No LCD Required! FRACTION secret that everyone should know! 

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!

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

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.

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

​​​​​​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.

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.

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

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

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 🙏👍💪👋🌎❤️

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

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.

milk milk milk

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

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.

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

That is the only way to do that, the denominators are both prime numbers so there is no common denominator.

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.

@@davidduncan1362TLDR, and anyway you added instead of subtracting

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

@@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.

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

@@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.

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

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

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