Don’t ADD these Fractions the Hard Way! Learn an easier way- NO LCD!

How to add fractions, find the LCD (lowest common denominator) - also how to add and subtract fractions without using the LCD.
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[@johngiorgi4000]

You talk to much. Get to the point, the problem. You side track all the time and it's very annoying.

[@carle5538]

Do not argue with your teachers. Be a good student

[@samwong3123]

$ return is directly relating to the length of the video because of advertise. $, $, $.

[@peteneville698]

I for one will never watch one of his vids again. It's like watching a recipe video that wastes time explaining the virtues and benefits of the very concept of eating food.

[@PaulLundell-ur8zi]

I enjoyed your challenge. I do have say that you "new" method for finding the answer is the method I was taught. I graduated HS in 1968 and engineering school is 1972. So what is the old way is now the new way. Note: I never used the first method to find the LCD. Thought is was very clever. Both methods are efficient as they both delivered the correct answer. I am 73 and enjoy the mind exercise. Thanks.

[@GoDemocracy9352]

I totally agreed with some comments below that the author should cut down the jibberish and get right to the point..

[@shamisonyamununa7448]

Yes thank you I love how you teach math Iike my self I am very slow but how you teach it help me a lot

[@BarerMender]

I listened for over six minutes and still hadn't got the method. I gave up.

[@lauriejerome9179]

Please solve the problem first. It's aggravating that you advertise your services and advise on what it takes to excel in math beforehand. Please.

[@nathanbaker9837]

Fat chance of that!

[@kateallsop6572]

I agree it's a long wait .when doing maths you need time not talking

[@asaprocky8195]

I just drag the video frame pointer to fast forward through the introduction and then play the video where it starts to explain the lesson. No big deal. Let him conduct his channel the way that he prefers to do so. Thank him for the lessons that he is kind enough to teach you without any obligation.

[@asaprocky8195]

Thank you for this and all of your other lessons. It’s good to go back and refresh our under utilized math skills so that we can maintain them.

[@olivemd]

Like your explanations. Remembered both ways.

[@krwada]

prime factorization is the key

[@star-ec9ic]

Omg I'm getting a head each I have to watch it over and over again to understand it thank you

[@mikedickerson1978]

Actually, I disagree with you on the simplest method of solving this fraction problem. The bow-tie method is not the easiest way to figure out the answer to this problem. The way the bow-tie method could be useful is if the LCD is the same as the product of the two denominators (i.e.: 3/7 + 4/11). If the denominators have a Greatest Common Factor (GCF) greater than 1, as was the case with this problem, then I find it easier to use the LCD method. Not everybody knows that 52 times 56 equals 2912. For fractions such as 5/12 + 7/16, then I just take the LCD of 12 and 16 by dividing one of the denominators by the GCF, which is 4, and then multiplying it by the other denominator. So, 12 divided by 4 equals 3, then 3 times 16 equals 48, and that is your LCD. The newly revised problem is now (5 * 4)/48 + (7 *3)/48, or 20/48 + 21/48, which equals 41/48.

[@carle5538]

So you want to be a rumbunctious and disobedient student with your teacher? LoL

[@timeonly1401]

That's the way I find my LCMs, too. Here's why it works: Let LCM be the least common mumtiple of a & b, and GCF = the greatest common factor of a & b. Then, LCM * GCF = a * b. Therefore, LCM = (a * b) / GCF = a * (b/GCF) = (a/GCF) * b . In other words, one can easily get the LCM by multiplying either of the denominators by the other denominator that's been reduced by the GCF.

[@romulopartoza5598]

@@timeonly1401 I think for me the easiest method is to multiply the denominators of each fraction!!....from the Philippines

[@timeonly1401]

@@romulopartoza5598 The real disadvantage of the bowtie method is when both denominators share a large GCF. Something like this: 5/36 + 11/48. I defy you to multiply 36 x 48 in your head, then multiply 5 * 48 and add to it 11 * 36 !! But I can easily find the GCF of 36 &48 (12), reduce one of those numbers by it (48/12) to get 4, then multiple 36 * 4 in my head (multiplying by 4 is same as doubling twice... so 72, 144), so LCD = 144. To finish, I know that 144 is 36 * 4 (of course, we got 144 by finding 36 * 4) and 144 is 48 * 3, so we find 5 * 4 + 11 * 3, which is easy to do mentally (20 + 33), to get 53. So the final anwer is 53/144. Of course I can find an even more ridiculous problem for the bowtie method: 4/3471 + 1/6942. The bowtie method would have us multiply 3471 x 6942 !! Then, do 4 * 6942 + 3471. And, after than, REDUCE the resulting fraction 31239/24199812 ! I can easily write down the answer for these types, where one denominator is a multiple of the other: 9/6942. How so fast & easy? Experience tells us that LCD(a, ka) = ka; ie, the larger number ka is the LCD! So we just use the multiplier of smaller number to give the larger (ie., k, in this case k=2), multiply by its numerator, then add to the other numerator, and put that result over the LCD = 6942. Done!

[@attica7980]

@@timeonly1401 You are correct. I would just add that the greatest common factor of 52 and 56 cannot be greater than 4, since 56-52=4. Since 4 is a factor of both 52 and 56, the greatest common factor is clearly 4. Hence all the talk about prime factorizations in the video in order to find the least common multiple is a total waste of time, since the least common multiple of 52 and 56 is 52*56/4=52*14, according to what you said.

[@joshc4519]

First, make sure both fractions are in simplest terms. Next, find the GCF of both numerator (1) and denominator (4) then factor that out to get (1/4)x(3/13 + 1/14). Next, do the cross multiply thing to get (1/4)x(55/182). Simplify the first fraction if necessary. The second one will already be fully reduced. Then just multiply them out to get your final simplified answer.

[@bhut1571]

I would have left the top as 3x56+ 52x1 and the bottom as 52x56 then just "cancel" or divide out some common factors like 4.

[@romulopartoza5598]

Yes brod. .... I considered your method the simplest and easiest one!!!.... from the Philippines

[@charlesmitchell5841]

What was the point of factoring the denominators into prime factors if you’re just going to solve the addition of the two fractions in the standard way?

[@SK_3PT1]

i was wondering this aswelll 😖

[@williamhoudersheldt7076]

He just wanted to post something on YT, you can tell by all the fluff talk to extend video length.

[@GGLD888]

I had to scroll and scroll and scroll to try and find the learning bit

[@youtuber1650]

So, don't look for the lowest common denominator but for the easiest common denominater, the ECD, then reduce. Say it in 5 minutes. Math means getting right down to business, no hour long chitchat.

[@philipethier9136]

Bingo. Did the 2912. Then the 168+52=220. 20 and 12 are both divisible by 4. 100 is divisible by 4. Divide the 200 and the 2912 each by 4. Get 55/728 and don't see any other simplification. Done.

[@danieldennis9831]

Before I watch the method you use, the best I can do is bowtie (which I learned from you - I only learned LCD in school decades ago). I am doing it without calculator because ... well that's how I prefer as I primarily watch and do your vids to practice mental acuity (in my 50s and one is never too old to stave off dementia; I also love simple algebra). 168+52/2912 220/2912 factor out obvious factors, 110/1456 55/728 ... 55 factors into only 55,11,5,1 ... 728 doesn't factor by 3 (7 2 8 add to 17, a number not divisible by 3 or 9) but it is even so 2*364 2*182 2*91 1,2,91 are the prime factors of 678 so 55/728 is the best I can do. That's abut half minute to 45 seconds of work (on the problem, took longer to type this). Now let's see if you are giving me a faster method.

[@jampamonlam3583]

Why not use 2x28=56 instead of 4x14=56 to find LCD?

[@Laguns-ij4hn]

Love your explanations.

[@88888gerald]

devisible by either three or five

[@Herzankerkreuz67]

For all those who are wondering.... This video isn't about mathematics it's about patience........

[@patientman2]

What a lot of waffle.......Does he ever get to the point?

[@SK_3PT1]

@@patientman2 innittt i dont have time to listen to a guy who waffles i just want one who gets to the point lol

[@randallhoward3231]

My easy way is the calculator on my phone which gives the final answer in decimal and fraction. (3÷52)+(1÷56)= 0.075549.... or 55/728.

[@davidjones-vx9ju]

why would you ever have to add them?

[@arlendavis]

I use the second method.

[@MrSesmith11]

The answer is who cares, you’ll never need to answer this question in real life without the aid of a calculator.

[@robertbrianhart818]

I used a modified bow-tie method: 3*56 + 1*52 / 52*56 = 168+52 / 4*13 * 4*14 = 220 / 4*13 * 4*14 = 4*5*11 / 52*4*14 = 5*11 / 52*14 = 55/728 No need to factor either the product of the denominators or potentially the LCD as the final stage.

[@scottdouglas6301]

When students who use this "bow tie" method in arithmetic enter into an algebra class and have to work with rational expressions, they are at a distict dissadvantage. Try this: 3/52 + 1/56 = (4/4)(3/52 + 1/56) = (1/4)(3/26 + 1/14) = (1/4)(55/128) = 55/728 Instead of finding the LCD, the student only needs to find the GCM and that can be done is steps. This allows a conversation about distrubuting mult. over add. and that's nice. IMHO. Note that "bow tie" is used when GCM=1.

[@tomesdut]

Error in 3rd step... 3/13, not 3/26

[@scottdouglas6301]

@@tomesdut Good catch - thanks!

[@gayeroberts8375]

Please show work out

[@Rgrazia1]

728

[@thatomofolo452]

Let's get it let's go 🚀🥳🤸

[@Rgrazia1]

55/728

[@spartanka12]

The “easier” solution is the most convoluted process - the original LCD solution is SO MUCH EASIER…

[@davidseed2939]

your method only worked because the denominator product was 4 times the LCD so striking out the surplus 2s was easy. But, what if instead of 4 the number was 7 or 13. the problem would not be easy. The best way to solve these problems is to find the Highest Common Factor (HCF) and leave it in factor form. so 3/52 +1/56 , HCF =4 (1/4) (3/13+1/14) now cross multiply (1/4) (3×14+13)/(13×14) (1/4)(42+13)/(182)) 55/(182×4) 55/728 if you find the LCM (728) directly you end up having to find the HCF indirectly meaning you are dealing with unnecessarily large numbers. behind this is the fact that for any two numbers x and y x.y=HCF(x,y).LCM(x,y)

[@toughenupfluffy7294]

Don't worry about the haters-your thorough explanations are welcomed by those of us who aren't well-versed in mathematics! :0)

[@maricelacervantes23]

You're always veering off the subject and your explanations are sooo long winded.

[@RickDuggan]

If this way were so easy, it wouldn't need an 18 minute video to explain!

[@thilakavathyb458]

9/7 is the answer

[@philipethier9136]

No. It's not.

[@victorfrancis5575]

That's much more complicated. I'll just stick to the LCD method.

[@michaellamp2165]

That's a wrong way to solve a fraction, l'm already 75 that's not what l have learned in grade school, my question is why did you multiply the denominators when you got already the LCD which is 728? if you add 1/2 +1/2 the answere of course is 1, in yours if you multiply the denominator will be 1/2 or 2/4

[@bobby4363]

...and this is the easy way? I am dead in my new job.

[@jsEMCsquared]

I say thirds

[@kimmimi-9183]

ما فهمت

[@maxpercer7119]

The rule " a/b + c/d = (a*d + c*b ) / (b*d)" is sometimes given as the definition of addition of two fractions. We can prove it. Claim: a/b + c/d = (a*d + c*b ) / (b*d) , where b and d are nonzero. Proof: a/b + c/d = a * 1/b + c * 1/d = a * b^-1 + c * d^-1 = a* b^-1 * (1) + c * d^{-1} * (1) = a* b^-1 * ( d * d^-1) + c * d^-1 * (b * b^-1) = a* d * (b^-1 * d^-1) + c*b * (b^-1 * d^-1) = ( a*d + c*b) * (b^-1 * d^-1) = ( a*d + c*b) * (b * d) ^-1 = ( a*d + c*b) * 1 / (b * d) . = ( a*d + c*b) / (b * d) . These identities are valid because the set Q is a field, (i.e. Q satisfies commutativity, associativity, distributive law, etc.)

[@fasihodin]

I am leaving this clip.

[@acethomas7425]

stick to the point and wrap it up, dang

[@SK_3PT1]

this vid would be 10x better if you waffled less imo

[@michaellamp2165]

Sorry ,ignore my comment l miss the whole picture

[@richardgammons3255]

Watching this made me rethink my 70+ year old arithmatic. So, I thought out two methods - the second, here given, is a more incisive versison of the first.: It was obvious that both denominators were dvisilbe by 2 (prime). So, 52 goes to 2 x 26 which then reduces to 2 x 2 x 13. Doing the same for 56 gives 2 x 2 x 2 x 7. But here I diverge from you. Your 'Bow Tie' recipe avoids explanating why you multiply top and bottom of both sides of the sum by the same number. i.e. 3/52 multiplied by (2 x 2 x 2 x 7)/(2 x 2 x 2 x 7) is the same as 3/52 multiplied by 1. but it enables the cancelling out of common factors. This applied to 1/56 gives top & bottom multiplied by (2 x 2 x 13)/(2 x 2 x 13). & 3/52 multiplied by (2 x 2 x 2 x 7)/(2 x 2 x 2 x 7). You can then cancel ommon prime factors to both sides until they have the same denominator. Then just add the remaining numerators (3 x 7 x 2) + (1 x 13). Once you realise that multiplying top and bottom by the same factors is the same as multiplying by 1 (one), then the rest is easy! The rest being just cancel common prime factors on each side of the sum from top and bottom of each side of the sum in order to end up with the same denominator (728 in this case) leaves us with ((3 x 7) + (1 x 13))/ (13 x 2 x 2 x 2 x 7) = (42 + 13)/728 = 55/728

[@GeneAutry2]

How long and convoluted can you make a “simple” method?

[@dirkbuys6613]

This is not the easy way i cot answer in 30 seconds

[@michaelhong5774]

You are making it more complicated. Why?

[@lagazofamily]

I'm so sorry but I disagree as well that this is an easy way. The way you're getting the LCD is one of the inefficient methods. Have you heard of the cake method is solving for the LCD? You don't have to do prime factorization as what you did.

[@daxzanos4427]

Too windy! You maybe good at math, but you took 5 minutes to go to the second activity in solving the problem.

[@philippusandriesw.a.labusc217]

Too much talk.

[@sergiodario58able]

I would follow this guy's maths videos a lot more, if he just stopped dragging it for so long and went straight to the heart of the problem, and stopped advertising himself at the beginning rather than the end of the video. He's all right but ffs it takes him 3 times the amount of time to come to a conclusion, and it's frustating as hell.

[@emjay2045]

Are you getting paid by the word? Minute ??? A LOT of damn rambling to get to the solution to solve a problem.

[@mikep6843]

Too long-winded!

[@QUABLEDISTOCFICKLEPO]

Too much talk. Get to the method. GET ON WITH IT!!! For Gawd's sake!!! zzzzzzzzzzzzzzzzzzzz. [He finally gets to the "Bow Tie" way about 12:00]

[@kumentador959]

I PERFECTLY AGREE WITH L. JEROME....OTHER THAN THE INTRO , TOO MUCH IRRELEVANT TALK/ STORY-TELLING IS SUPER ANNOYING ! ...SIMPLE LESSONS BECOME LONG ROADS GOING TO A DRINKING FOUNTAIN FOR SOMEONE WHO IS KNOWLEDE-THIRSTY....This is my last video. I stopped my subscription and just go to YOU TUBE ..." math short cuts "...or math hacks.

[@acethomas7425]

u talk in circles

[@lawrencemoore2414]

Insanely boring! I feel for maths students in your class. And for those with less aptitude for maths your suffering is much worse.

[@charlesspence9593]

redundant! repetitive!boring!

[@joseantoniomclauchlan2859]

you talk too much

[@pauldalnoky6055]

Stars? Really?

[@rogueshadow93]

You do a lot of extraneous talking

[@dwaipayandattaroy9801]

55 / 728