99% of Math Students Still Find This Difficult 

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.

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.

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.

6 minutes and he finally starts solving for LCDs.

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.

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!

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.

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.

I multiply 40 x 85 =3400 and use this as a CD. Im 72 and thats how I was taught

This video is like watching paint dry, far too long.

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.

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.

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.

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 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.

The reason they find it difficult is because the instructor drones on till everyone is asleep and they miss any info

I've never seen anyone take so long to say nothing!

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

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.

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.

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.

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.

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

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.

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.

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.

For someone the emphasizes focus, YOU are all over the place.

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?????

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.

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.

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

I had teachers that made it so difficult to learn anything. You are confounding.

You couldn't just give us the "91". Doing it in your head adds another level.

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.

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.

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.

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.

Cut to the chase please Sir...it ain't an essay. Thank You for the free math lesson just the same.

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 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.

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.

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

I've gone away-put up a new boundary fence-come back and he's still waffling on...

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.

Judging by this comment section, it seems your “99%” hypothesis may have to be adjusted.

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!

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.

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 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

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.

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.

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.

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?

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.

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

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.

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.

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.

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.

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.

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?

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.

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.

If 99% find this arithmetic problem hard, then there's no mystery why we are so hopelessly messed up.

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.

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.

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.

Hmm... You didn't actually ADD those fractions, you only found the LCD!

I had a math teacher like you and that’s why I suck at math today!

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 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.

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

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 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!

Many thanks. This was an excellent reminder of how to do large LCDs.

I know that this was explained to me poorly as a kid and never made sense until now. Thank you. This gets another Wow!

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.)

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

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.

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.

Grades 11 and 12 I had great math teachers. With this teacher I would have had a sleep during math period.

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!!!

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.

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.

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.

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 ;)

In the problem picture of the video, I would include the what is sought. As stated, the answer is 91/680. There is no indication that you are seeking the LCD. I found it exceedingly helpful to calculate it first, however, in arriving at the solution.

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

I simply straight multiplied the denominators, getting 3,400 Then cross multiplied the numerators, getting (255/3400)+(200/3400) Added the numerators to get, 455/3400 Simplified it down to 91/680 by dividing both numerator and denominator by 5 Finding the LCD is simply a way to keep the numbers small. If you aren't intimidated by big numbers, then and common denominator will due, as long as you simplify afterwards. the easiest way, for me, to find a common denominator is just to multiply the denominators.

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.

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.

I finished my education about 30 years ago and just like these videos to - again - learn the things I forgot 😁

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.

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.

The "Bowtie" method is a game changer. Solved the problem in less than 2 minutes!

I worked it out, but it took me a few minutes. Thank you.

Thank you. I have always used the "bow tie method", although I was not taught it at school, because it simply made more sense and was far faster.

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.

also old school here 2.125 :D >> 3* 2.125 / 40 * 2.125 + 5 / 85 = (6.375+5) or 11.375 /85 or x 8 to clean it 91 / 680 >> without calculator. We did learn this trick in high school but i never ever used it after :D. the .375 comes in a multiplication of 0.125 hence i could do it without calculator.

did what I remembered and cross checked it with decimal conversion... once trained, it is time consuming, not hard.