make this video?
It was a pdf document. Hypercam2 was used to record. Zoomit was used to write.
goood! I needed this!
thank you very much
I am glad it helped!
Thanks for teaching me i am so smart so as u thanks again
I am glad it helped...
Me too
Is this really u
👍😁
Is this really u even though this video was made 8years ago
thank you so much!
Thank you.
Sir ,how to divide smaller fraction by bigger fraction visually ...
The same technique should work. Try it! Hard to explain in text.
@@Coolblueocean2001 thankyou for the reply... Tried alot by the same method .....will try again .....
Finally got it...the same method works for improper fractions..thanku so much
Very comfortable proses. Exlant
I'm glad that the video helped. What level do you teach at?
3rdgrade
cool! thanks a lot for the clarity brother :)
In that case the answer will look like the fractional part of the answers shown in the video.
can u model this these fractions for me please 1 5/8 divided by 3/4 using rectangle
+Pinpin Paski I will model it and upload the video. Give me a couple of days.
Thanks Sir
+Pinpin Paski Here is the video you asked for.ua-cam.com/video/eaDRR6EOAzg/v-deo.html
+Pinpin Paski May I ask you what you need the video for. What level of mathematics are you at? Are you a student or a teacher?
What if one on the fraccions is improper?
Just draw the improper fraction, and try the same method.
I wish you could show a scenario where the divisor is greater than the dividend.
If I get a chance, I will make a video. This might help. Visualize 1/4 divided by 3/4. You are asking how many times 3/4 goes into 1/4. The answer is only 1/3 times. I hope this gives you an idea.
what if was 1/4 / 1/2 = 1/2 what is the 1/2
+shahid akhtar 1/2 goes into 1/4 1/2 a time...
it was very helpful!
Thank you!
thank you thank you thank you !
I am glad you enjoyed it.
GOD BLESS YOU
Thank you!
an you make a model of 2/3 x 5/6 and 3/4 x 2/5 and 3/5 x 2/3? Now?!
thank you very much®®®®
Thank you!!!
Thank you
You are most welcome!
We can discuss these issue via email. That's fine.
Where do I find your email?
I will remove the email address soon from here. Let me know when you have it.
Got it
This makes sense
7/9÷5/9 can you visual method
watch?v=yMEdEAFKSNQ
A+
Sorry i meant the other way around..
👎🏿👎🏿👎🏿👎🏿👎🏿
Thank you a lot!
You are welcome