This is the best explanation I have found to understand the concept. One of my tutoring students asked why the reciprocal is used when dividing a fraction and I had no clue. I read/watched many explanations and I was totally confused. The lightbulb came on while watching this video. Now I can confidently give an answer to my student. Thank you!!!
Really helped me visualise why this works (multiply denominator by reciprocal in order to get 1 so the problem can be simplified later, multiply numerator in order to maintain equality). Thanks!!
For those who who did not get it In example a/b ÷ c/d is equivalent to a/b × d/c, the rest is explanation why For example, everything devided by 1/6 is going to be 6×bigger, that means everything miltipled by 6/1 is also going to be 6×bigger, that's it You can also do it like this -> b/a ÷ c/d = b÷c/d÷a
For those who are still wondering why do you need the reciprocal. I GOT YOU! One of the definitions of division is : 10 balls divided by 5 boys, how many balls does each boy get? Answer : 2. 10 balls are for 5 boys. 2 balls for each. 6 oranges divided by 2 girls, how many oranges does each girl get? Answer : 3. 6 oranges are for 2 girls. 3 oranges for each. ------ The goal here is to find out how many of something (numerator) does EACH(denominator) get! The EACH in this sentence is equivalent to 1 in Math. ------ The definition maintains for any type of division. 10 balls divided by 0.5 boy, how much will 1 boy get? Answer : Well, if 10 balls are for 0.5 boys, then it would be 20 balls for 1 boy.
How about this? In general a ÷ b × b = a. Because multiplying by something after dividing by that same thing does not change the number. Now we have a/b ÷ c/d × c/d = a/b. But we also have a/b × d/c × c/d = a/b. So this yields a/b ÷ c/d × c/d = a/b × d/c × c/d and this gives a/b ÷ c/d = a/b × d/c.
so you're going to explain how dividing by a fraction is equivalent to multiplying by the reciprocal by simply doing exactly that? where was the explanation?
@@strafer8764 Yeah this isn't a good video but I think I understand it. If you think about it in decimals it makes more sense. 1/4 divided by 3/8 is the same as saying 1/4 divided by 0.375. And 3/8 divided by 1/4 is the same as saying 0.375 times by 1/4. Multiplying by a decimal naturally will give you the same answer as dividing by the fraction, as a fraction is simply a decimal in a different form.
@@tomcass240 bro i just got its explanation Say 1/2 / 1/4 means 0.5 / 0.25 here according to reciprocal we should do 1/2 * 4/1 = 4/2 = 2 and in decimal it is 0.5 / 0.25 = 2 because we when we divide then we read table and in table of 0.25 * 1 = 0.25 and 0.25 * 2 = 0.5 hence we can simply do reciprocal of it
2 роки тому
I actually found this video astonishing, and it gives the proof why and how it works. However I’ll leave here a reasoning that will help you understand the logic behind this. Let’s say you are dividing 30 by some numbers: 30/5 = 6 30/3 = 10 30/2 = 15 30/1 = 30 Can you notice a pattern? The lower the number you divide a number for, the larger de product, so what do you think is the product of *30/0.5*?
It works because of the principle that everything you do to the denominator, you must do to the numerator. In this case, when you multiplied the denominator by 8/3 to get it to one whole (thereby getting rid of the complex fraction), you did the same thing to the numerator. Voila- the numerator (original dividend) is now multiplied by the reciprocal of the original divisor.
This is the best explanation I have found to understand the concept. One of my tutoring students asked why the reciprocal is used when dividing a fraction and I had no clue. I read/watched many explanations and I was totally confused. The lightbulb came on while watching this video. Now I can confidently give an answer to my student. Thank you!!!
That is great to hear! I appreciate you leaving your comment.
Really helped me visualise why this works (multiply denominator by reciprocal in order to get 1 so the problem can be simplified later, multiply numerator in order to maintain equality). Thanks!!
That was INCREDIBLY helpful, as I now understand WTF is actually happening. Thank you!
I am glad the video helped you understand better. :)
For those who who did not get it
In example a/b ÷ c/d is equivalent to a/b × d/c, the rest is explanation why
For example, everything devided by 1/6 is going to be 6×bigger, that means everything miltipled by 6/1 is also going to be 6×bigger, that's it
You can also do it like this -> b/a ÷ c/d = b÷c/d÷a
nice, thanks!
wowowow! such nice explanation!!!! thank you very much for helping people who want to understand, understand!
Thank you! It was extremely helpful for my 6th grader to understand how this works
I am happy to hear the video helps. I appreciate you leaving a comment. :)
For those who are still wondering why do you need the reciprocal. I GOT YOU!
One of the definitions of division is :
10 balls divided by 5 boys, how many balls does each boy get?
Answer : 2. 10 balls are for 5 boys. 2 balls for each.
6 oranges divided by 2 girls, how many oranges does each girl get?
Answer : 3. 6 oranges are for 2 girls. 3 oranges for each.
------ The goal here is to find out how many of something (numerator) does EACH(denominator) get! The EACH in this sentence is equivalent to 1 in Math. ------
The definition maintains for any type of division.
10 balls divided by 0.5 boy, how much will 1 boy get?
Answer : Well, if 10 balls are for 0.5 boys, then it would be 20 balls for 1 boy.
How about this? In general a ÷ b × b = a. Because multiplying by something after dividing by that same thing does not change the number. Now we have a/b ÷ c/d × c/d = a/b. But we also have a/b × d/c × c/d = a/b. So this yields a/b ÷ c/d × c/d = a/b × d/c × c/d and this gives a/b ÷ c/d = a/b × d/c.
I’m astonished. Thanks!
Thanks, this was really helpfull
I get it now !! Thank you
so you're going to explain how dividing by a fraction is equivalent to multiplying by the reciprocal by simply doing exactly that? where was the explanation?
I’m wondering the same thing.
@@strafer8764 Yeah this isn't a good video but I think I understand it. If you think about it in decimals it makes more sense. 1/4 divided by 3/8 is the same as saying 1/4 divided by 0.375. And 3/8 divided by 1/4 is the same as saying 0.375 times by 1/4. Multiplying by a decimal naturally will give you the same answer as dividing by the fraction, as a fraction is simply a decimal in a different form.
@@tomcass240 bro i just got its explanation
Say 1/2 / 1/4 means 0.5 / 0.25 here according to reciprocal we should do 1/2 * 4/1 = 4/2 = 2 and in decimal it is 0.5 / 0.25 = 2 because we when we divide then we read table and in table of 0.25 * 1 = 0.25 and 0.25 * 2 = 0.5 hence we can simply do reciprocal of it
I actually found this video astonishing, and it gives the proof why and how it works.
However I’ll leave here a reasoning that will help you understand the logic behind this.
Let’s say you are dividing 30 by some numbers:
30/5 = 6
30/3 = 10
30/2 = 15
30/1 = 30
Can you notice a pattern?
The lower the number you divide a number for, the larger de product, so what do you think is the product of *30/0.5*?
You didnt explain WHY it works you just showed a different way of solving those types of problems....
It works because of the principle that everything you do to the denominator, you must do to the numerator. In this case, when you multiplied the denominator by 8/3 to get it to one whole (thereby getting rid of the complex fraction), you did the same thing to the numerator. Voila- the numerator (original dividend) is now multiplied by the reciprocal of the original divisor.