Why do we 'invert and multiply' to divide by a fraction?

This video addresses the case of a whole number divided by a unit fraction, which corresponds to the 5th grade standard in the CCSSM.

[xenamerry]

Wonderful explanation! Why don't more people who teach things stop assuming we understand the terminology etc. that they do and explain EVERYTHING in detail? I hate math and fractions is where I bogged down. Thanks so much.

[emmahoslett]

you're the only video that actually let me understand this - THANK YOU

[ScienceDiscoverer]

1:20 In elementary school I was only told the left kind of explanation for division. Later nobody presented to me the right kind. So because of this I ended up never understanding how fractions work. Great education system!

[cathyhart]

This is the clearest explanation I've ever heard. I think I actually get it now! EXCELLENT!!

[cathyb]

I've been trying really hard to find a way to explain to my 5th grader WHY we flip the fraction to its reciprocal, and have been unsuccessful until THIS video. It's still a little heady, but it's the best I've found. And maybe now that I'VE been refreshed on why, I will be able to break it down for him. Thanks!

[JackSmith-uldp]

Yes this video makes a lot of sense. Like a lot. Trying to prep for an interview and their question. "why?" Perfect explanation.

[geraldillo]

Really helpful explanation, thanks for sharing!

[miasara]

Thank you so much!!! Really helps with my upcoming fraction test on Friday!

[harrykhan]

Wow, thank you, very interesting explanation. I was struggling teaching my son this today, but now I can easily make him understand.

[tomrose]

It could also be explained by making each number the same "type". So, 5 is the same as 5/1, and multiplying by 4/4 (i.e. 1) gets 20/4. The question 5 ÷ 1/4 then becomes 20/4 ÷ 1/4, i.e. each number being the same "type", and the answer is visually obvious, as 20. It can also be seen that getting 20 was achieved through multiplying by the inverse of the divisor.

[starquake]

I finally could understand that! Thank you so much!

[martm]

Very good and clear. Thank you so much.

[zelaznygirl]

This is a great explanation! How would you explain a whole number divided by a fraction such as 3/8? How would you explain that 8/3 is how many copies of that fraction to compromise a whole?

[strafer]

This is nice for whole numbers but then what visual do you use when it’s fractions divided by fractions without multiplying? What kids are being told is that they have to multiply to divide, opposite processes. How is that visualized with real world examples. How do you show something whole that you don’t have in order to show what you will have and why do you do it?

[deepathiruparkadal]

Thanks for the video really helpful
Can you make a video on dividing fraction by fraction logic for elementary kids

[xenamerry]

We were taught to make a whole number a Fraction by placing a 1 underneath the whole number like 5/1. This doesn't change it from a whole number because it is 30 whole numbers over 1 piece. If you divide 1 into 30, as you do when trying to simplify a large fraction, you still get 30. Not 1/30, as that is 1 piece of 30. Is multiplying fractions different? I remember multiplying the top of the first fraction by the bottom of the inverted Fraction but this doesn't work for this division, as you have to multiply both denominators and that would make the 2nd one a 1 when it should be 4. You turn the second fraction upside-down, so you can multiply the bottom numbers (denominators) diagonally. Not sure why you do it diagonally. Must be to do with different fractions you have to multiply or divide. Is that another way of dividing into even numbers or something. I remember we crossed out numbers as we divided into them to reduce them. I understand what you did but I'm still confused as to the diagonal stuff I remember.