99% of Math Students Still Find This Difficult
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- Опубліковано 6 бер 2022
- TabletClass Math:
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Math help with find the LCD (lowest common denominator) when adding or subtracting fractions. For more math help to include math lessons, practice problems and math tutorials check out my full math help program at tcmathacademy.com/
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This misses out the first step: check to see if the fractions can be simplified. Working with 1/17 is far easier than working with 5/85.
Agree!
Yeah I agree.
It took me less than a minute to do this by head...
My steps where:
5/85 = 1/17
multiply numerator and denominator of the other fraction with 17 and add 40 to the numerator (because the other faction is now 1/17 and we're going to multiply there with 40)
so that very quicly gives you 91/680.
Obviously at that point I should have checked if we could simplify, with which I haven't bothered yet.
(Than again I used to be a physics major, not a math one... so when it comes to actually calculating stuff, rather than being good at math theoretically, I've probably had a better education)
I think one of the biggest failings of the video is waving away simplification as “easy” when in reality, I think it’s usually just as hard as “lcd” which he said was hard as well.
Simplification usually means gcd, which is a very close concept to lcd, and I think needed to be explained as well.
Other than that, he also didn’t explain his “bowtie” method AT ALL. he just showed it on the simply examples.
Its just another dry “trick” that doesn’t teach anything at all. He should’ve shown that, for example, for 3*85/40*85 == 3/40 because you are multiplying by 85/85 == 1, which can easily find you a common multiple (maybe not lcm, but enough to solve). Then showed the “bowtie” method as the steps to take for simple add/subtract examples. This also enforces the idea of fraction manipulation, where multiplying the top and bottom is always the same, and also demonstrates what simplification is doing (taking away that fraction that equals one).
good point overlooked that and did the cross multiplication by head
what was shown in the video is nonsense. I agree with you: first simplify to 1/17 then cross-multiply and you're done. So a nonsense what was shown there
I got this right in a couple minutes using the old math I learned in the 70’s. If you were my math teacher back then I would have slept through your class.
I did it in my head in like 2 seconds. lmao... I quickly knew the denominators were both divisible by 5. That left 8 and 17. I multiplied the 1st numerator by 17 and the 2nd numerator by 8. I added them together. Then I chose a denominator that looked easy to multiply by. I chose 85*8, which I know is 680. Answer is 91/680. 91 is a prime number. That is the solution. Easy.
Wow, he calls this a short cut. LOL It took a couple of minutes using the old school method. I'm 62
Honestly, if he were my math teacher I would have ignored him and asked my mom how to do it. I have done it before, this method seems too convoluted and it probably won't work once you start working with variables and functions (ie. sine, cosine, secant, etc.).
Boomer is right
Agreed... 5/85 is 1/17... cross multiply to get 91/680. Only took more than 2 seconds because I don't multiply by 17 in my head too often... so, 10 or 12 seconds maybe.
Just graduated from nursing school with honors at age 61, but given that math was a struggle in the 70's, I find this not only healing the inner child but rewarding as well. Now I get to put the teacher on pause, and make her repeat what I didn't get. Love it! Thanks. I just subscribed!
Congratulations George! I am 66 and just found this channel. It’s never too late to correct the deficits of our education way back then. Just so many sources and learning tools these days, and as you said , you can put the teacher on ˋPause ´ . Love it!
One year later, so how are you liking nursing?
It has been very rewarding in many ways. Thank you for asking.@@cl5193
Good job George. If I knew where you are, I’d invite you and family to dinner. 👨🎓
Most of us agree that such math isn't difficult AFTER the basics are understood... That those of us who struggle with math AREN'T STUPID but, rather, had a STUPID instructor.
Personally I think you made a very simple problem difficult. 3/40 + 5/85 is the same as 3/40 + 1/17. Since you can't simplify the two fractions more, you cross multiply the denominators and you get 51/680 + 40/680 = 91/680. Always try to simplify the individual fractions.
Oh!
I totally agree with you and I think I can say it a bit different. I might be wrong, might not ALWAYS work, but in this example he gave it does.
Basically you bring down each of the fractions you want to add to its lowest denominator. In this case 3/40 couldn't be lowered, but 5/85 simplifies to 1/17, once both fractions are simplified you do the criss cross/bow tie trick.
Perhaps doing it my way, in some examples you might end up with not simplified results ( 2/4 instead of 1/2) and with his approach you would always end up with the simplified result.
That is how I did it, in my head.
I think that the point of the video was not so much to solve the problem but to teach finding LCD. Also, you can simplify the problem even further than that. 40 is a great number it consists of 10x4 so you have 3/10|4 and as you said 1|17. 4 multiplied by 17 is 68 so 3/10*17+1*4|68 --> 51/10+4|68 ---> 5.1+4|68=9.1|68
@@Fenixix7 that's pretty clever too I never thought about dividing one side by 10 for larger numbers. I gets for really large numbers you could divide both sides by ten then multiply by 100 at the end
The correct answer is 91/680. To get to this solution, you first need to reduce the 5/85 to lowest terms, which is 1/17. Therefore, you are adding 3/40 to 1/17. The lowest common denominator between 40 and 17 is 680, simply because 17 is a prime number. Now, you multiply each of the 3/40 by 17 to get to 51/680, and then you multiply each of the 1/17 by 40 to get to 40/680. You then add the two new fractions, 51/680 plus 40/680, and you get your answer, which is 91/680. Easy as pie.
Thanks. Good response! (Maybe I'm saying that because I did the same thing, but it's true nevertheless.)
Same way I did it but I’m 71 years old and I did not think about factoring. Maybe the reason I did not visualize algebra very well.
Or you can just do some quick multiplications and find the LCD in a moment or two, and cross multiply. Bingo 91/680ths. 30 second problem, assuming the kid knows basic multiplication.
It's quicker to simply multiply the denominator to 3400. Giving the result of the addition as 455/3400. Divide both by 10 to get 45.5/340, then multiply both by two to get rid of the decimal and you have 91/680.
That is how I did it, as well. To add a bit of clarity, perhaps, to your answer for some readers.... You can multiply a number by 1 and not change the value. So, if you multiply 3/40 by 17/17, it is the same as multiplying it by 1, but the value is now expressed as an equivalent fraction 51/680. Similarly, multiplying 1/17 x 40/40 does not change the value, but the value now is expressed as 40/680. Each fraction is now expressed with a common denominator. Obviously, the result of one denominator multiplied by the other will be the same, ie. 40x17 = 17x40 = 680, thus the reason for choosing the opposite denominator in creating a fractional equivalent of one, ie. 17/17 and 40/40.
Alternatively, before we use prime factoring to determine LCD, we could simplify 5/85 down to 1/17. Since 17 is a prime #, the LCD will be 40 x 17 = 680.
that what i did
Only if you want the LCD, but I do not see anything on the board asking to find the LCD, poorly done video
I did *2 to get 10/170, then *4. I tried 340 as well, but 40 doesn't go into it.
What are you doing in here if you know these equations. 😊
@@kangacrew540 sorry. I will leave.
6 minutes and he finally starts solving for LCDs.
After a bit of time, much more than 5 minutes into this, the problem is starting to get solved. If I took that much time in my class to get beyond yacking, my kids would have fallen asleep.
You are spot on. This man suffers from verbal diarrhoea.
5 minutes of promotional material and then end up with a crappy solution.
This sucks
Gotta stretch it for the algorithm lol
I multiply 40 x 85 =3400 and use this as a CD. Im 72 and thats how I was taught
I’m 76 and ditto Terry… except bow tie that bad dog = 455/3400, AND needs to be reduced by 5 = 91/680
@@CATMANROG Just seems easier than all that factoring
Yeah, us old fart scientists and engineers can still do it!
Not very well explained why 5 is not treated as the number 2 that repeated itself 3 times - 5 appeared 2x so it should be 5 squared right? Can someone explain this better?
Meanwhile, some of us were making out in the book room with Lola Betancourt...
To find the LCM, build a fraction, reduce it, and find a cross product between the fraction you built and its reduced form. Behold:
40/85 reduces to 8/17. 40x17=680, and 85x8=680. The LCM is 680. Works every time.
I am 82 and learned my math by the time I was a junior at WSU. I got 91/680. I reduced 5/85 to 1/17. We were never taught this BowTie method by Mr. Gaither my 5th and 6th grade teacher.
You’ll run out of time taking that long per problem. Multiply denominators, there’s your common denominator. Add and reduce at the end, done.
Yep, quick and dirty. Works every time.
That’s what he’s doing for his “bowtie” method which he claims to be a “better method than finding the lcd.”
I think this video is for those who were once taught with finding the “lcd” to make fractions, but I think a better way to explain why his “bowtie” works is to, show why this works, which is exactly why multiplying the denominators.
Here is what I would’ve tried to explain:
Multiply the top and bottom of (3/40) by 85 is always the same, and so the fractions still have the same value (3*85/40*85 == 3/40) and same with the other fraction. This creates a common denominator of 40*85, and the values can be found using this “bowtie trick.” But then, also remember to explain how to simplify the fraction afterwords.
Also, the fact that he simply waves away that “simplifying the end fraction is easier” really irks me. The video should’ve told you how to simplify if your teacher requires you to (probably gcd method?) as it could potentially lead to some points off if you just use the “bowtie” when your teacher is expecting a simplified fraction at the end (of which lcd kinda avoids). Simplifying (GCD) imo is potentially just as hard as LCD, for those whose brains can’t immediately recognize it for simple numbers.
Yeah.......that's the way I did it.......then reduce the answer
much faster to reduce the fraction when the numerator and denominator both end in five.
This video is like watching paint dry, far too long.
Hopefully he isn't teaching our kids in school. No wonder kids fall a sleep in class.
This guy is the kind of teacher who, if this is his usual teaching style, drives away most children from loving maths and therefore harms the progress of science and many things in everyday life.
Agreed
His nasal voice and 'trying to be cute' delivery make me want to shriek.
And the paint isn’t even dry at the end because you not even told the answer!
I used the bowtie method and got 455/3400..... then reduced the fraction by dividing each by 5 which gives me 91/680. I was also in school in the 70's.
That's exactly what I did.
Correct. I too was in 4th grade in 1971. Which is when I remember fractions being introduced in school Math. The year before Mom had me recite times-tables (1-12) every day after school. Our Old School Math is, IMO, far superior & more reliable.
I did exactly the same.. also from 70s South Africa
Good job, but reducing 5/85 to 1/17 first would have saved you some of your #2 pencil. Always check to reduce the individual fractions first. I also was in school '67 to '78.
@@bolwinklemoose1999 You used a pencil?
I learnt the “bow tie method” at school when I was 10, although I was not know it by this , or any , name. Now 62 years later , to keep my brain working, I’ve been trying to fill in a number of gaps in my maths which made my engineering course at University harder than it needed to be.
I do recall that at school , I nearly always applied this method to “robotically “ and of course I was very often swamped by the shear magnitude of the numbers involved, and inevitably this can lead to mistakes……no electronic calculators available then , just logarithms , and a slide rule at Uni.
So to avoid this , keep everything as simple as possible…..reducing 5/85 to 1/17 achieves that. Secondly , the principles of manipulation in fractions is really really important, as the student progresses to more advance topics.
I’ve been helping my neighbours children with their fractions , which is why I was drawn to this video.
I had teachers that made it so difficult to learn anything. You are confounding.
Find the CD by multiplying the two denominators together, multiply each numerator by the opposite denominator, add the products together, then figure out what you can reduce the fraction by. Ultimstely both the numerator and denominator were factors of 5, yielding a LCD of 680.
just multiple each summand by 1
@@joelwillis2043 multiplying the summands by one doesn't change anything. Do you mean add one to each summand? IMO that doesn't make the problem any easier, just messier, as you have to subtract it later, and doesn't get you any closer to the LCD.
N Hennessy is just describing the naive cross-multiply then simplify trick, which gets you A common denominator, but not the Least common denominator. You get the LCD after you're done simplifying the answer, whereas the idea behind finding the LCD is it's supposed to help you solve the problem in the first place.
I used a variation on the cross multiply trick, where I multiplied the denominators to get a common denominator, then reduced it until you get the LCD (40*85, 3400/40, 36/2, 680/40 to verify it's still a multiple). Then I cross multiplied with the LCD.
What annoys me about my way and the naive cross multiply trick is they aren't really feasible without a calculator, or at least a pen and paper, whereas the LCD method is easier without a calculator (though still not exactly easy unless you're well practiced in mental multiplication).
@@jeffwells641 Adding 1 changes the number, by multiplying by doesn't. 1 is the multiplicative identity. Further, if we have a/b + c/d we can multiply a/b by 1 and c/d by 1, this simplifies everything. We just multiply a/b by d/d and multiply c/d by b/b yielding ad/bd + cb/bd when we add these we have (ad+cb)/bd. We are done.
@@joelwillis2043 What's 3 * 1? It's 3. 40 * 1? It's 40. 3/40 * 1 is 3/40. "Multiply by 1" does absolutely nothing to the problem in any way, shape, or form.
What you're describing is cross-multiplying, which is LITERALLY WHAT N Hennessy DID, except you've described it incorrectly!!
You don't just multiply by 1, you multiply by 1 AS A FRACTION WITH THE OPPOSITE DENOMINATOR - that is, 3/40 is multiplied by 85/85, and 5/85 is multiplied by 40/40. THAT'S LITERALLY CROSS MULTIPLYING. You may think this is trivial, but multiplying 3/40 by any fraction other than 17/17 or 85/85 will not help you solve the problem in any way.
I don't expect you to understand any of this, because you had no idea what was going on in the first place.
@@jeffwells641 The problem is to add two fractions, 3/40 + 5/85. That is it. a/a = 1 for all real numbers a except 0. Let us begin, 3/40 * 85/85 = 3/40 and 5/85 * 40/40 = 5/85. We are multiplying by 1. Now we have 3*85 + 5*40 all divided by 40*85. I hope you've learned something.
One thing. You don't need to find a LCD... you just need a CD. It certainly doesn't have to be L in order to add and subtract.
My math teacher in 7th grade made the same error. You find any common denominator, then add them. After that you can reduce it. When I pointed this out he was not happy being corrected so I think the LCD is just a teacher thing.
@@markxxx21 yeah. Your *final* answer should have the LCD, but you can get there however is easiest.
This would be a typical question in junior school in the 60’s. We used to get pages of these questions for homework. I would expect most 8-9 years would work this out back then. I’ve never forgot the technique.
Yep. Doubt they even teach it today... just like phonics.
Same here, in another part of the world. It seems a lot of teachers nowadays prefer the kids to be fluent in genders rather than maths.
Dollars to donuts kids nowadays can't solve it.......lololol
Same here (junior schools in Italy).
So, 4 minutes in and it's safe to say that the LCD is important. LSD might get important, too, if I want to get to the end of this endless video
Of course they find it hard if they follow your (obsessive) method of finding the LCD. In the UK we would just multiply the denominators and cross multiply the numerators, that is the 'bow tie' method but missing out how to find the LCD which in my view just makes the whole approach harder. The 'hardest' thing this way is to multiply 40 and 85 which isn't really that hard.
Yeah, just give me the mechanics of the solution, and quit the 15 minutes of bull. But you know UA-cam videos must be a like a run on sentence explaining someone's first name. LOL
Excellent response to the "new math"...and it isn't even that. Why this guy thinks this is a clear explanation is beyond me.
That's what I was thinking of also.
@@samconagher8495 I think these are clearly videos for students who are still learning how to do these kinds of problems in school, not for those who already know how to do it. And he is a tutor, so... yeah, he kind of has to belabor the point, and method of solution. Nonetheless, I do agree with everything you guys have commented here.
If this video was about the general method of how to find the LEAST common denominator, that's one thing, but he did it in the context of solving a problem, and in doing so only made it more difficult and complicated than it had to be.
@@mydogskips2 Whether that is the case or not, his explanations are greatly lacking in ease of understanding. IF I were just learning right now and followed his methods I would have given up long ago. It is layered with unnecessary complexity. BTW, I teach too as well as apply mathematics in my main profession. This guy keeps it up, there will be no one left who understands basic math.
Wouldn't reducing 5/85 to 1/17 be the obvious first step. Seems like there could be a better example to showcase prime factorization.
No. Modern calculators can add and display fractions easily. So the first step is obviously to use a calculator.
@@Barreloffish Back in elementary school in the 70s when I learned this, you simplified fractions first to simplify the math because you were doing it by hand. You were the calculator. Smaller numbers are "usually" easier to work with. If the result needed to be simplified or normalized that was expected as well.
In this particular case, if you simplified first, you already got rid of the extra 5.
Showing work was expected when learning this stuff and you wouldn't get full credit if you weren't showing how you got your results.
@@mikechappell4156 I was being sarcastic. Sorry it's hard to tell over texts. I was a math tutor in my local community college. Most of the students would always reach the calculator, even for something like 6 divided by 1... So it's obvious that using the calculator is the first step, haha.
I AGREE 100%!
I don't remember this method of figuring out the LCD in school. It was interesting to learn. I knew the LCD couldn't end in 5, so I just kept multiplying the 85 by anything that would make it end in 0 until I found a number I could also divide by 40. I got up to 8, which gave me 680. And when I divided that by 40, I got 17. So I multiplied the 5 by 8 to get 40, the 3 by 17 to get 51, added them and got 91/680.
I’m 70 and I forgot about the bow tie method. Had to clear out a lot of brain cobwebs but I was able to get the right answer the old fashioned way and the bow tie method. This is why I watch your videos. I love to play along.
Before anything else 5/85 should have been reduced to 1/17. Thus the addition is 3/40 + 1/17. Multiply denominators to find new denominator 680 and cross multiply denominators and numerators.
Result 51 + 40 all over 680
= 91/680
yup, did this in my head. Why does this video need so long to explain this. I'd dislike this video if I could.
@@jaketherake71 As I did, in about 30 seconds. I'm 79.
I've never seen anyone take so long to say nothing!
You are not alone in that thought. I guess I'm going to have to block this channel from appearing in my feed because the temptation to not comment about his irrelevant rambling is just too great. I'm frustrated because people are somehow just blindly following him and praising him. I would be like people who praise a chef whose food tastes like meow mix.
UA-cam forces him to stretch the explanaton. Like going around the block and ending back here. You could go this way, of you could go that way; you could walk, or run; you could crawl on your knees going that way, or the opposite way; you could scoot on your butt; you could hop on your feet, or you could roll from side to side, but when you go around the block, you always end up on the same spot if you're careful. Ca-ching.
I guess you've never listened to politicians speak, have you? jk
I think they take the cake, but yeah, this explanation of a simple problem, with a straightforward method for finding the solution, which he didn't do in favor of doing something unnecessarily convoluted and tedious may rival them in terms of bloviating and stupidity.
@@mydogskips2 yeah... I lost my head for a minute
I wish I never commented on this channel because now it shows up randomly on my feed, so, stupid me watched a little bit more of various videos (I love math), but this channel just seems so questionable to me. Every video I have skimmed through takes over 15 minutes to explain what any reasonable teacher could in less than 5 (and that's pushing it). This guy just rambles, and it's quite discouraging when people praise him because obviously these people like having their time wasted. How in the world this channel has 270+K followers is seriously beyond me. I'm certainly not trying to be mean, but knowing that this guy has this kind of following just makes me question why.
I always considered maths class to be a down payment on the time I will have to spend in purgatory, or hell!
My thoughts exactly. I suggested on another video that his channel is a spoof. There is a certain comedic value to his videos as you watch him grossly overcomplicate the simplest of problems to deliberately bore and confuse his viewers. If he is actually some kind of maths teacher as he claims then I find that quite sad.
The "bow tie" method is exactly the same as the "standard" method, its just presented in a different way. In both cases, you are multiplying the numerator and denominator of one fraction by the denominator of the other fraction. IT is, however, easier to "see" in your mind's eye and remember as a methodology. But I would hesitate to call this a "different" method. Just a different way to look at it. I also have to point out that this method doesn't in fact produce the LCD in your other example of 3/10 + 1/5. The "bow tie" method applied here would result in a common denominator of 50. 15/50 + 10/50 + 25/50 = 5/10 = 1/2 The part of this that ALWAYS drove me nuts in school was the phrase LOWEST common denominator. Why not just solve for COMMON denominator (as you are here) and then simplify? That makes SOOOOO much more sense, is easier to understand, and simplifies the overall problem into three simple steps. The term LOWEST is the real problem here. So, why not just do the bow-tie - 3/40 + 5/85 = 255/3400 + 200/3400 = 455/3400 Both are divisible by 5, which gives us 91/680. SOOOO much simpler than doing all of that factoring ahead of time! WHY IS THERE NO COMMON SENSE IN MATH ANYMORE?????
Method I use
I totally got all the check marks. Good to refresh the fundamentalism of the fractioning of things. 👍 i would just multiply 40 and 85. Go from there.
I attended public school in the 50's and 60's. The first thing I noticed to find LCD was to divide each denominator by 5, yielding 8 and 17 as the equivalents. So multiplying each numerator and denominator by the appropriate number yields 51/680 and 40 /680. Not that hard.
Same
Went to school in a different country
They're making it needlessly complicated in U.S.
I attended grade school in the 70's and figured out the answer the same way in my head. These new math techniques are much more difficult. Why fix something that is not broken.
You didn't explain why you divided the denominators by 5 and what you did with the numerators to get 51 & 40 though.
I also attended school in the 50s and 60s. Did it in my head, easily. Math really is not as hard as it's made out to be. I'm always amazed at how much trouble so many others seem to have with it. But then, most of them were not in school in the 50s and 60s. Hmm. I sense a correlation.
Yeah, same here, Danny. Escaped the monstrosity in olde '63; still attending the University of Autodidact. (From that one, one does not graduate 'till demise, it being of lifetime matriculation. It is only after, that you are graded.)
Damn..I wish you were around when I started going sideways in math 45 yrs ago in 8th grade. My brain woke up late in life . Your videos helped me translate the mathematics so much that was able to achieve my General ticket.( aka General class ham license ) I don't fear it anymore. Thank you sir!👊
I love your arithmetic puzzles. My approach to this one was more intuitive, I multiplied the bottom numbers together and tried a few possible common divisors, came up with 5 and divided that into 3400 to give 680. I take the point that in algebra, there may not be an intuitive factor to start with and I will practice using your method, thanks.
this is far harder than it needs to be. use the old easy method, it's much much faster.
You couldn't just give us the "91".
Doing it in your head adds another level.
For someone the emphasizes focus, YOU are all over the place.
I'm gonna give you a smily face with a star.
like most maths teachers - because they know how to do it they manage to turn it into alphabet soup when explaining
I did it a little differently in my head.
I just multiplied 40 x 10 and 85 x 4 to get 400 and 340. Then subtracted 1.5 units from the 30/400 num/denom to get 25.5/340 + 20/340, adding up to 45.5/340, then I doubled the num/denom to get 91/680.
Unorthodox, I know, but it worked.
I had a lcd of 340 because I used 1.5/20 &. 1/17 as the fractions. The way he goes on and on and on I can imagine most people falling asleep before he gets to the answer.
Honestly, this one was simple enough to do in my head. Of course this got me into some trouble as I got into higher math. I learned why it was important in more basic math to show your work. Learn the process and save yourself a headache later, even if math comes easy to you.
Being in an Odds Business. I took just 12 seconds HOWEVER my answer is 1 over 226.67 which are the odds but that may have not been the question:)
My first step was to simplify 5/85 to 1/17. Then the LCD is simply 40x17.
But the method described is probably a more thorough process.
Agreed. It really depends on how big the numbers are that you're working with. The cross-multiplication method works no matter how big the numbers are---then it's just a matter of simplifying the final fraction.
no it's not more thorough-- it's more complicated with extra steps-- it's the opposite of good math --
To be honest your method was much simpler than mine. I multiplied both denominators and then multiplied both numerators by the other denominator. Then I saw that after adding the resulting fractions that they were both divisible by 5, so I divided both by 5. I got the same number as you but it was a bit more cumbersome. Full disclosure, I am 60 so I graduated from elementary school a few years ago, but I am happy I retained at least a rudimentary understanding of how to do this.
The way you get to the Lowest Common Denominator is one way to take. I was taught to look if they have a common denominator by which both can be divided. And yes, we see right away, that both are a multiplication of five. 8 x 5 = 40 and 17 x 5 = 85. So how do we make them match? By crossing the numbers over. So when I take 17 x 40 (= 680) and 8 x 85 (= 680) I already have the LCD. Now I also use the same crossed over number for the numbers above the lines. So 17 x 3 = 51 and 8 x 5 = 40.
Which makes the equation 51/680 + 40/680 = 91/680. 91 is not a prime number but is 13 x 7. When I divide 680 by 7 or by 13, I don't get a round number. So I just leave it at 91/680.
As an Engineer, I'll get lost in Mathematics. In the field, you don't do Math IQ but a lot of work ethic common sense. After 30yrs outside any classroom, I still cherish any Math. It reminds me of my failures and how to overcome it.
455/3400.........................4.55/34..........etc
I'm an engineer I just saw, about 1/10th less than 1/10th so 1/10th so 2/10ths =1/5th then x by 3, 3/5ths so .6 so order 5/8ths steel plate. But really lets be honest, just let the computer do it.
@@hansvonpoopinheim4215 as an engineerp you should be able to do it ...so am I...the fraction should suffice without a computer n mentally m...this is easy stuff
@@hansvonpoopinheim4215 Finally. A fellow engineer crack the code. In my last my final exams of Strength of Material class, my Civil Engineer professor said open books, open notes and use any modern calculator during the exam. You all need it, once in the field. That is so true.
@@atta1798 Not that I can't I focus on structural steel tanks, not worth the time in the end. I got bigger things to deal with like welders not doing their jobs right and certifying paperwork.
Intros are a bit too long. Time is precious. Would be great if we can think of a way to get right to it if possible. Thanks for making the videos!
The author of this video at 13:52 says it's generally easier to reduce fractions than to find the LCD! So the original problem was 3/40 + 5/85. Using the authors own advice then we should have reduced 5/85 as we're taught in school to always reduce fractions first by order of operations to get 1/17 and then multiply 40 x 17 = 680 LCD rather than start to introduce a long convoluted explanation using 2 to the 3rd power etc? Maybe there's a reason 99% of students find this difficult.
Many thanks. This was an excellent reminder of how to do large LCDs.
Cut to the chase please Sir...it ain't an essay. Thank You for the free math lesson just the same.
91/680 I understand how to do this, and I don't know if it can be further reduced, but at least this I understand. But the GED questions are high level like someone in chemistry or maybe architecture but I have never seen anywhere that I've ever needed these equations and the only thing I've ever needed was the circumference of a pipe and that was half the diameter times pi or the radius times pi
But all these other cone equations where you have to find the area inside of the cone and that formula is so crazy and none of the books I've read none of the videos I've seen explains what you do first what you do second and why and that should be the first thing that they explain what the order of functions is
One is prime the other isn't.
But you do use these everyday. The human brain is actually quite good at guessing too. I will give an example, although quite simplistic. When you drive, you constantly perceive speed over time. A fraction, ratio, whatever you want to call it. It's a linear function. So we teach it at the beginning, y=mx+b. You have a rise over run, that you can inherently understand, even if you can't explain it in the language of math. When people ask me when they will use math, I tell them hopefully every single moment of your life. It's enlightening. An enlightenment that keeps you out of the trailer parks.
@@cammontreuil7509 That was was first instinct on this, but I believe they call it relatively prime or something similar since they have no common factors. 7*13/2*2*2*5*17.
They only made us learn up to the 12 times table in school, but you only need to check for possible prime factors up to the square root when factoring. Tests for divisibility by 2 and 5 are obvious. You can check for divisibility by 3 by checking if the sum of the digits is divisible by 3. I don't think there is a way to check for divisibility by 7 without doing the math, but the math is still relatively simple. Once you had the prime factors of the numerator, you really only need to check that they don't go into the denominator evenly.
For the first exercise my method was to first recognize that 8×5 is 40, and since 80 is a direct multiple of 40, the LCD is at least 8 times 85 (since the number can't end on a 5, and the LCD of 5 and 40 is 40, aka 8×5) so 8×80 + 8×5=680, or 17×40
Try again my friend. You are on the right track. Common knowledge should be available to all. I wasn't great at helping my children grow, but they grew on their own and with the internet. Love.
Judging by this comment section, it seems your “99%” hypothesis may have to be adjusted.
I did this without the factoring step because that's how I was taught 60 years ago. Do you include the factoring because understanding that step will be useful in more complicated problems and/or algebra?
They use it cuz it's a stupid complication
I'm retired but wish we had these online tutoring tools in the late 60's-mid 70s! The grandchildren will definitely benefit and a very very good Instructor!
not this one though. it's been over complicated by t he teacher.
You don't have to do all of that work to get the lcd. I just multiply them to get 3400 as the denominator. Then from 455/3400, reduce. They're both multiples of 5.
p.s. but your teaching methods are great!
This isn't difficult, you just have to find the smallest common multiple of 40 and 17. and since 17 is prime, it is the product of those two:
3/40 + 5/85 = 3/40 + 1/17 = 51/680 + 40/680 = 91/680.
Since 91 is prime, you can't shorten this fraction.
91 is composite but relatively prime to 680
17 and 40 are co prime (40 being 2*2*2*5) which is why you need the product, not just because 17 is prime.
91 is not prime, it is 13*7
I solved this by multiplying each fraction on each side by one, or in other words, the 85 denominator-side by 40/40 and the 40 denominator side by 85/85, which doesn't violate any math laws. The denominators will then both be a common 3400.
No but your denominator is far too big and takes too long to do.
@@GazzaDazzle not really because then you end up with 455/3400 which can be easily divided by five giving you 91/680. This is a very neat trick I didn't know. It's still easier if you you 1/17 though because then you end up with 51/680 + 40/680 giving you 91/680 and that takes very little time as 91 is only divisible by 7 and 13 which 680 is not
@@wesleyowens4089 Which, since we're not talking specifically integers, is equal to approximately .1338235, or 13.3825% .
LOL been so long since I ever had to do this type of math.. for some reason the video appeared in my list and I skipped around in it to refresh my memory. Thanks for the refresher ;)
Fractions can always be converted to decimals. .075 + .0588 = .1338 That is rounded because 5/85 runs on forever. But .1338 is the approximate solution, and it gives the target
for you to use to check your math. Next I multiplied 40 x 85 and got 3400 as a denominator. 255/3400 + 200/3400 = 455/3400 .... Then 455/5 = 91, and 3400/5 =680,
that leaves the final solution as 91/680. Checking that division it comes to .1338 just like the original. My ma was a math major. She taught me when I was very young to
play with the numbers every possible way. She always told me to check myself by arriving at the answer using many different methods.
Leroy, this is the exact method I used! My 69 year old brain must have been paying a little attention while in school .. LOL. As an Aussie, I still prefer decimal though!
I thought I had the answer within a fraction of a second: "The LCD is right in front of me!" ....but then I remembered I have an OLED
Bwahahaaa! Should've gotten a QLED: you'd be brighter! (teehee)
@@truthmatters1950 what does Q.L.E.D. mean?
Quot Levis Erat Demomstrandum?
@@miff227 Nah, I'm not familiar with that technology - anything to do with jeans manufacturing?
@@truthmatters1950 there's a tradition to write Q.E.D. at the end of a maths proof. Quot Erat Demomstrandum means "what was to be shown" though my maths teacher said it was for "Quite Easily Done"
Levis is Latin for light (I know, the wrong meaning lol but I needed an L word) so I was suggesting QLED here stood for "what light was to be shown" 😁👍
I did this in my head. Of course I am old enough where I was actually taught math in school. Our public education system sucks and needs to be defederalized and taken out of the hands of corrupt politicians and union bosses.
I did the LCD in my head because 80 is divisible by 40 and 40 is divisible by 5. That meant that 85 had to be multiplied by at least 8 to also contain a multiple of 40. Which is 680. The mental math was doing 8x8 and then adding a zero and adding the extra 40. I did the same for 40 since it is half of 80, it needed to be multiplied double. 4x16, add the zero and the other 40. It sounds a lot more convoluted when I type it out, but it's much more intuitive when it's happening in my head lol.
What am I missing here?
The problem is to add two fractions 3/40 + 1/17 (immediately 5/85 is written as 1/17, why keep it as 5/85?).
RTF: the sum of 3/40 + 5/85 expressed as 3/40 + 1/17
1. Let 3/40 + 1/17 = x (algebraic x for the unknown quantity, since I cannot use a proper math symbol here).
2. LCM = 40X17 = 680.
3. Multiply both sides of equation in Line 1 by 680.
4. 680(3/40) + 680(1/17) = 680x
5. 680X3/40=17X3=51
6. 680X1/17=40X1=40
7. 51+40 = 680x
8. Dividing both sides of the equation by 680,
9. Therefore: x=(51+40) /680 = 91/680
Answer = 91/680
99% who found this hard had teachers that overcomplicated the problem, and all the math talk bored them. Kind of like this long lecture. Bow tie method just explain it and you’re done. No one gets 100% for finding LCD only. Good grief. This isn’t participation class. Getting the right answer is the only important issue, this is why most people hate math.
I agree. I don't even know what the lcd is (unless it's the display unit of a device) because I just use calculator.
While I find your "Bowtie" method amazing, the fact that you didn't reduce the 5/85 leads me to believe nothing you say is trustworthy... Sorry but 2nd graders would know to always reduce before any operation. 1/17 makes your system MUCH easier to use and the fact that you NEVER show the actual problem being solved is ridiculous. Reducing this AFTER the Bowtie method is much harder then just reducing first!
Which is easier to reduce 5/85 or 455/3400?
It does cut down the number of reductions, though. I'd always just get straight to the bowtie and then rationalise afterwards. It might be my inherent laziness showing through. I always tech my son that the correct answer which demonstrates all of the 'working out' is good enough.
I know that this was explained to me poorly as a kid and never made sense until now. Thank you. This gets another Wow!
I'm glad the video was 16 minutes long. It took me that long to figure it out myself, checking and double checking, rewriting and triple checking. (Then again, it took me 5 tries in 3 colleges to get a B in algebra.) Subscribed.
Can somebody please explain why anyone would ever have to go through this hassle rather than simply doing: 3/40 = 0.075, then 5/85 about 0.0588 = adding to 0.1338 ? Why this obsession with fractions when I can see no point to them when the answer can be gotten in seconds regardless of how complicated the fractions, yielding a real number.
In a lot of cases I will do just that. Although this exercise is important when you want to keep them fractions to use algebraic magic.
Let me try:
Think about 1/3. It is impossible to represent that number exactly using fractional numbers. It would be 0.3333... with endless repeating '3's. If you stop writing '3's you are essentially saying 'close enough' but you also introducing an error depending on how many '3's you decide is enough, the error or inaccuracy will be smaller or larger, and your final answer is fundamentally 'incorrect' even if it is 'close to correct'.
What if you have a problem where these numbers show up over and over again? The small errors can compound and before you know it the 'answer' you get at the end is off by a lot more than you expect. It is important to teach this distinction, because some people will end up working in fields where this actually matters a lot.
@@Sindrijo Thank you, but it seems that for practical purposes, real numbers work in all cases, correct? So this seems to amount to a sort of intellectual nitpick, right? Can you give a practical example of how 1/3 and 0.3333333333... can matter a lot?
My impression is that some people just enjoy solving puzzles, like crossword puzzles, even if there is no real point to it.
@@falsedragon33 Ah... can you give an example of this? I believe I know what you mean, but I am curious the extent to which this can be done using real numbers. I am curious because as a computer scientist, that is what I have to use. Perhaps the reply will be that basic computers can't do algebra, and it requires another software layer like Mathematica to really do this?
I have a masters in mechanical engineering and probably took much more math than most people, including teachers. I am now retired and not once in my engineering career was I ever asked or needed to find the least common denominator. In my opinion, in a world of calculators, just let the kids punch it in and get an answer. This is the worthless kind of math taught in schools that does kids no good in the future. Teach kids what they really need and not stuff like this.
THERE ya go! Spot-on.
I also have 3 degrees in engineering, civil mechanical and naval architect. While I also never used LCM in my job, but to discount the fundamental of maths is like saying what is the point of working at McDonalds when I can just buy a burger from a different shop. Maths teaches fundamental logic and thinking process. Not do we need to calculate at a job. Is about how your brain process info in the form of maths. People who think like that are usually people who don't have open mind. Also I never need to play music at my job why do we need to learn music art PE history geography
This is the wrong take. Being able to do fractions just adds another tool to your bag and increases your ability to solve mathematical challenges quickly.
While I might be able to climb a mountain with one hand, if I have two I should use two.
In the late 80.s I was doing shop math. And not carpenter or actually shop class math this math touched on as lot of other maths
1. Simplify 5/85 as 1/17.
2. Numerator: 3(17) + 40 = 51 + 40 = 91.
3. Denominator: 40 x 17 = 680.
Answer: 91/680. (And I did the math in my head.)
Well, that's what happens when you think you can come up with a "new math" to teach students. Just like the way we have to put up with 99% of Americans under 40 who can't handle simple _emotions,_ and _that's_ what happens when you raise a generation where _everyone_ is a winner and gets a trophy, even the _Losers;_ and lets have a _graduation ceremony_ for Every Single Grade, you know, to make children feel like they've "accomplished" something...when they haven't.
I had a math teacher like you and that’s why I suck at math today!
No, you suck at math because you expect the teacher to entertain the class rather than teach.
But it's not too late to learn math. There are many videos to assist you in learning math.
@@shadowgarr7649 Total BS answer. He expected the teacher to their job. You know what they say. "IF you can, you do, if you can't you teach". It applies in this case.
I had similar problems until I encountered a mathematics instructor who knew how to teach. I went from failing to A+ grades in one semester. Once the light came on, I went from there. We don't have many teachers like that any more. The majority would rather bitch about Covid and CRT rather than do what they are paid to do.
@@samconagher8495 the "light" never came on for me. In fact the bulb is smashed into a billion pieces on the classroom floor!
@@shadowgarr7649 I have only one response to your missive, in dear gods name why!
40x5=200. 85x3=255. Add those totals to get 455. Then multiply 40x85=3400. You will then have 455/3400. All you have to do now is reduce to lowest terms. 91/680.
Yup, I think that's what most of us did, although some smarter folks simplified the 5/85 to 1/17 first, then cross multiplied. Doing it that way gets you the 680(40 x 17) in the denominator straight away.
Another smart guy above said,
"It's quicker to simply multiply the denominator to 3400. Giving the result of the addition as 455/3400. Divide both by 10 to get 45.5/340, then multiply both by two to get rid of the decimal and you have 91/680."
To which I wholeheartedly agree, and only wish I thought of that myself.
@@mydogskips2 You know I thought about the 5/85 to 1/17 right after I made my post. I started to change it b/c the result would be the reduced answer of 91/680. Decided to leave it the way it was though. What’s funny is, about 40 years ago, when I did fractions in school, my teacher would tell me I was doing it wrong for solving them that way. I would ask how is it wrong if I came up with the same answer she did? On top of that, I’m using less space on a sheet of paper to solve it. She would just look at me and say “it just is”. 😂🤣😂
Oh this looks easy, until I found all the cobwebs! I got there in the end, however I did not reduce result to its lowest terms. Use it or loose it. My career involved budget forecasting, "sadistics" some calculus and solving the problem of getting the torpedo from a submarine to a ship on the surface. Anything on matrices? Thank you. Narragansett Bay.
I am almost 60 and I see these help learn videos which didn’t exist in 1976. I can only say I am glad I never had kids but by subscribing I can save and share with my nieces.
I’m starting to experience those feelings of terror that I felt during maths lessons at school! I can’t understand a word of what you are saying.
To completely solve this, I'd first reduce the second fraction to 1/17, then bowtie.
Numerator = [3x17] + [40x1] = 3x10 + 3x7 + 40 = 30 + 21 + 40 = 51+40 = 91
Denominator = 40 x 17 = 4x17x10 = [40+28]x10 = 68x10 = 680
If they are just after the LCM, I'd reduce the second one until only factors that aren't common to the first one remain. Then I'd multiply the 2 together. 5 is common to both, so I'd ignore it, so it's 40x17 = [4x10 + 4x7]x10 = 680. This can be done in your head by simply keeping a running total.
40 + 20 [sitting at 60] + 8 [sitting at 68] x10 =680
680
That is one way to solve it, but to me it sounds a bit convoluted. The way we were taught, I would simplify the fractions and since only 5/85 can be reduced that gives you 1/17. Then I would find the LCD by multiplying 17 by the numerator (17x3), by the denominator (17x40), and then work on the simplified fraction by multiplying by 40; numerator (40x1), denominator (40x17). Add the fractions as they now have the same denominator (680), that leaves you with 51+40 or 91 as the summation of the numerators; and the answer is 91/680.
I understand his method but it does seem easy enough to lose track of what you are doing. At least for me.
I suggest explaining the logic that first, in order to add fractions, we have to have that common denominator. Once that is understood, which we assume the student has that fact, how we get that common denominator is posing the question, "what is (in this case) 3/40 times 1?" Well of course any number times the number 1 = that same number. Assume the student has that logic. Also, what is any number, divided by that same number? Again that is the number 1. So understanding we can multiply both denominators together to get the common number we also point out we need to multiply "by 1" so we do not change the fraction values. That means (85/85)x(3/40) is the same as 1 x 3/40, which is "safe". (40/40) x (5/85) is also "safe" since it is only 1 x(5/85). End result you change the form of the fraction so the denominators will be the same value, and the top (numerator) is correct for that denominator, because you only multiplied these fractions, time 1. This boils down to the student understanding two things. In this example, you have to multiply the 40 by 85, but make that 85/85 (since that is 1), then the 85 by 40 but make that really 1 with 40/40.
Multiply the numbers and add the numerators and get 455/3400. Reducing that result is also just multiplying by 1. That is, 455 and 3400 appears both divisible by 5. Cool, so divide the top and bottom by 5. That is, multiply the top by (1/5), and the bottom by (1/5). And what is (1/5)/(1/5)? Yep, that's 1 also. And my timeframe is fractions about '65.
I also caught the commentary/debate about reducing first, then proceeding. Realize how you do it is not an error, unless you don't get the correct answer at the end of the process. Time is also less of a factor if you know how to solve the problem, compared to those struggling to get through the process.
Factoring prime has allows been hard for me. Any help or shortcuts for solving to Prime number
I found 680 by simply reducing 5/85 to 1/17. Then i multiplied 17 by 40. Easy breezy.
Im a homeschooling mom so ive been watching your videos as refreshers and making sure im not forgetting rules. Thank you.
Great video. I had forgotten about the bowtie method. I was a little concerned that the video didn't go thru the process of finding the results of these two fractions then I realized that the subject of the video is to only find the LCD of fractions with large numbers in the denominator. Reducing fractions and or simplifying fractions is different topic and process in working with fractions.
One of the things I really like about mathematics is that there are so many ways to do everything.
It took me about 2 minutes to do it in my head.
Yes I'm another old fogy at 70 years old.
My high school math teacher was a welder. He taught us math,
not algebra, but math during the school year and during summer
break he welded. He told us he made more money welding 3mo
than teaching 9mo. Welding requires a lot of athletic ability. You
may have to weld laying on your back or twist yourself into a
pretzel to get in amongst a pipe field or under a simi truck or
underground or up on a rooftop. This guy was getting older and
he was having trouble getting into these positions so he got his
teaching credential & taught math, a welders specialty. He would
give us a test an sit at his desk reading car magazines.
!
I'm 55 and enjoy these types of videos. It would be nice if there was a bookmark so we could skip the part when you tell us how to do it. Thanks
Hi. I want to take first year of Calculus in the Fall 2022, but it has been nearly two years since I last took a math course (the last course I took was Pre-Calculus). Is there a refresher course that can help me get ready for Calculus? Asking for a friend.
The objective is to find the sum of 3/40+5/85. The first move I made was the bow tie move until I came up with (3×85+40×5)/40*85. Before I took care of any multiplication, I checked to see if there were any common factors to simplify this multiplication. Be careful when you use common factors to simplify multiplication. We have 3×85 and 40×5 at the top, 40×85 at the bottom. When there is addition or subtraction involved, the common factor to simplify multiplication must go in all three products or no products at all. In this case, the common factor I came up with is 5. After dividing everything by 5, I now have (3×17+40)/8×85. At this point, I took care of the multiplication to simplify like this: (51+40)/(8×80+8×5), then (51+40)/(640+40), then I took care of addition to get 91/680. 91 can be broken down to 7×13 with both factors being prime. I know that 13 goes evenly with 650, then I continued to test 13 with the difference, which is 30, but that does not work. I know that 7 works with 700 and the difference between 700 and 680 is 20, but 7 does not work with 20, so the best I can do at this problem is 91/680 as my answer. If you are trying to test the factorability of troublesome large numbers, find a large factorable number that is cake for you and calculate the difference, then test the factorability of the difference and there you go.
You took the long way around but you got the right answer.
I think the name, "Bow Tie" is the most useful thing in this video for me. I was already familiar with this method, but I couldn't count on remembering it in a pinch, whereas I can never forget the inferior method I learned in school. So, if I was confronted with a test on fractions, I would first have to check to see if I had remembered it correctly. If I hadn't, I'd have to proceed in the "normal"way. As to the other tips, I've already forgotten most of them. Anyway, I think the word,"Bow Tie" will help me remember what to do. Finally, less pointless talk, MUCH LESS, and more math, would improve this video considerably. PS: I'm going to review the forgettable/forgotten part (factoring technique) again. "ONE REPRESENTATION OF A FACTOR." Okay, No, OF COURSE. GOT IT! . Now, if I were back in school, I'd be able to enjoy using these techniques. Thanks
I worked it out, but it took me a few minutes. Thank you.
I asked Alexa and it added it to my shopping list. Guess it didn't know the answer either.
Off Topic Question: What tablet and whiteboard program are you using to get smooth writing? I have a wacom tablet, but I can't get such nice writing.
in the case of 3 / 40 + 5 / 85
i like to take the ratio of denominators : 40 : 85 = 8 : 17
and use the 8 and 17 to compute the new numerator : 3 / 8 + 5 / 17 so new numerator is 3 * 17 + 8 * 5 = 91
and new denominator can be found by either doing 8 * 85 or 40 * 17 = 680
so the answer to 3 / 40 + 5 / 85 = 91 / 680
did what I remembered and cross checked it with decimal conversion...
once trained, it is time consuming, not hard.
I haven’t done this math in 40 years but still know how to get a common denominator……and then add it up. Easy peasy.
Gotta say - "old" math is the best! I'm 64 and still remember this AND didn't have to bother with exponents.
Reduce the fraction if you can, leaving 3/40 + 1/17. 40*17 =680 as LCD Voila!!!
El mcm de 40 y 85 es 680. Por lo tanto esto quedará 680/40x3 = 51/680+ 680/85x5=40/680... Todo esto es igual a sumar los numeradores y se parte por común denominador = 91/680. Esto es bastante sencillo, amigo. Gracias por compartir. Todo es cuestión de tener base sobre números. Saludos y feliz semana.
This problem should be solved by first reduce the 5/85 fraction to 1/17. Then it is simple 3/40 + 1/17. LCD will be 40x17=680. then the problem becomes (3x17)/680 + (1x40)/680, then final answer is 51/680 + 40/680 = 91/680
If 99% find this arithmetic problem hard, then there's no mystery why we are so hopelessly messed up.
We need a lot more than useless fractions to un-mess us. Maybe social skills and critical thinking would be a good start. Improved math skills would still leave us divided with no denominator.
I too grew up in the 1970s. I wonder if LCDs were more important then because that was before electronic calculators were commonplace, so keeping the sheer number of digits to a minimum was important.
Perhaps you should make a video about how to simplify (a/b)/c/(d+c)/d).
I took the two denominators and kept doubling them until I found what could be a mutual LCD between them.
85 * 2 = 170, not compatible with 40. I knew any odd multiplications (x3, x5, etc.) would end in 5 which is definitely incompatible. 85 * 4 = 340, still no, 85 * 8 = 680...go back to 40...40, 80, 160, 320, 640...680 was gonna work. Find how out much I multiplied 85 by to get to 680 (which was 8 times), check out many times I multiplied 40 to get to 680 (17 times), apply the same multiplications to the numerators (3 * 17 = 51 and 5 * 8 = 40), add those numerators together (51 + 40 = 91), so 91 / 680, and then see if there's any way to reduce them. In this case, it turns out there aren't any, so 91 / 680 is the simplest fractional form.
Knowing 'equivalent fractions" leads to adding, subtracting, multiplying and dividing fractions which in turn leads to being able to do algebra which leads to Calculus.