I'm 50 years old, and I watch these videos every week. I watch when having a cup of tea/coffee, or on a break. He is teaching me things that my teachers could not teach me (despite them trying - they were all lovely people) 40 years ago! I've now started teaching my two youngest children these techniques. Thank you thank you thank you!
I was taught this in grade school, and tried to use it in high school. My teacher was astonished when I showed her, and she had to convince herself that it was a valid method! She concluded that it was.
Thanks so much for posting these great math videos. Since watching these, my grandson now wants to become a math teacher. I was fortunate to have a great math teacher in high school who made math fun and challenging. He went on to get his masters and then while teaching jr college went on to get his doctorate degree.
You're actually putting both fractions over a new denominator that is the product of the two previous denominators. This is because you can only compare fractions if they are like-for-like (i.e. if they have the same denominator), so for co-prime denominators (those with no factors in common) you must multiple together each of the denominators to get a new denominator, and then mutliple each numerator by the denominator of the other fraction to convert the fractions into ones with the new denominator. In the first example of 6/11 vs 5/9 you are converting both in 99ths. So 6/11 is the same thing as 54/99 and 5/9 is the same thing as 55/99, so the latter is 1/99 larger.
I’m sure the vast majority of people know why this works but if you don’t: you’re simply converting both numbers to the same common denominator. For example, 5/9 vs 6/11. Multiply 5/9 by 11/11 to get 55/99, and multiply 6/11 by 9/9 to get 54/99. Since the denominators are now the same, we can compare the numerators to see which is larger. This tip just skips the step where the denominators are multiplied because we know that they’re going to be the same so it doesn’t matter what the actual value of the denominator is.
That’s what is being done here as well, it’s just that the value of the common denominator is irrelevant when doing a simple comparison of the numerators
So. how do you use this method when working with more than 2 sets of unlike denominator fractions?? (I teach a Pre-GED course to Adult Students in CA/USA and this method/channel are so helpful! But I still need to help them understand the basics, and often they've got more than 2 equations needing a solution!)TIA!
Hi Josh. I had a question about another video in the past which I ask here as I thought it would have a better chance of being seen. You showed a method of squaring numbers up to 1000 where u first square the digits. I've been wanting to try it with 4 or more digits but wondering how? Thanks very much if u know and can help. It's only because you've gotten me interested again and I saw another video where some math genius squared a 5 digit number mentally but using a different method more complicated. Same formula however it seems.
This is one of those things you can sort of pick up by yourself. They teach you how to multiply by 1 to get a common denominator and that’s all you’re doing here. You’re getting a common denominator (which is what you would have to do if adding or subtracting fractions) so you can directly compare the numerators and just disregarding the denominator because its value isn’t relevant
What this video is missing is an explanation of why this method works. What does it mean when you're multiplying the numerator of one fraction with the denominator of the other fraction, and how that product determines one fraction's value to be greater than the other.
You're actually putting both fractions over a new denominator that is the product of the two previous denominators. This is because you can only compare fractions if they are like-for-like (i.e. if they have the same denominator), so for co-prime denominators (those with no factors in common) you must multiple together each of the denominators to get a new denominator, and then mutliple each numerator by the denominator of the other fraction to convert the fractions into ones with the new denominator. In the first example of 6/11 vs 5/9 you are converting both in 99ths. So 6/11 is the same thing as 54/99 and 5/9 is the same thing as 55/99, so the latter is 1/99 larger.
Of course that would be nice but the point of these videos appear to be to teach people to quickly solve math in the head rather than to provide a rigorous proof of why these tricks work.
@@ACitizenOfOurWorld wisdom with no knowledge of why can only lead to further misunderstanding. Even if one has a hard time understanding the WHY, knowing they can find the answer to that question can only lead to good things in the future. If we're gonna help people, we gotta be thorough. Or else, it's like using a vaccine alone to stop a pandemic without understanding why and how the virus is spreading in the first place.
That is how my dad taught me how to do these… I tried telling my teacher this when I was a mere 9 years old 41 years ago… she informed me that I had to do it the LONG way… I refused telling her I had more important things to do than to waste time doing something the long way… tetherball on the playground was calling my name!
I love your story. I’m a couple of years older and I remember those days before kids were sat in front of tv and device screens, when kids were well rounded and got physical activity from playing outside even if they weren’t athletic. I wasn’t athletic but I just remember that pure joy I got when I was a kid, running around, playing, using my imagination. Now I know that part of it was a release of endorphins and I think a lot of kids miss out on that natural good feeling because they do less physical activity. I think it really has contributed to the increased amount of depression in kids not to mention obesity which also has a psychological effect. It sounds like you were well rounded as a kid in your school work and your physical activity. I never had homework until I was in middle school (didn’t affect me later. I went to college abs got my degree) and my poor kids, especially my youngest (2020 graduate), was overloaded with elementary school homework every night. Nightmare! I always allowed my kids to wind down right after school, play outside, and relax over dinner before we hit the books. There has to be a balance. We had a tetherball set up for our kids in the yard and it was great even though there were a few smacked faces and bloody noses. My husband just told the kids if they learned to play right that wouldn’t happen! Lol
Something that may be quicker is if we have 5/7 and 3/4, subtract numerator and numerator to get 2 and subtract denominator and denominator to get 3. then put those together to get 2/3 and if you look, 2/3 is bigger than 3/4 which means 5/7 is bigger. Test this out yourself :D
After watching your channel for a bit now, I really must as you the following questions. 1)don't you think it's past time to permanently divorce the "problem" from the math equation? 2)shouldn't mathematicians be able to develop a much simpler way to teach math in schools? Or is it intentional?
I enjoy this channel. But , while it's fun to almost instantly tell which fraction is larger ; a math teacher in school teaching to a curriculum would teach you how to figure BY HOW MUCH one of the fractions is larger .
Think about it this way: the methods that are taught in school cover a wide array of uses, like an adjustable wrench covers a wide range of bolt and nut sizes. A trick like this is only useful in one case like some specialized tool that sits in the toolbox never being used. The reason this works is because you’re finding a common denominator for both numbers, it’s just happening in the background and we don’t really care what it is if all we want to do is compare the numbers. If we just convert the fractions to ones with common denominators, we can find which one is larger BUT we can also see how much larger one is than the other. Without the denominator we have no way to know that. 5/9 is 55/99 and 6/11 is 54/99 so we know that 5/9 is bigger but we also know that it’s not much bigger, only 1/99 bigger. This is a trick that really isn’t useful, but what is actually going on to make the trick work IS useful and IS taught.
@@jth_printed_designs I understand and agree on this particular trick. And I was fortunate when I took some advanced math, my instructor did teach some quick tips, only after he taught the looong way. And although I never found an application where the quick tip could not be applied, there may be such a case. But how most instructors teach math tends to turn students off, in many cases for the rest of their lives. And there are some cases like my son, who in 2 months completed algebra, calculus and what the school called advance calculus, largely without anything but the books, this is not the case with most children. I hate t see so many turn away from mathematics, before they even know how it applies to so much in real life.
You have to find a common denominator, of which the easiest to find is by simply multiplying all of the denominators together. Once you have converted all of your fractions to ones with a common denominator, you can compare the numerators. Example: 2/3, 3/4, 5/8 The common denominator for these is 96 ( 3 x 4 x 8 = 96 ) To get 2/3 to have a denominator of 96, we will multiply it by a 1 in the form of ((4x8)/(4x8)) find that 2/3 is equal to 64/96. The 4x8 comes from the other numbers denominators. This same thing is done with 3/4, multiply it by a 1 in the form of (3x8)/(3x8) to get 72/96 And finally 5/8 is multiplied by a 1 in the form of (3x4)/(3x4) to get 60/96 Now that we have a common denominator, we can compare them. The trick in the video simply leaves out the denominator side of things because we don’t really care what the value of the denominator is as long as they’re the same as each other. You could do the same trick of not finding the common denominator by multiplying the Numerator of fraction #1 by the denominators of the rest of the other numbers (but not the #1 denominator) then do the same with #2, #3, and so on.
You're actually putting both fractions over a new denominator that is the product of the two previous denominators. This is because you can only compare fractions if they are like-for-like (i.e. if they have the same denominator), so for co-prime denominators (those with no factors in common) you must multiple together each of the denominators to get a new denominator, and then mutliple each numerator by the denominator of the other fraction to convert the fractions into ones with the new denominator. In the first example of 6/11 vs 5/9 you are converting both in 99ths. So 6/11 is the same thing as 54/99 and 5/9 is the same thing as 55/99, so the latter is 1/99 larger.
You’re finding a common denominator but also disregarding the value of the denominator because you are just trying to see which is bigger, not determine the actual value.
I used to have an elderly math teacher who every so often would remind us, "You damn fools." Glad to report that he's 6ft under for quite a long while now while I'm still enjoying a good life!
I knew it was 5/9 because my teacher taught us when comparing two fractions pick the one with the numbers as being the biggest. 1/5, 1/4 or 1/2... the answer for largest number is 1/2, while 1/5 is the smallest fraction. It is depressing to see that math isn't taught the easy way any more and this is due to the standardize tests being so complicated and forcing students to explain answers through telling each step of an equation. Don't blame the teachers, blame the superintendents and those at the top for selling your kids to corporations.
Your awesome but stop using the word “and” when saying numbers. Not 100 and 8, or 1o8… it’s just straight one hundred eight 108. Keep umm com’in your good. Too good actually!
Most English speaking people do say 'one hundred AND eight' rather than 'one hundred eight'. I think it's only in the US (and possibly Canada) where the 'and' is not said. To my British ears it actually stands out as very odd when I watch US youtubers' videos and they say something like 'one hundred eight' without the 'and', as it just sounds so wrong to my ears.
I'm 50 years old, and I watch these videos every week. I watch when having a cup of tea/coffee, or on a break. He is teaching me things that my teachers could not teach me (despite them trying - they were all lovely people) 40 years ago! I've now started teaching my two youngest children these techniques. Thank you thank you thank you!
👍
Heck yeah it helps you keep it fresh in your mind. I love these videos. 👍
@TopMath Great to see yours as well~👍
@@Maria-ud1yv nice to 'be here' with you, Maria!
As I’m sitting here drinking tea I thought, 50? Ha! Old people lol. Then I remember I’m 52. 😃
That one I can remember. Thanks; enjoy all your many mini lessons.
I was taught this in grade school, and tried to use it in high school. My teacher was astonished when I showed her, and she had to convince herself that it was a valid method! She concluded that it was.
I had a bad teacher(s) who ruined math for me. You’re making it fun; thank you!
@PJ PachasaJr wow. That’s insane.
@PJ PachasaJr
SO FUNNY.
Yay, math I can actually do in my head!
I like when someone explain the math in like that simple way without too many steps. thank you so much
This guy is just a life saver since 2009
Thanks so much for posting these great math videos. Since watching these, my grandson now wants to become a math teacher. I was fortunate to have a great math teacher in high school who made math fun and challenging. He went on to get his masters and then while teaching jr college went on to get his doctorate degree.
That's great to hear!
Funnily enough I started life as a geologist and then moved into science teaching. Maths came later!
this is so easy and quick to do, thanks for sharing this tip
This is excellent. I was taught in school to determine this using the laborious Common Denominator method. This is much quicker! Thank you!
Nice, you are a god among men!
Great trick and complements what I’ve recently learned about fractions
My math teacher is one of the best teachers ive ever had maybe even THE best but your channel is still very helpful!
THIS is literally the method our teacher is teaching us
Good tip, I'd not heard of it at school.
5 years ago when I was in 3rd grade I did that and it worked and helped alot
Brilliant as usual!
Thank you sir
Omds! You’re a blessing!!
Hey mate thanks for the work. I think the 'how' is explained well but it would be great if you could explain the 'why' too.
You're actually putting both fractions over a new denominator that is the product of the two previous denominators. This is because you can only compare fractions if they are like-for-like (i.e. if they have the same denominator), so for co-prime denominators (those with no factors in common) you must multiple together each of the denominators to get a new denominator, and then mutliple each numerator by the denominator of the other fraction to convert the fractions into ones with the new denominator. In the first example of 6/11 vs 5/9 you are converting both in 99ths. So 6/11 is the same thing as 54/99 and 5/9 is the same thing as 55/99, so the latter is 1/99 larger.
@@MrDannyDetail I'll stick to the how and leave the why to you...😄
This is brilliant!
Amazing:) thanks for your great job:)
Thank you so much for this trick. I went through 4 years of high school math and 3 years college and never picked up this trick
Yup, knew that one ^^
Thanks anyway, I've discovered some pretty impressive tricks with some of your videos :)
I’m sure the vast majority of people know why this works but if you don’t: you’re simply converting both numbers to the same common denominator.
For example, 5/9 vs 6/11. Multiply 5/9 by 11/11 to get 55/99, and multiply 6/11 by 9/9 to get 54/99. Since the denominators are now the same, we can compare the numerators to see which is larger.
This tip just skips the step where the denominators are multiplied because we know that they’re going to be the same so it doesn’t matter what the actual value of the denominator is.
My daughter’s math has improved so much from this site. Thank you.
Fantastic. Thanks
Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding.🌻🌻🌻🌻🌻🌻🌻🌻🌻🌻🌻🌻🌻🌻
A good method. But, good bookmaker would smash it
Please tricks for ci and si , love your work
Math mysteries are solved easily😊 really enjoy them
I wish I had known this before writing out all those subtraction problems for my son. I had to keep changing the denominators. Haha.
That’s what is being done here as well, it’s just that the value of the common denominator is irrelevant when doing a simple comparison of the numerators
Brilliant!
So. how do you use this method when working with more than 2 sets of unlike denominator fractions?? (I teach a Pre-GED course to Adult Students in CA/USA and this method/channel are so helpful! But I still need to help them understand the basics, and often they've got more than 2 equations needing a solution!)TIA!
Just as I originally learned it.... love replaying math..like my favorite songs
Hi Josh. I had a question about another video in the past which I ask here as I thought it would have a better chance of being seen. You showed a method of squaring numbers up to 1000 where u first square the digits. I've been wanting to try it with 4 or more digits but wondering how? Thanks very much if u know and can help. It's only because you've gotten me interested again and I saw another video where some math genius squared a 5 digit number mentally but using a different method more complicated. Same formula however it seems.
I love these! Why do they not teach like this in school?
This is one of those things you can sort of pick up by yourself. They teach you how to multiply by 1 to get a common denominator and that’s all you’re doing here. You’re getting a common denominator (which is what you would have to do if adding or subtracting fractions) so you can directly compare the numerators and just disregarding the denominator because its value isn’t relevant
Thanks
How does this work in a situation were there are they are asking to compare more than two fractions at once?
What this video is missing is an explanation of why this method works. What does it mean when you're multiplying the numerator of one fraction with the denominator of the other fraction, and how that product determines one fraction's value to be greater than the other.
You're actually putting both fractions over a new denominator that is the product of the two previous denominators. This is because you can only compare fractions if they are like-for-like (i.e. if they have the same denominator), so for co-prime denominators (those with no factors in common) you must multiple together each of the denominators to get a new denominator, and then mutliple each numerator by the denominator of the other fraction to convert the fractions into ones with the new denominator. In the first example of 6/11 vs 5/9 you are converting both in 99ths. So 6/11 is the same thing as 54/99 and 5/9 is the same thing as 55/99, so the latter is 1/99 larger.
@@MrDannyDetail you right. And that needs to be explained in the video to make the explanation complete.
Of course that would be nice but the point of these videos appear to be to teach people to quickly solve math in the head rather than to provide a rigorous proof of why these tricks work.
@@ACitizenOfOurWorld wisdom with no knowledge of why can only lead to further misunderstanding. Even if one has a hard time understanding the WHY, knowing they can find the answer to that question can only lead to good things in the future. If we're gonna help people, we gotta be thorough. Or else, it's like using a vaccine alone to stop a pandemic without understanding why and how the virus is spreading in the first place.
Superb
sir do you have any ebook written by you please reply
Interesting. I was correct on all of them but I did it in my head with a ruler ... seeing the ruler in my head. (I do a lot of woodworking)
That is how my dad taught me how to do these… I tried telling my teacher this when I was a mere 9 years old 41 years ago… she informed me that I had to do it the LONG way… I refused telling her I had more important things to do than to waste time doing something the long way… tetherball on the playground was calling my name!
I love your story. I’m a couple of years older and I remember those days before kids were sat in front of tv and device screens, when kids were well rounded and got physical activity from playing outside even if they weren’t athletic. I wasn’t athletic but I just remember that pure joy I got when I was a kid, running around, playing, using my imagination. Now I know that part of it was a release of endorphins and I think a lot of kids miss out on that natural good feeling because they do less physical activity. I think it really has contributed to the increased amount of depression in kids not to mention obesity which also has a psychological effect. It sounds like you were well rounded as a kid in your school work and your physical activity. I never had homework until I was in middle school (didn’t affect me later. I went to college abs got my degree) and my poor kids, especially my youngest (2020 graduate), was overloaded with elementary school homework every night. Nightmare! I always allowed my kids to wind down right after school, play outside, and relax over dinner before we hit the books. There has to be a balance. We had a tetherball set up for our kids in the yard and it was great even though there were a few smacked faces and bloody noses. My husband just told the kids if they learned to play right that wouldn’t happen! Lol
Something that may be quicker is if we have 5/7 and 3/4, subtract numerator and numerator to get 2 and subtract denominator and denominator to get 3. then put those together to get 2/3 and if you look, 2/3 is bigger than 3/4 which means 5/7 is bigger. Test this out yourself :D
After watching your channel for a bit now, I really must as you the following questions.
1)don't you think it's past time to permanently divorce the "problem" from the math equation?
2)shouldn't mathematicians be able to develop a much simpler way to teach math in schools? Or is it intentional?
I enjoy this channel.
But , while it's fun to almost instantly tell which fraction is larger ; a math teacher in school teaching to a curriculum would teach you how to figure BY HOW MUCH one of the fractions is larger .
Think about it this way: the methods that are taught in school cover a wide array of uses, like an adjustable wrench covers a wide range of bolt and nut sizes. A trick like this is only useful in one case like some specialized tool that sits in the toolbox never being used. The reason this works is because you’re finding a common denominator for both numbers, it’s just happening in the background and we don’t really care what it is if all we want to do is compare the numbers.
If we just convert the fractions to ones with common denominators, we can find which one is larger BUT we can also see how much larger one is than the other. Without the denominator we have no way to know that. 5/9 is 55/99 and 6/11 is 54/99 so we know that 5/9 is bigger but we also know that it’s not much bigger, only 1/99 bigger.
This is a trick that really isn’t useful, but what is actually going on to make the trick work IS useful and IS taught.
@@jth_printed_designs I understand and agree on this particular trick. And I was fortunate when I took some advanced math, my instructor did teach some quick tips, only after he taught the looong way. And although I never found an application where the quick tip could not be applied, there may be such a case. But how most instructors teach math tends to turn students off, in many cases for the rest of their lives. And there are some cases like my son, who in 2 months completed algebra, calculus and what the school called advance calculus, largely without anything but the books, this is not the case with most children. I hate t see so many turn away from mathematics, before they even know how it applies to so much in real life.
What if you have three or more fractions to compare please?
You have to find a common denominator, of which the easiest to find is by simply multiplying all of the denominators together. Once you have converted all of your fractions to ones with a common denominator, you can compare the numerators.
Example: 2/3, 3/4, 5/8
The common denominator for these is 96 ( 3 x 4 x 8 = 96 )
To get 2/3 to have a denominator of 96, we will multiply it by a 1 in the form of ((4x8)/(4x8)) find that 2/3 is equal to 64/96. The 4x8 comes from the other numbers denominators.
This same thing is done with 3/4, multiply it by a 1 in the form of (3x8)/(3x8) to get 72/96
And finally 5/8 is multiplied by a 1 in the form of (3x4)/(3x4) to get 60/96
Now that we have a common denominator, we can compare them.
The trick in the video simply leaves out the denominator side of things because we don’t really care what the value of the denominator is as long as they’re the same as each other. You could do the same trick of not finding the common denominator by multiplying the Numerator of fraction #1 by the denominators of the rest of the other numbers (but not the #1 denominator) then do the same with #2, #3, and so on.
@@jth_printed_designs thank you so much! 😊
payda eşitliyor işte
Yupp, was taught this one when first studied comparing fractions..
Thanks anyways though ❤️
yoinks
Yoinks and away!
Easy does it
Can anyone tell me what's the logic behind this method? Why does it work
You're actually putting both fractions over a new denominator that is the product of the two previous denominators. This is because you can only compare fractions if they are like-for-like (i.e. if they have the same denominator), so for co-prime denominators (those with no factors in common) you must multiple together each of the denominators to get a new denominator, and then mutliple each numerator by the denominator of the other fraction to convert the fractions into ones with the new denominator. In the first example of 6/11 vs 5/9 you are converting both in 99ths. So 6/11 is the same thing as 54/99 and 5/9 is the same thing as 55/99, so the latter is 1/99 larger.
You’re finding a common denominator but also disregarding the value of the denominator because you are just trying to see which is bigger, not determine the actual value.
3/4 3/4 9/12
55/99 54/99
عالی 👌👌👌👌
I used to have an elderly math teacher who every so often would remind us, "You damn fools."
Glad to report that he's 6ft under for quite a long while now while I'm still enjoying a good life!
im surprised how most of the people in the comments are being introduced to this method rn lol (regardless of their age btw)
I am proof not all Asians excel in math😣...but I like this😁
I knew it was 5/9 because my teacher taught us when comparing two fractions pick the one with the numbers as being the biggest. 1/5, 1/4 or 1/2... the answer for largest number is 1/2, while 1/5 is the smallest fraction. It is depressing to see that math isn't taught the easy way any more and this is due to the standardize tests being so complicated and forcing students to explain answers through telling each step of an equation. Don't blame the teachers, blame the superintendents and those at the top for selling your kids to corporations.
4/5 bigger
That's not how I did it. I divided the bottom into the top to turn it into a percentage. The one with the higher percentage was the larger fraction.
But ... but ... but, why?
Why does it work ?
5/9 bigger
how on earth is this legit?!
Your awesome but stop using the word “and” when saying numbers. Not 100 and 8, or 1o8… it’s just straight one hundred eight 108. Keep umm com’in your good. Too good actually!
Most English speaking people do say 'one hundred AND eight' rather than 'one hundred eight'. I think it's only in the US (and possibly Canada) where the 'and' is not said. To my British ears it actually stands out as very odd when I watch US youtubers' videos and they say something like 'one hundred eight' without the 'and', as it just sounds so wrong to my ears.
Apa kamu sedang bindeng?
Sorry not interesting