No LCD Required! FRACTION secret that everyone should know!

How to add and subtract fractions without finding the LCD (lowest common denominator). Learn more math at TCMathAcademy.com/.
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[@lisabruneau3801]

Wow never thought math could be made this difficult.

[@marscience7819]

Agreed. This is just a waste of time. This doesn't need a "hack".

[@mapleext]

Wow, that took you forever!!!!!

[@russelllomando8460]

got it 1/15 easy one. thanks for the fun.

[@steve_weinrich]

One does not need the LCD to add or subtract fractions. Just multiply the two denominators. After the remaining operations one is left with a single fraction which may or may not be able to be simplified.

[@reddblackjack]

Agreed. I was taught that an LCD isn't necessary in the process but reducing the fraction at the end cleans it up. Sometimes finding the LCD is a waste of time because of the fact that you have to reduce or simplify the fraction anyways. I skip it. Bowties baby!

[@maryseaman312]

I would have never understood the purpose of this kind of math until I met (and married) a carpenter who measured things in 1/32 of an inch! I had never considered of heard of such a thing, but he was a very good finish carpenter - - I could not argue with him. There is a lot in the math world I have never considered.

[@juliafoster9433]

This shortcut method should only be introduced (some may figure it out for themselves) after the common denominator method is taught so students understand why it works

[@brettnaysmith3949]

Must be getting paid by the hour for this explanation

[@raystevens1458]

Old school math, so many changes have occurred since I have been in school but you can't change this! .

[@johnnyrosenberg9522]

If the video really needs to be almost 17 minutes long, then it can't be a good shortcut.

[@TheFreeascent]

It's a great shortcut. Spend the time now, save time later.

[@reddblackjack]

Yeah, he's just doing it slowly because not everyone picks math concepts up easily. I would like quick, shortcut packed videos from this guy though.

[@RustyWalker]

If this isn't cross-multiplying I'm going to be very surprised.

[@gavindeane3670]

Indeed that's what it is. Although I'm not really sure how the process he talked about before he introduced the hack was different to the hack. He solved the initial question by multiplying the two denominators and adjusting the two numerators accordingly. Then he introduced a hack which works by multiplying the two denominators and adjusting the two numerators accordingly.

[@MikeStallings2023]

Listened to several minutes of preamble just to learn there was no trick.

[@KAF128]

​​​​​​Indeed ... LOL! This is definitely not my understanding of what constitutes a hack, i.e. a clever way to solve a problem. It is, I understand, now the way it is taught in the U.K, e.g. it gives autistic students a consistent framework. I see 16 to 18 year old GCSE maths resit students who call it the butterfly method, but some of them mess up the method. I understand it is basically what I learned but I was taught fractions at age 8 or 9, in the early 70s where the Lowest Common Denominator often makes the numbers smaller and therefore easier to deal with, on a non calculator paper. This so-called 'hack' isn't a hack at all, since it often actually makes the numbers harder to work with (they are weak on their times tables) and often necessitates additional cancelling of bigger numbers at the end ... more alarm bells . . !! I try to encourage our students, rather than faffing around with 8 x 4 = 32, and the resultant bigger numbers, to see that both numbers are in the 8 times table, so use that. This has the additional advantage that one of the fractions does not need changing ! And both his later examples had IDENTICAL working to the traditional method.

[@dannygjk]

Exactly.

And blindly cross-multiplying could cause the mess he mentioned about finding LCD. Lets say we have this: 37/308 + 47/77 With cross-multiplying: (37*77)/(308*77) + (47*308)/(77*308) Not ugly even a little bit. With LCD: 37/308 + (4*47)/308 => (37+(4*47))/308 I would say this is much better.

[@theredkitechannel3194]

Skip to the middle for the actual “hack”

[@arubaguy2733]

I honestly didn't know there was any way besides this to do this. This is a "shortcut"? What is the "long way"?

[@reddblackjack]

The long way involves baking two pies and cutting them into fractions and comparing the difference! Lol 😂

[@juancarlosgutierrez460]

Hi, what software do you use to make this video?

[@brotherofiam]

Might point out that any number multiplied by 1 stays the same. 7/7 = 1 and 3/3 = 1 so each fraction is essentially being multiplied by 1 before the operation is done.

[@dorenandsara]

That was a great short cut.

[@gopherspace8571]

So great Mr J I got it from watching your videos Thank you so much You won't believe this: Tonight I was coming home and that serious math problem was was on my mind. Math in math math

[@gopherspace8571]

Out so I said what if I did this another number bigger. Started with 44 already knew when I saw that it worked.! Any number. That's how it is applyable I never knew that. To check your math do it one way then check it again if you don't have a calculator. 👍 It works for any number Do 44 do 45 do 46 then 11 You'll get it I'm sure Can never thank you enough 🙏👍💪👋🌎❤️

[@WXLM-MorganNicole619]

Thanks for the hack

[@drziggyabdelmalak1439]

Good stuff, but I wish you had shown how to do this with more complicated fractions [like the example you jotted down with a 3-figure denominator]!

[@ItzSeannyy]

Refreshing my math for my asvab

[@volkerschmoll4731]

Sehr interessant. 🌻

[@MrMousley]

No LCD required ? 2/5 - 1/3 = 6/15 - 5/15 = 1/15 What could be easier ? I'll watch your video to see.

[@tqnism]

You do not need LCD. You need just any CD. But if your CD is not LCD, you will not get reduced fraction as a result. On the other hand, using LCD does not guarantee reduced fraction either. Advanced problem to think: what to do if you need to add more than 2 fractions? 3? 4? How does that shortcut change?

[@dannygjk]

This is something you quickly notice on your own after learning how to add and subtract fractions. There are plenty of other 'secrets' you notice during your study of arithmetic.

[@okaro6595]

I though this was the normal way. With mixed fractions you handle te whole parts separately. 3 1/2 + 1 1/7 = 4 + 7/14 + 2/14 = 4 9/14.

[@ellentronicmistress4969]

'Kiss and smile' - been around for a long time

[@cynthiabrown1438]

The shortcut was not addressed until almost 10 minutes in; is there any room for improvement?

[@edwinlandy]

There may have been some LCD involved.

[@mychaelsmith6874]

When you reduce the fraction after adding them, you are essentially finding the LCD.

[@lamagra0152]

Alge-bare-ic at 1:46 derailed it for me.

[@1Skeptik1]

Convert to decimals: .4 (2/5) minus .333 (1/3) Yes?

[@b213videoz]

0:33 "easy as PI" 😂😁🤣

[@user-xp9zf4ji5l]

Risposta : 1/15

[@wandapease-gi8yo]

Dry usegul! Do kids still memorize the multiplication tables?

[@dannygjk]

If they want to be able multiply large numbers quickly yes they need to memorize the tables.

[@krunoslavregvar477]

= 1/15

[@tedbristol894]

He did it the hard way,

[@PeerAdder]

How to make a simple problem complicated. That isn't a "hack", it's the standard way of adding and subtracting fractions. You only need to worry about the LCD at the end, in order to present your answer in its simplest terms. So if the answer had been 3/15 you would simplify it to 1/5. Funny how you didn't go back and apply the method to the whacky fractions you chose to hammer home the obvious point that finding the LCD can be difficult.

[@PaulHarris-sl1ct]

Easy as PI?

[@guerdachery3395]

3/5

[@GoofballFlyer]

What if you have 3, 4, or 5... fractions to add/subtract?

[@brotherofiam]

take 2 fractions use this method to find the answer, then use the results of the first 2 and add/subtract the next fraction. repeat this process until only 1 fraction remains, which would be the results of adding/subtracting all the fractions.

[@GoofballFlyer]

Right. I was actually wondering if there was some clever "shortcut" like this example was supposed to show.

[@dannyknight1348]

0.70

[@kenfisher531]

1/15 -Ken

[@nancyholmquist2690]

How does this make sense?

[@screambushbaby9085]

It’s hack time!!!!!! 😁

[@dazartingstall6680]

6/15 − 5/15 = 1/15 However, in this case cross multiplying results in the LCD, so nothing much is gained. Try this: 5/12 − 7/18 90/216 − 84/216 6/216 1/36

[@davidduncan1362]

I know an easier way to solve 5/12 - 7/18. Try this: 5/12 - 7/18 (18×5+12×-7)/(12×18) I am going to leave the multiplication unsolved for now because if all three multiplication products have a common factor, we can start reducing right away. Be careful, though. There must be a common factor for ALL three of these products or else this method will not work. If we have (18×5+12×-7)/(18×12), we see that all three of these products can be divided by six, so we can replace eighteens with threes and that twelve with a two to make it look more like this: (3×5+2×-7)/(3×12). Now, we can start solving the multiplication: 3×5=15, 2×-7=-14, 3×12=36 and we come to this: (15-14)/36. The last step is first grade subtraction: 15-14=1 and after this, we get 1/36 and we are finished. This trick can enable you to solve bow tie multiplication with third grade times tables when dealing with fractions. Don't make your life complicated.

[@jonnamechange6854]

@@davidduncan1362TLDR, and anyway you added instead of subtracting

[@jonnamechange6854]

I find it best to look for commonality of how many prime factors are required in each denominator. In your example: 5/12 - 7/18 we break down each denominator to look at what prime factors each denominator comprises. So the denominator 12 needs two 2's, and a 3; where as 18 needs a single 2, and two 3's As a result the new common denominator needs the bare minimum of two 2's and two 3's 2*2*3*3 =36 So we divide each fractions' denominator into the discovered LCD. For 12 it's 3 times, so we multiply both numerator and denominator by 3 to get 5/12 = 15/36 For 18 it divides into the LCD twice, so 7/18 = 14/36 Just substitute your converted fractions back into your original equation So, 5/12 - 7/18 = 15/36 - 14/36 Which = 1/36

[@dazartingstall6680]

@@jonnamechange6854 I agree in cases where factorisation is fairly easy, like these. I find cross-multiplication (what John calls the bow-tie method) more useful when the numbers are outside the range of easy mental arithmetic. Partly it's just personal taste of course: I'd rather simplify just one possibly quite hefty fraction at the end than spend time and effort checking the common factors of two earlier.

[@GerardPinzone]

Video starts at 8:11. You're welcome.

[@Mal1234567]

I solved this in 1/15 of a second in my head.

[@gingasouls6504]

Wait... The hack is to find Any Common Denominator instead of the Lowest Common Denominator? The method is the exact same for many fraction where the denominators multiple together IS the LCD. Good news is: I didnt miss any hack during elementary school.

[@DougLaubach]

How would you use the bowtie method in your earlier example? 2/358+1/762

[@cliffmerryman4164]

I was also disappointed... My guess is to use a calculator since we can't factor/reduce denominator much. 2/358 = 1/179 but that doesn't help enough except to preempt final answer reduction

[@dannygjk]

@@cliffmerryman4164 You should be able to double or halve numbers in your head. Naturally to be able to do it quickly and easily requires practice. When I show people how fast I can do multiplication by hand on paper people are amazed but it isn't because of any special ability it just comes from practice. I'm old school and back when I learned arithmetic in school we were drilled like machines until we could do it quickly and accurately.

[@maxinemcafee4893]

I learned this in 4th grade.

[@user-vd1cm6be4r]

1/2

[@suewiersema8166]

1/15 or one fifteenth

[@EHenterprises]

Negative. 13

[@benquinneyiii7941]

Advanced

[@sr2291]

I just did it mentally 1/15

[@drziggyabdelmalak1439]

Yeh, so did I...but you can't do really complex ones mentally, can you? 37/89 - 41/39...?

[@sr2291]

@@drziggyabdelmalak1439 Probably with a paper and pencil unless you know a mental trick to solve it.

[@johansteyn8526]

Answer = 1/15.

[@waynethomas3638]

1/15

[@its-a-bountiful-life]

I get 1/15, in my head, but forget the exact process of the cross-multiply process. That works for the numerator, then I just multipled straight across for the denominator. Now, I want to watch to refresh my memory. Thanks.

[@avishudlin3998]

The answer is 1/15

[@LTV_inc]

It took you 17 minutes to explain a ratio. If you were my math prof. I would have never became an engineer. 🤦‍♂️

[@pawelpap9]

Isn’t it 1/15? I got this answer after 2s watching the video. I wonder what 16 minutes might he devoted to.

[@BrianONEILL-qf2cs]

0.40-0.33 =0.07. That doesn't take 16 minutes.

[@cliffmerryman4164]

Disappointed. - Hoped to learn how this old hack could be used on more complex problems. - Hinted that the hack can be modified to work with large denominators then did not produce!

[@tedwalford7615]

I see nothing new. The Fraction Secret STILL uses a common denominator, as one must, and it still gets the new numerators via the same and only way you can. And yes; you should still simplify if you can. - I guess the bowtie-method visuals are valuable for visual learners, but the math aspect is the same, as it must be.

[@Astrobrant2]

"Algebraic", not "algebaric".

[@bienramos7587]

A simple problem it takes 17 minutes to solve.. 😂

[@rosssabah]

OMG... and he's a math teacher (note - with a Masters). Sad for all the kids he "teaches".

[@slimdugger99]

One fifteenth. Can’t type fractions on this keyboard.

[@arubaguy2733]

Don't you have numbers and a forward slash? 1/15. Here's another: the asterisk (shift 8) means multiply.

[@rickythomas6593]

Poor sound quality

[@tbl-tj9oz]

You really give a very complicated explanation, it is very annoying. Actually there is a very simple solution.

[@LoriHoppman]

I like what you're doing, but you might get more subscribers if you're less wordy. People are busy these days. They don't like to give up more time than they have to. Great job otherwise! Thanks for the refresher!

[@lwh7301]

This is 5th grade math.

[@markg7963]

Hopefully this guy isn’t teaching math somewhere. Took forever.

[@emilyhutjes]

please don't talk so long------ get to the point please.

[@icarus877]

You make mathmatics very hard work and very boring, 17 minutes to explain this is very poor teaching. You are not explaining this concept from scratch to kids as is evident from your vocabulary. YOU ARE GIVING MATH A VERY BAD NAME.

[@martincalero7390]

You talk way too much.

[@simonbowen1]

That was cataclysmically boring. And you claim to be a teacher?

[@tammmacdonald7723]

You talk to much

[@tanialelaj6327]

=1/15

[@rgrinnell]

1/15

[@mossesmadjemite2289]

1/15

[@chrisrardin5043]

1/15

[@stevencraven4897]

1/15

[@BanksfMax]

1/15

[@jimburt4473]

1/15

[@subasu478]

1/15

[@drsierra1]

1/15

[@janetgrant7571]

1/15

[@guerdachery3395]

1/15

[@farjanajahan3222]

1/15

[@garyhalsey786]

1/15

[@chrisdissanayake6979]

1/15

[@SherriRice48]

1/15

[@josephlaura7387]

1/15

[@rodfulford4306]

1/15