50 years ago I took College Algebra from a young professor named Charles Miller. He clarified things is such a way that I actually learned Algebra. He wrote his own textbook but it wasn't published yet, so he put it in 3 ring binders and we used it. The last time I saw that textbook it was in it's 8th printing.
It is called "cross multiplying". It is not a trick, or a hack. It is the standard method. I have taught this for decades, and I find it hard to believe that there are maths teachers ANYWHERE who do not .
@@chadlhorton Yeah, I think you're right. This is not a hack or a trick, it's mathematically sound. I think the concept that needs to be stressed is that when you're getting a common denominator (least or otherwise), all you're doing is multiplying each fraction by 1. For the original problem: 3/7 + 4/12, you can do some reducing up front which will help you. It's good to look for that. Then, 3/7 + 4/12 = 3/7 + 1/3 = (3/7)(3/3) + (1/3)(7/7). The tactic here is to get a common denominator, so each fraction is multiplied the other fraction's denominator-over-denominator. Doing that is 100% OK because you're multiplying things by 1 when you do this. So, (3/7)(3/3) + (1/3)(7/7) = 9/21 + 7/21 = (9+7)/21 = 16/21. Is 16/21 reducible any further. No. Prime factorization of 21 is 3 and 7. Is 16 divisible by 3 or 7? No. The final reduced answer is 16/21. Boom, done. Even if you miss the step of reducing 4/12 to to 1/3 in the beginning and start out (3/7)(12/12) + (4/12)(7/7)......, no big deal. It's not wrong. You'll do some reducing on the back-end of the problem. Do it right and you'll arrive at the same answer and full credit for the problem. Doing reduction up-front is a good habit but not a show-stopper if you miss that step. Like a lot of posters here, I don't like this being called a hack or trick. It's not. It is mathematically sound and you still go through the proper steps to do the problem, it's not a shortcut (many shortcuts that get passed around by kids are not mathematically sound, will often get you the wrong answer, and should be avoided).
This is a pretty standard method. I was taught it over 50 years ago. There is a risk in using it as a shortcut if you don’t understand what you’re really doing. Students learning to add or subtract fractions need to know what it is they’re really doing before blindly applying such “hacks.”
very good point Murray. I am a semi-retired engineer, or so I tell people when business is slow. I was taught cook book math which is the norm, solving provided equations as homework. You won't understand what you are doing unless or until you can set up the equations - applied math.
@@ericdussell7421The same applies to about anything-if you understand HOW something works, you have a good chance of fixing it. Mathematical, mechanical, electrical, the list goes on.
@My Reading Room Channel Exactly. 95% of the things people "discovered" or whatever I had already figured out on my own. 'Course, I'm an old guy anyway, so I would be dumber than I actually am, if I hadn't figured out by now.
Excellent. What a wonderful way to illustrated an accurate calculation fractions without Lowest Common Numerator... which does not matter. Thank you for your teaching. (Old UCLA Math grad)
Thanks for the video. I was never taught this in school. Was always taught to find the LCD and do it the first way. Appreciate the work you put into your videos.
It seems some schools put too much emphasis on LCDs. The fact is, to add or subtract fractions you only need to have a "common" denominator. It doesn't have to be the LOWEST. If you multiply both of the denominators together you will get a COMMON denominator. It may not be the lowest but it doesn't have to be. So that's all this bow tie is doing is converting the fractions to this common denominator. Which is why it may result in a fraction that can be reduced, because it wasn't the lowest.
Thanks man, i just applied for a job and they asked me to do a fraction sum. I honestly was lost. After watching your video i was back in the game, thanks so much for your time. God bless your heart!
It's been so many years since I worked on my undergrad. I was fortunate that what I majored in didn't require a whole lot of math, outside of getting my real estate license, Science classes, and of course electronics. I started college 33 yrs ago, most of the math was that yr, freshman year. I am turning 51 in a few days, my hair is solid gray (colored,) and I just don't remember it, and really don't care to go back over it again. I appreciate the video, because if i had a child it would be so helpful. It was hard to remember basic math such as small fractions. Oddly, I remember the real estate math equations more easily, even though our broker always took care of that part of the sell of a home.
I had a difficult time understanding algebra in high school but our teacher taught us this method of dealing with fractions and I still remember it 58 years later.
The order in which you do the two upward facing arrows is significant in that sometimes you get a negative number depending on which arrow you do first when subtracting.
Can you prove that? Whilst it might seem facetious it's actually a valid question. Maybe we should teach students how to prove that these operations actually work whether you are dealing with natural numbers or these different 'types of numbers' that we call fractions. I have seen a maths professor lament that his undergraduates cannot do this yet he can teach primary school children to verify that these operations do work as the should. Its also a nice way to introduce algebra into young minds. I have tried it out with some success.
Thanks for a great video. I am an electrical engineer and do math for a living. Always looking for things to share with my 11 year old grand daughter. I read some of the comments (from the Karens below) and am disappointed at the lack of decorum.
Hello John My name is Alex, age 73 following your videos from Waterford Ireland. I am a very mature student attending Adult Education Class. I have always been interested in Maths,
I taught myself to do these kinds of problems as a 3rd grader...9 years old, in 1965 (born in 1956)... while reading my 5th grader sister's Math textbook;her studies were more interesting than mine and I'd steal her books to read them for fun 🙂. All of 'em. If you understand LCD and Cross Multiplication, a "hack" isn't needed. I knew the answer to "3/7 + 4/12" seconds after I saw it...16/21. All the other ones were easy to solve, too.
Maybe I'm just extremely old, but when they taught us how to do addition & subtraction for fractions, they said (Cross multiply and then add/subtract as needed) So the 2/3 + 1/5 you would do the following... 2*5 + 1*3 over 3*5 ===> so you would get 10 + 3 over 15 or 13/15. The top problem was pretty quick, but there was a bit of simplification to do first. 3/7 + 4/12 ===> 3/7 + 1/3 ===> 3*3 + 7*1 over 7*3 ===> 9+7 over 21 or 16/21 It is easier if you do simplification before you do the cross multiply and add/subtract. When you master the concepts, you can do most of them in your head and just write down the right answer, and then lose points because you didn't show your work. 😣
Thank you so much John. I am 76 (a long time since junior school!) I find your bow tie way so much easier, especially when outside and not with stationary at my disposal. Love it! You have made my life a lot simpler!
The concept of this hack method is, in effect, the same as the traditional method of finding common denominators first. The benefit of this hack is that it streamlines the procedure for finding the numerators. I would only encourage students to use the hack method if they understand the principle of the traditional method first.
At 14:25 you refer to 1128 as 1-28, again at 14:40; and at 14:44 you refer to 1678 as 6-78. You must be a pilot, as they skip - in the USA - the first digit of the radio frequency, when they read it back to the Air Traffic Controller ! Great math hack for fractions. Have never determined an LCD, since I learned how to do it 50 years ago. Always used this most useful hack. Matt Lee
1st video I’ve watched on your channel. Subscribed. Long story short I didn’t apply myself in high school in math. Once I attended college I struggled. Had an algebra teacher that was one of the BEST I ever had. His methods of teaching really made me see the light and I enjoyed algebra! NEVER thought I’d say that. Graduated college in ‘87 and still feel to this day the professor was a highlight in my life! So I’m watching RUclips and I see this “refresher course” and absolutely enjoyed it! Thank you sir! I’m going to watch daily and sharpen those math skills! Very excited👍 For the know it alls in previous comments some may not know the bow tie method and therefore the “excessive verbiage” may bore you but for others is a continuation of learning. Go brush up on your psychology and join us common folk when we get to your level😅
Me, too. Not great in HS math. Always thought of myself as mathematically challenged, but really wanted to learn it. Yes, I will subscribe here. Thank you TABLETMATHCLASS!!
Great story. You should try teaching/coaching others with your skills (as a hobby). Your enthusiasm is infectious and you will be passing a gift on to someone else.
Your teaching method is so easy to grasp. I am used to getting distracted with anything mathematics. Currently taking job placement assessments and this is a helpful refresher. Thank you!
I used to tutor math from GED clear through college algebra. This is a good tutorial for students in lower math classes: beginning algebra, intermediate algebra, even perfect for elementary math students. Very interesting tutorial. Hopefully, it will help many students!
@@manoshawad7993 GED (general education diploma) is the equivalent of a high school diploma, but is not the same. People who have dropped out of high school get their GED later in life.
Wish when I was jn high-school had you as my math teacher with a kind calmly voice n great at explaining long way n short way n being careful to choose correct method n not to be fooled
I think this is wonderful and I wish I had had you as a teacher in school. I had really smart math teachers that couldn’t teach. When anyone told them that they didn’t understand a problem, they would repeat what the student didn’t understand in the first place, in the same words. Teachers who care find different ways to explain things. Further, you do not teach only to the kids who get it. Teach to the ones who don’t. It the whiz kids get bored, too bad. Give them silent work to do in their seats. Also, don’t talk down to the students, or make fun of them if they don’t understand. Everyone learns differently. It is your job as teachers to teach ALL children, not just the “smart, quick ones” who get your teaching. I struggled with math as a military brat who moved every year in the summer. I’d go to one school and something had already been taught. I’d go to another and I had learned that back two states ago. I went to 13 different schools in 12 years and it was not easy to catch up. It’s easier for children to learn when they stay in one place throughout their school years. I will be 71 this week and this still upsets me a great deal. It is hard getting an education with bits and pieces of knowledge picked up in all the different school systems. I wish the states all had the same curriculums. That would have solved my problems, and I am sure many other children’s problems.
Texassews -- I know the feeling too... We moved about the same and I hated it that I could never have friends in school, because, we were going to leave soon, and I would never see those great kids again... Now, sometimes, I remember their names and can see their faces in my mind, and wonder how they did.... I pray that they are all good and doing fine... Perhaps one day in Heaven, I may be able to find them all again and catch up... The absolute Best Teachers I ever remember were in Dallas Texas... They absolutely rocked their positions, and always told us that "We were going to learn a lot of things and for sure, we were going to learn how to get through life with all the things we were going to learn that year... And I/we Did !!!!! I can do anything I try to do and I am almost the same age as you !! Will also want to catch up with these great Teachers up there and see how they did and thank them again for being there for me.... God Bless you and yours ! Fran Danco
The BowTie method is how I do fractions in my head. It always works, and you can reduce fractions after you're done, which is easier (to me) than doing the LCD first. Likewise, it's basically the only way you CAN do it when you have algebraic variables involved.
Also, for a soapbox moment, I personally think reducing fractions and figuring out LCD is mostly pointless in life. I mean, it doesn't hurt to know it, but it doesn't actually assist you much either. No one is EVER going to think of 52 cents as 13/25ths of a dollar, for example. And I personally believe it's more useful for everyone to understand that 8/16 = 128/256 and you don't even have to consider 1/2 in that, because then you get an actual understanding of how numerators relate to denominators. If you make everyone reduce fractions all the time, you're basically saying 1/2 is "more mathematically real" than 128/256 is. But 128/256 might be more important than understanding that it reduces to 1/2 in certain contexts...like if you're dealing with computer code or RAM or anything else in binary, for example.
I'm 77 and still learning. I remember at eight my father reducing me to tears because I couldn't understand what an LCD was, (many years later in his papers I found his old school reports where I learned he was weak at maths).🤣
Almost as old. My father, may he still be roasting over the flames of Hell, didn't ever teach me anything, but took great delight in telling me how good he was in Math at school. Somehow I managed to obtain a PhD and ended up teaching Math for 35 years. Pure luck, he would say.
Lol My father was exceptional at maths but he never taught me anything. I struggled with maths. It was only much later when I came back to the subject looking at how it is or could be taught that I discovered he had laid down a rich tapestry of stories that used to tell me that I now realise were all mathematical problems & insights but in a quirky sort of way that left me curious and puzzling over. I think he just wanted me to find my own way whatever I did but I can't help smiling when I find myself telling young children the same quirky stories and having fun trying to work things out. That is why I enjoy the so called 'Vedic maths' approach. It does things in different ways that are playful and fun to learn and much much faster.
My dad was a math major but is TERRIBLE at teaching, his brain just functions at a higher level, he skips too many steps and didn't understand why I'd get confused, he couldn't simplify things. I do not miss high school tutoring sessions lmao. This teacher is exactly who could have helped me back then! Sigh
Back in the day when I was a wee bit lad, I could not do this because I could not figure out what X was. Could not get past that until I had a shop teacher who told me to turn it into a decimal for machine shop class. To me that was easier than dealing with fractions. This make more sense to me now (50 years later) never had the opportunity to learn this in school.
It's always desirable to simplify the arithmetic up-front before applying the bow tie method. In the last example, 12/110 reduces to 6/55 and we have: 6/55 + 5/94 = (564 + 275) / 5170 I'm terrible at arithmetic so that's why I gotta' put the big stuff into the cuisinart first (so to speak).
Stop hating guys this is good for students who never learned this process. Get off if you know it n do not need it. Also, todays students love and learn anything with the word hack Ok
Retired engineer speaking. Rather than struggle to find the LCD, I usually just multiply the two D's to get a CD, and multiply the N's by whatever is needed to leave the fractional values unchanged - which is exactly what you're doing here! I never saw it codified so simply and directly as you've shown us. My only suggestion would be to move the heads of the diagonal arrows to the bottom, rather than the top - that way you can just proceed from left to right starting at each arrow's "nock" for subtraction as well as addition. Thanks! Any day you learn something new is a good day!
Cross multiplication refers to one fraction equal to another fraction. This is simply using the common denominator rather than the Least Common Denominator.
Brilliant! I am an evangelist for easy ways to do math. I always preach that a%(b)=b%(a), so that you can swap the two terms because of the commutative principle.
A tip for mixed numbers: set the whole number aside, do the bowtie and then bring back the whole number. From your example: 3 1/8 + 2/5 = 3 + 1/8 + 2/5 = 3+ (5+16)/40 = 3 + 21/40 = 3 21/40. Great explanation, shared it with my kids. Don't know where I learned this, but I've always done this method and had never bothered with LCD.
Exactly correct. No need to convert a whole number to an improper fraction so just set it aside until you have dealt with the fractions and then bring the whole number(s) back at the end of the process.
It just seems to me that we are going backwards. Don’t get me wrong. The access to help and info is wonderful, especially compared to when I was learning mathematics. But, it just feels to me, that compared to 4 decades ago, this stuff should be 3rd or 4th grade level sight-solving math.
yes, I taught 4th grade...and this is what we taught. We try to keep civilization moving forward, but historically there are drops in advancement, and humans start over.
@@RebaCampbell1984 I can’t agree that there are historical drops in advancement which result in Humans starting over. At least, I don’t see that in our recorded history. Of course, Civilizations have risen and fallen, but I’m not sure any of them slipped back to their inception as a result. There are pockets of Humans who may not have advanced alongside others, but the Romans didn’t drop their possessions and begin walking naked back into the Wilderness. 😜 Either way, let’s hope we are able to one day find a common value to place onto our Children and their abilities to survive in what is becoming a much more advanced and competitive world.
@@troycrum9294 that would be very good if our children continue to advance. It is more possible, except for things happening as they have for eons...If you look at the archaeological record, especially before writing, there are periods where humans' advancements did retreat, and we don't know How they build incredible structures...Or either by climate challenges, or geological forces like the Doggerman Landmass or Mediterranean seaside cultures that were wiped out by sudden water rushes. We know they had advance cultures, but sharing/advancement of knowledge was reduced. Another example, the amazing 2,000 year old 'computer'calendar that was found in the Mediterranean, the Antikythera mechanism, and it couldn't be just one of a kind, yet mankind didn't get to that level of advancement again until 14th Century. That knowledge was lost for many centuries.
You just need ANY common denominator, the least (lowest) common denominator is preferred but NOT required in order to solve the problem. So unless the LCD is obvious (if, for example, one of the two denominators is a whole number multiple of the other), it's easiest to just use the product of the 2 denominators as the common denominator (which often will be the LCD, BTW), do the addition or subtraction, and reduce the fractional answer at the end.
That mixed fraction you can exclude the whole number. Just add 1/8 to 2/5 for the fractional portion then add it to the whole number. 1/8+2/5 is 21/40 then add 3 to get 3 21/40 for the smallest version the quickest
Good, well explained for those who are still starting. Though here in India, cross multiplication is standard procedure in junior math class, for probably 8,9 year olds
More like _barely_ explained. I know it's nice to be nice, but you're being excessively generous. Cross-multiplication is/has been standard procedure for most primary-aged students on the planet. But to give this rambling, tautological mess an elephant stamp for being "well-explained" is just not right. It was far, FAR from _well_ explained. He couldn't even decide whether he wanted to call it a trick, a hack, or a method... and forced us to share and revisit that painful dilemma with him... again and again! Freaking awful. Mostly filler!
4/12 can be reduced to 1/3 then can Mutiple both top and bottom of 1/3 by 7 to get 7/21 and multiple both top and bottom of 3/7 by 3 to get 9/21 then add 7/21 to get 16/21. 2/3 Mutiple both top and bottom by 5 gives 10/15 and 1/5 both top and bottom by 3 gives 3/15 so add both together to get 13/15. This should have been learned in Elementary school.
This "bowtie" method is easier when the numbers are small, so one should always look to reduce fractions *before* applying it. Why use the method on 25/75 + 24/48 when you can reduce first, and use the trick on 1/3 + 1/2 ?!
And to understand, instead of mindlessly following a procedure, here is the explanation (short version, using variables) ... Trivial rule a: 1*x = x (any number multiplied by one always is the same number again) Trivial rule b: x*y = y*x (the order when multiplying numbers does not matter) Trivial rule c: x/x = 1 (any number, other than zero, divided by itself always is one) Examples: 1*9 = 9, 1*-9 = -9 2*3 = 3*2 9/9 = 1, -9/-9 = 1 Solving 3/7 + 4/12 with (more) comprehension: 7*12 = 12*7 and 7/7 = 1 and 12/12 = 1 1*(3/7) = (12/12)*(3/7) = 36/84 1*(4/12) = (7/7)*(4/12) = 28/84 36/84 + 28/84 = 64/84 (which can be simplified to: 16/21. As 4/12 can be simplified to: 1/3) Note: It is easier to show on a blackboard/screen where you can write/show the numerator above the denominator. Additionally, for a full comprehension it should also be explained why 2 fractions with the same denominator can be added by simply adding the numerators above the same denominator (i.e. this might not be so trivial,. Can be explained using pie charts). E.g. 2/9 + 3/9 = 5/9 Or more generic/formerly: x/z + y/z = (x+y)/z
Really worth to watch and learn your video teachings. Especially if everyone learn maths & geometry their life will be easy similar to an engineer to find solutions to various techniques. Even aptitude test they can crack very easily.
Totally agree. Good vid but this isn't worthy of 17 minutes. This is like the video that discussed how to solve division of fractions such as: 3/8 divided by 1/4. I can tell you how to do that in 1 minute if I'm being slow, this guy took 17 minutes. You flip the 1/4 and turn it into a multiplication problem. Now it's converted to: 3/8 * 4 = 12/8 = 3/2 = 1-1/2 = 1.5 (depending on what form you want your answer in).
@@Skank_and_Gutterboy some people learn slower I think he is trying to cover the full spectrum of learning speeds. You could always speed up the video if it’s too slow for you. Your learning speed is not the standard in the world.
Learning truly is all about teaching! I had a good teacher for Beg. Algebra and got a B. Then I had a not so great teacher for Adv. Algebra and got a D. Took Geometry the next year with the first teacher again and got a B again. I felt really miserable about the D but cheered up a bit after I realized that it wasn't totally my fault.
That was when school was about teaching math and other useful disciplines and not gender pronouns, critical race theory and various other pieces of useless garbage..
17 min. long, could have covered this in 2 min. If you know anything about mathematics, this is not a hack, by any means. In fact, most schools teach this method!
Exactly, this is not a hack or a trick, the math is sound and this is how it's taught. All you're doing is multiplying your fractions by 1 (which is what a fraction like 3/3 or 12/12 equals) to get a common denominator. Then you just add the new numerators and reduce as necessary. Piece of cake, calling it a "hack" or "trick" is wrong. Among kids, I remember hacks and tricks being passed around that were wrong and would usually give you the wrong answer (or you'd fall ass-backwards into the right answer but they would lead you to bad concepts). This method is not like that, it's the right way to do it.
I hope those who teach it also teach there students common courtesies like not being rude to people who are trying to help people who are not as knowledgeable.
@@susancook9228 you are absolutely right. I appreciate the length he took to explain the process. There will always be little people also known as haters who have to hate. Shame on them!!😡
Thanx for the review. Now i remember why i never liked math enough to go in to algerbra. Double talk by the teachers n malicious students who caught on how to dumb down others. Thanx for not being a malicious teacher.
Good video and hack! Wondering though,…why not just ignore the whole number of the mixed fraction and simply apply the hack on the fractions…and then bring the whole number over? 3 1/8 + 2/5 Rewrite as 3 and 1/8 + 2/5… which becomes 21/40 and bring over the 3 Final answer = 3 21/40 Beauty of this is it avoids converting a mixed fraction to improper and then back to a mixed fraction. Still a great video, thanks!
Correct. Think of the mixed number 3-1/8 (read: "Three and one-eighths". Sorry, the notation for mixed number uses a hyphen; it's not the subtraction symbol) as 3 + 1/8. (since 3-1/8 **is** 1/8 more than 3; convince yourself of this on the number line). Then: (3-1/8) + 2/5 = (3 + 1/8) + 2/5 = 3 + (1/8 + 2/5) = 3 + 21/40 = 3-21/40 (Three and twenty-one fortieths).
Really ? This was taught to us in the 2nd grade, in 1962. Just goes to show how far backwards our education system has gone in all these years. Thanks to teaching to the lowest level in the class instead of pushing everyone to achieve a higher level. Thanks a lot, " no child left behind ".
Then you were at a rare school. Generally third grade introduced times tables, even back in the olden golden days. You weren’t adding and subtracting fractions before learning basic multiplication. This is not a “no child left behind” problem, it’s a misremembering of your precious youth. Oh, and I polled multiple people who would have been in second grade a few years before and after 1962, representing both coasts and the heartland. Pretty consistent curriculum.
@@shaalijones3484 Amazing how some people think they know what someone else experienced in life. I do not claim to have gone to exceptional school, but we did have some exceptional teachers. Yes, we did learned our multiplication tables in second grade, which I struggled with. My older brother and sister took turns drilling me with our own flashcards. Pretty arrogant of you to think you have any idea of what was taught to others. I actually still have my school books from then. My parents bought a set for me since I was having so much difficulty with it at that time.
Still, the older generation needs to be refreshed from time to time, while the newer generations need to simply learn some basics, and the more techniques they learn, the better the brain works and something in it clicks when there is an irregularity, and a flaw is seen, even when the brain hasn't consciously "computed" it, as yet. Like gamblers who spend their time learning and practicing card tricks. Not for the amusement of the audience, but to keep their brain nimble. We don't have as many Nimble Brains these days as we had in the 1940's and 50's - much less the 1880's-1940. Numbers are stable blocks of measures, totally equidistant from eachother. The more someone handles them in the brain, like a juggler, The sense in the Brain of the Balance and Regularity will help the workman "FEEL" as well as anything else, whether everything is properly fitting together, clean and tight. You may think this is something that goes without saying, but having worked with a few hundred kids on their math skills, I can tell you that over the decades, their sense of the "right feel" of the math they are working on has gone drastically downhill. And it is reflected in the deteriorating politics of our day. My baby sister was only 3 1/2 yrs younger than me, but all the parent outrage at the "NEW MATH" that started in Elementary school in her grade, not the class above hers, worked to distort a wide variety of LOGIC in the schools and thus to the next generations of politicians and voters as this "Fun House of Mirrors" was forced into that and the following generations, until the students in many schools could NOT TOLERATE sound mathematical teaching or anything else that depended on a hefty grasp of Logic. Now look at the MATH of last year's Election and tell us all how so many Millions of peoples world wide cannot figure out how badly distorted from Reality the Election Counts in dozens of nations are so messed up. They have no SENSE in their Brain Function of the Logic of the Numbers - it simply does not compute, they are overwhelmed.
When calculating the equivalent resistance of resistors in parallel requires: first add the Reciprocals of all parallel resistors and then take Reciprocsl of answer.. ie 1/[(1/R1 + 1/R2)] your 'hack' is commonly employed here
Every video he puts out might be someone's first time viewing him-of course he should be allowed to introduce himself and the products he offers for sale each time! too dumb to know how to fast scan with the youtube progress bar?
For Thousands of years, in fact. It is still a Hack, and there are STILL huge numbers of people who do not know it. It being an OLD HACK, or a brand new hack, doesn't change its importance, or its clarity. And now, thousands of years later, too many Americans are tolerating and even celebrating a Destructive Ignorance of Simple Logic.
It was different when I went to high school. I forgot a lot. But when I see it I remember. No algebra 2 for me worked too hard with Algebra 1...love this video..
50 years ago I took College Algebra from a young professor named Charles Miller. He clarified things is such a way that I actually learned Algebra. He wrote his own textbook but it wasn't published yet, so he put it in 3 ring binders and we used it. The last time I saw that textbook it was in it's 8th printing.
Wow you’re old as dirt!
Hi. I looked on Amazon for the book you loved. Which one is it? There are a couple there. I’d love it if you could let me know. 👍🏻
Yes, I would like to know the name of the book too please.
Name of the book pls
@@chriswebster24 but what is the age of the tree growing in that dirt and how many leaves are currently on it?
I don't remember how I was taught the LCD method, but this has always been how I add/subtract fractions. I never thought of it as a trick or hack.
Same here. I mean what other method can you use to add or subtract fractions?
Me either. I don’t worry about reducing until I’ve added the top. And the first example was easy to reduce in my head.
Fully agree, also if taught this way then adding up algebraic fractions is easier.
50 years ago I was taught to "Cross multiply"
In this video, the narrator calls his method, "Bow Tie"
I think they are identical to each other.
Same here!
It is called "cross multiplying". It is not a trick, or a hack. It is the standard method. I have taught this for decades, and I find it hard to believe that there are maths teachers ANYWHERE who do not .
When I was in school learning this, I was taught LCD as well as this method. I was never taught the cross-multiply method as the "standard method".
What I think would be beneficial is for people to be taught the reasons why this method works.
This is not cross multiplying or at least how cross multiplying is taught
@@chadlhorton
Yeah, I think you're right. This is not a hack or a trick, it's mathematically sound. I think the concept that needs to be stressed is that when you're getting a common denominator (least or otherwise), all you're doing is multiplying each fraction by 1.
For the original problem: 3/7 + 4/12, you can do some reducing up front which will help you. It's good to look for that. Then, 3/7 + 4/12 = 3/7 + 1/3 = (3/7)(3/3) + (1/3)(7/7). The tactic here is to get a common denominator, so each fraction is multiplied the other fraction's denominator-over-denominator. Doing that is 100% OK because you're multiplying things by 1 when you do this. So, (3/7)(3/3) + (1/3)(7/7) = 9/21 + 7/21 = (9+7)/21 = 16/21. Is 16/21 reducible any further. No. Prime factorization of 21 is 3 and 7. Is 16 divisible by 3 or 7? No. The final reduced answer is 16/21. Boom, done. Even if you miss the step of reducing 4/12 to to 1/3 in the beginning and start out (3/7)(12/12) + (4/12)(7/7)......, no big deal. It's not wrong. You'll do some reducing on the back-end of the problem. Do it right and you'll arrive at the same answer and full credit for the problem. Doing reduction up-front is a good habit but not a show-stopper if you miss that step.
Like a lot of posters here, I don't like this being called a hack or trick. It's not. It is mathematically sound and you still go through the proper steps to do the problem, it's not a shortcut (many shortcuts that get passed around by kids are not mathematically sound, will often get you the wrong answer, and should be avoided).
All math teachers should teach the metric system only. Otherwise, you are in the great company of only Liberia and Burma.
This is a pretty standard method. I was taught it over 50 years ago. There is a risk in using it as a shortcut if you don’t understand what you’re really doing. Students learning to add or subtract fractions need to know what it is they’re really doing before blindly applying such “hacks.”
Exactly, there is no point teaching some cute hack which a trained monkey can repeat adnauseam, they have to understand WHY?
very good point Murray. I am a semi-retired engineer, or so I tell people when business is slow. I was taught cook book math which is the norm, solving provided equations as homework. You won't understand what you are doing unless or until you can set up the equations - applied math.
@@ericdussell7421The same applies to about anything-if you understand HOW something works, you have a good chance of fixing it. Mathematical, mechanical, electrical, the list goes on.
@My Reading Room Channel Exactly. 95% of the things people "discovered" or whatever I had already figured out on my own. 'Course, I'm an old guy anyway, so I would be dumber than I actually am, if I hadn't figured out by now.
Absolutely correct. No shortcuts without understanding. His bow tie method is akin to cranking a car and saying that you understand why it starts.
I crashed and burned when I got to fractions. Now, at 62, I learn math because I want to. This is amazing. Thanks.
fractions, decimals and percentages are easy
@@fallback8314 That's just YOUR opinion. For some people it's not that easy.
If ya crash and burn at fractions it's probably cuz you have other priorities lol.
@@fallback8314 decimals are fun, percentages are fun. Fractions are a bit tricky and takes a while, but not that hard to grasp.
I found out that learning my times tables helped immensely
Excellent. What a wonderful way to illustrated an accurate calculation fractions without Lowest Common Numerator... which does not matter. Thank you for your teaching. (Old UCLA Math grad)
Thanks for the video. I was never taught this in school. Was always taught to find the LCD and do it the first way. Appreciate the work you put into your videos.
It seems some schools put too much emphasis on LCDs. The fact is, to add or subtract fractions you only need to have a "common" denominator. It doesn't have to be the LOWEST. If you multiply both of the denominators together you will get a COMMON denominator. It may not be the lowest but it doesn't have to be.
So that's all this bow tie is doing is converting the fractions to this common denominator. Which is why it may result in a fraction that can be reduced, because it wasn't the lowest.
Thanks man, i just applied for a job and they asked me to do a fraction sum. I honestly was lost. After watching your video i was back in the game, thanks so much for your time. God bless your heart!
It's been so many years since I worked on my undergrad. I was fortunate that what I majored in didn't require a whole lot of math, outside of getting my real estate license, Science classes, and of course electronics. I started college 33 yrs ago, most of the math was that yr, freshman year. I am turning 51 in a few days, my hair is solid gray (colored,) and I just don't remember it, and really don't care to go back over it again. I appreciate the video, because if i had a child it would be so helpful. It was hard to remember basic math such as small fractions. Oddly, I remember the real estate math equations more easily, even though our broker always took care of that part of the sell of a home.
I had a difficult time understanding algebra in high school but our teacher taught us this method of dealing with fractions and I still remember it 58 years later.
Same here
and THAT is exactly why this method is not a "hack".....in addition to the fact this has become the most overused word on the internet
@@danstrayer111 And that's why I used the term "method" as did others.
@@autumnisnothere and that is the right word.
4/12=1/3 3/7+1/3. LCM 21. 3/7=9/21. 1/3=7/21 9+7=16. 16/21. Ans
You just showed my age, lol. As a youngster decades ago this is how they taught grade 8 fractions. This was a good refresher for me!
The order in which you do the two upward facing arrows is significant in that sometimes you get a negative number depending on which arrow you do first when subtracting.
That's bullshit.
@@SharpObserver1A 10:35
Doesn't matter which arrow you start with, as long as the answer you get for that arrow is placed at the point of that same arrow…
Thank You!
I am a retired EE with a minor in math, AND I have NEVER seen this method, but I LIKE, it.
Thank You , Gary
One of the things about math is that for most operations, if two methods get the same results for all inputs, they are really the same method.
😂 not according to my hs trigonometry teacher
Can you prove that? Whilst it might seem facetious it's actually a valid question. Maybe we should teach students how to prove that these operations actually work whether you are dealing with natural numbers or these different 'types of numbers' that we call fractions. I have seen a maths professor lament that his undergraduates cannot do this yet he can teach primary school children to verify that these operations do work as the should. Its also a nice way to introduce algebra into young minds. I have tried it out with some success.
Thanks for a great video. I am an electrical engineer and do math for a living. Always looking for things to share with my 11 year old grand daughter.
I read some of the comments (from the Karens below) and am disappointed at the lack of decorum.
Hello John
My name is Alex, age 73 following your videos from Waterford Ireland. I am a very mature student attending Adult Education Class. I have always been interested in Maths,
Just to thank you for taking the mystery out of learning. Kind regards Alex
I taught myself to do these kinds of problems as a 3rd grader...9 years old, in 1965 (born in 1956)... while reading my 5th grader sister's Math textbook;her studies were more interesting than mine and I'd steal her books to read them for fun 🙂. All of 'em. If you understand LCD and Cross Multiplication, a "hack" isn't needed.
I knew the answer to "3/7 + 4/12" seconds after I saw it...16/21. All the other ones were easy to solve, too.
Wow…..stroking that all the way. 😑 what an ego.
I always struggled with math, especially fractions in school. As an adult, I hope to learn how to do it with a little more ease.
Maybe I'm just extremely old, but when they taught us how to do addition & subtraction for fractions, they said (Cross multiply and then add/subtract as needed)
So the 2/3 + 1/5 you would do the following... 2*5 + 1*3 over 3*5 ===> so you would get 10 + 3 over 15 or 13/15.
The top problem was pretty quick, but there was a bit of simplification to do first. 3/7 + 4/12 ===> 3/7 + 1/3 ===> 3*3 + 7*1 over 7*3 ===> 9+7 over 21 or 16/21
It is easier if you do simplification before you do the cross multiply and add/subtract.
When you master the concepts, you can do most of them in your head and just write down the right answer, and then lose points because you didn't show your work. 😣
My son and daughter experienced that very thing.
Thank you so much John. I am 76 (a long time since junior school!) I find your bow tie way so much easier, especially when outside and not with stationary at my disposal. Love it! You have made my life a lot simpler!
The concept of this hack method is, in effect, the same as the traditional method of finding common denominators first. The benefit of this hack is that it streamlines the procedure for finding the numerators. I would only encourage students to use the hack method if they understand the principle of the traditional method first.
At 14:25 you refer to 1128 as 1-28, again at 14:40; and at 14:44 you refer to 1678 as 6-78.
You must be a pilot, as they skip - in the USA - the first digit of the radio frequency, when they read it back to the Air Traffic Controller !
Great math hack for fractions. Have never determined an LCD, since I learned how to do it 50 years ago.
Always used this most useful hack.
Matt Lee
1st video I’ve watched on your channel. Subscribed. Long story short I didn’t apply myself in high school in math. Once I attended college I struggled. Had an algebra teacher that was one of the BEST I ever had. His methods of teaching really made me see the light and I enjoyed algebra! NEVER thought I’d say that. Graduated college in ‘87 and still feel to this day the professor was a highlight in my life! So I’m watching RUclips and I see this “refresher course” and absolutely enjoyed it! Thank you sir! I’m going to watch daily and sharpen those math skills! Very excited👍 For the know it alls in previous comments some may not know the bow tie method and therefore the “excessive verbiage” may bore you but for others is a continuation of learning. Go brush up on your psychology and join us common folk when we get to your level😅
Me, too. Not great in HS math. Always thought of myself as mathematically challenged, but really wanted to learn it. Yes, I will subscribe here. Thank you TABLETMATHCLASS!!
Great story. You should try teaching/coaching others with your skills (as a hobby). Your enthusiasm is infectious and you will be passing a gift on to someone else.
i know this is meaningless to most but my favorite teacher taught math and science and ALWAYS wore a bow tie!!!
Your teaching method is so easy to grasp. I am used to getting distracted with anything mathematics. Currently taking job placement assessments and this is a helpful refresher. Thank you!
You can simplify the third one before you use the "bow tie" method. 12/110 + 5/94 = 6/55 + 5/94 that will give you smaller numbers to work with.
I used to tutor math from GED clear through college algebra. This is a good tutorial for students in lower math classes: beginning algebra, intermediate algebra, even perfect for elementary math students. Very interesting tutorial. Hopefully, it will help many students!
What is ged
@@manoshawad7993 GED (general education diploma) is the equivalent of a high school diploma, but is not the same. People who have dropped out of high school get their GED later in life.
Thank you
@@manoshawad7993 you are quite welcome.
Wish when I was jn high-school had you as my math teacher with a kind calmly voice n great at explaining long way n short way n being careful to choose correct method n not to be fooled
I think this is wonderful and I wish I had had you as a teacher in school. I had really smart math teachers that couldn’t teach. When anyone told them that they didn’t understand a problem, they would repeat what the student didn’t understand in the first place, in the same words. Teachers who care find different ways to explain things. Further, you do not teach only to the kids who get it. Teach to the ones who don’t. It the whiz kids get bored, too bad. Give them silent work to do in their seats. Also, don’t talk down to the students, or make fun of them if they don’t understand. Everyone learns differently. It is your job as teachers to teach ALL children, not just the “smart, quick ones” who get your teaching. I struggled with math as a military brat who moved every year in the summer. I’d go to one school and something had already been taught. I’d go to another and I had learned that back two states ago. I went to 13 different schools in 12 years and it was not easy to catch up. It’s easier for children to learn when they stay in one place throughout their school years. I will be 71 this week and this still upsets me a great deal. It is hard getting an education with bits and pieces of knowledge picked up in all the different school systems. I wish the states all had the same curriculums. That would have solved my problems, and I am sure many other children’s problems.
Agreed, and happy belated birthday!
@@JackOfAllRAIDs Thank you so much!
Texassews -- I know the feeling too... We moved about the same and I hated it that I could never have friends in school, because, we were going to leave soon, and I would never see those great kids again...
Now, sometimes, I remember their names and can see their faces in my mind, and wonder how they did.... I pray that they are all good and doing fine...
Perhaps one day in Heaven, I may be able to find them all again and catch up...
The absolute Best Teachers I ever remember were in Dallas Texas... They absolutely rocked their positions, and always told us that "We were going to learn a lot of things and for sure, we were going to learn how to get through life with all the things we were going to learn that year... And I/we Did !!!!!
I can do anything I try to do and I am almost the same age as you !!
Will also want to catch up with these great Teachers up there and see how they did and thank them again for being there for me....
God Bless you and yours !
Fran Danco
The BowTie method is how I do fractions in my head. It always works, and you can reduce fractions after you're done, which is easier (to me) than doing the LCD first. Likewise, it's basically the only way you CAN do it when you have algebraic variables involved.
Also, for a soapbox moment, I personally think reducing fractions and figuring out LCD is mostly pointless in life. I mean, it doesn't hurt to know it, but it doesn't actually assist you much either. No one is EVER going to think of 52 cents as 13/25ths of a dollar, for example. And I personally believe it's more useful for everyone to understand that 8/16 = 128/256 and you don't even have to consider 1/2 in that, because then you get an actual understanding of how numerators relate to denominators. If you make everyone reduce fractions all the time, you're basically saying 1/2 is "more mathematically real" than 128/256 is. But 128/256 might be more important than understanding that it reduces to 1/2 in certain contexts...like if you're dealing with computer code or RAM or anything else in binary, for example.
Okey what we have for dinner party bayan bibi day boñtag
I'm 77 and still learning. I remember at eight my father reducing me to tears because I couldn't understand what an LCD was, (many years later in his papers I found his old school reports where I learned he was weak at maths).🤣
Almost as old. My father, may he still be roasting over the flames of Hell, didn't ever teach me anything, but took great delight in telling me how good he was in Math at school. Somehow I managed to obtain a PhD and ended up teaching Math for 35 years. Pure luck, he would say.
Lol My father was exceptional at maths but he never taught me anything. I struggled with maths. It was only much later when I came back to the subject looking at how it is or could be taught that I discovered he had laid down a rich tapestry of stories that used to tell me that I now realise were all mathematical problems & insights but in a quirky sort of way that left me curious and puzzling over. I think he just wanted me to find my own way whatever I did but I can't help smiling when I find myself telling young children the same quirky stories and having fun trying to work things out. That is why I enjoy the so called 'Vedic maths' approach. It does things in different ways that are playful and fun to learn and much much faster.
My dad was a math major but is TERRIBLE at teaching, his brain just functions at a higher level, he skips too many steps and didn't understand why I'd get confused, he couldn't simplify things. I do not miss high school tutoring sessions lmao. This teacher is exactly who could have helped me back then! Sigh
Thanks John for this and thanks for speaking with me today 😊
A hack indeed, totally bypassing the concepts of an LCD and equivalent fractions. Should only be used after understanding the former and latter.
Back in the day when I was a wee bit lad, I could not do this because I could not figure out what X was. Could not get past that until I had a shop teacher who told me to turn it into a decimal for machine shop class. To me that was easier than dealing with fractions. This make more sense to me now (50 years later) never had the opportunity to learn this in school.
It's always desirable to simplify the arithmetic up-front before applying the bow tie method.
In the last example, 12/110 reduces to 6/55 and we have:
6/55 + 5/94 = (564 + 275) / 5170
I'm terrible at arithmetic so that's why I gotta' put the big stuff into the cuisinart first (so to speak).
Stop hating guys this is good for students who never learned this process. Get off if you know it n do not need it. Also, todays students love and learn anything with the word hack Ok
Retired engineer speaking. Rather than struggle to find the LCD, I usually just multiply the two D's to get a CD, and multiply the N's by whatever is needed to leave the fractional values unchanged - which is exactly what you're doing here! I never saw it codified so simply and directly as you've shown us. My only suggestion would be to move the heads of the diagonal arrows to the bottom, rather than the top - that way you can just proceed from left to right starting at each arrow's "nock" for subtraction as well as addition. Thanks! Any day you learn something new is a good day!
Thank you. I watched this video and subscribed. You have awakened a love that I had forgotten about... numbers!!
This is how I learned to add fractions 60 years ago
Kimberly I wish I was in your class. This is soooooooooooooooo
easier than remembering all those rules.
MATH WAS THE SCARIEST THING IN SCHOOL FOR ME!! I JUST COULD NOT GET IT! BUT NOW I HAVE HOPE THANK YOU PEACE AND LOVE 💜💙💚💛🧡❤
Ok I'll
Ok
I'll
Ok
You are such a good math teacher 👍🏻
Never heard of this method before - I learned the first method. Thanks for the tip!
Thank you. I am teaching my grade 5 daughter how to do these. Thank you for the Bow tie method, I grew up with the first one only.
Spoiler alert: it's cross multiplying, and the video starts at 6:04.
Cross multiplication refers to one fraction equal to another fraction. This is simply using the common denominator rather than the Least Common Denominator.
Brilliant! I am an evangelist for easy ways to do math. I always preach that a%(b)=b%(a), so that you can swap the two terms because of the commutative principle.
A tip for mixed numbers: set the whole number aside, do the bowtie and then bring back the whole number. From your example: 3 1/8 + 2/5 = 3 + 1/8 + 2/5 = 3+ (5+16)/40 = 3 + 21/40 = 3 21/40. Great explanation, shared it with my kids. Don't know where I learned this, but I've always done this method and had never bothered with LCD.
Exactly correct. No need to convert a whole number to an improper fraction so just set it aside until you have dealt with the fractions and then bring the whole number(s) back at the end of the process.
Thank you for your help as I struggle with fractions.
It just seems to me that we are going backwards. Don’t get me wrong. The access to help and info is wonderful, especially compared to when I was learning mathematics.
But, it just feels to me, that compared to 4 decades ago, this stuff should be 3rd or 4th grade level sight-solving math.
yes, I taught 4th grade...and this is what we taught. We try to keep civilization moving forward, but historically there are drops in advancement, and humans start over.
@@RebaCampbell1984 I can’t agree that there are historical drops in advancement which result in Humans starting over. At least, I don’t see that in our recorded history. Of course, Civilizations have risen and fallen, but I’m not sure any of them slipped back to their inception as a result.
There are pockets of Humans who may not have advanced alongside others, but the Romans didn’t drop their possessions and begin walking naked back into the Wilderness. 😜
Either way, let’s hope we are able to one day find a common value to place onto our Children and their abilities to survive in what is becoming a much more advanced and competitive world.
@@troycrum9294 that would be very good if our children continue to advance. It is more possible, except for things happening as they have for eons...If you look at the archaeological record, especially before writing, there are periods where humans' advancements did retreat, and we don't know How they build incredible structures...Or either by climate challenges, or geological forces like the Doggerman Landmass or Mediterranean seaside cultures that were wiped out by sudden water rushes. We know they had advance cultures, but sharing/advancement of knowledge was reduced. Another example, the amazing 2,000 year old 'computer'calendar that was found in the Mediterranean, the Antikythera mechanism, and it couldn't be just one of a kind, yet mankind didn't get to that level of advancement again until 14th Century. That knowledge was lost for many centuries.
@@RebaCampbell1984 now we’re getting into another, and as far as I’m concerned, fascinating realm of discussion.
@@RebaCampbell1984 my guess though, is that we are not related in any way to them though.
Just think 🤔....All these years I actually thought I was horrible in math, when all I needed was a GREAT math teacher 🤦🏻♂️
Thanks
I would have liked you to show how to find the Lowest common Denominator in every circumstance, as you must determine it prior to solving .
look up the euclidean method :)
Reduce terms the find the common denominator then add
You just need ANY common denominator, the least (lowest) common denominator is preferred but NOT required in order to solve the problem. So unless the LCD is obvious (if, for example, one of the two denominators is a whole number multiple of the other), it's easiest to just use the product of the 2 denominators as the common denominator (which often will be the LCD, BTW), do the addition or subtraction, and reduce the fractional answer at the end.
That mixed fraction you can exclude the whole number. Just add 1/8 to 2/5 for the fractional portion then add it to the whole number. 1/8+2/5 is 21/40 then add 3 to get 3 21/40 for the smallest version the quickest
Good, well explained for those who are still starting. Though here in India, cross multiplication is standard procedure in junior math class, for probably 8,9 year olds
More like _barely_ explained. I know it's nice to be nice, but you're being excessively generous. Cross-multiplication is/has been standard procedure for most primary-aged students on the planet. But to give this rambling, tautological mess an elephant stamp for being "well-explained" is just not right. It was far, FAR from _well_ explained. He couldn't even decide whether he wanted to call it a trick, a hack, or a method... and forced us to share and revisit that painful dilemma with him... again and again! Freaking awful. Mostly filler!
Looks like a great 4 minute video squeezed into almost 17 minutes. Genius.
4/12 can be reduced to 1/3 then can Mutiple both top and bottom of 1/3 by 7 to get 7/21 and multiple both top and bottom of 3/7 by 3 to get 9/21 then add 7/21 to get 16/21. 2/3 Mutiple both top and bottom by 5 gives 10/15 and 1/5 both top and bottom by 3 gives 3/15 so add both together to get 13/15. This should have been learned in Elementary school.
This "bowtie" method is easier when the numbers are small, so one should always look to reduce fractions *before* applying it. Why use the method on 25/75 + 24/48 when you can reduce first, and use the trick on 1/3 + 1/2 ?!
@@timeonly1401 I plainly said to reduce first. 25/75 is 1/3 and 24/48 is 1/2 then convert to divisions of 6 and 2/6 + 3/6 =5/6
love this method I'll be using it from now on and I'm 63 YO. I've had a problem in the past with fractions but not anymore.
That is NOT a hack - that's the way it's done.
That's the Common denominator method, but the Least Common Denominator is taught as the "way it is done" as it minimizes simplification.
And to understand, instead of mindlessly following a procedure, here is the explanation (short version, using variables) ...
Trivial rule a: 1*x = x (any number multiplied by one always is the same number again)
Trivial rule b: x*y = y*x (the order when multiplying numbers does not matter)
Trivial rule c: x/x = 1 (any number, other than zero, divided by itself always is one)
Examples:
1*9 = 9, 1*-9 = -9
2*3 = 3*2
9/9 = 1, -9/-9 = 1
Solving 3/7 + 4/12 with (more) comprehension:
7*12 = 12*7 and 7/7 = 1 and 12/12 = 1
1*(3/7) = (12/12)*(3/7) = 36/84
1*(4/12) = (7/7)*(4/12) = 28/84
36/84 + 28/84 = 64/84 (which can be simplified to: 16/21. As 4/12 can be simplified to: 1/3)
Note:
It is easier to show on a blackboard/screen where you can write/show the numerator above the denominator.
Additionally, for a full comprehension it should also be explained why 2 fractions with the same denominator can be added by simply adding the numerators above the same denominator (i.e. this might not be so trivial,. Can be explained using pie charts).
E.g. 2/9 + 3/9 = 5/9 Or more generic/formerly: x/z + y/z = (x+y)/z
Really worth to watch and learn your video teachings. Especially if everyone learn maths & geometry their life will be easy similar to an engineer to find solutions to various techniques. Even aptitude test they can crack very easily.
I didn't know fractions and you teach me how to do fractions🎉❤😊
Damn get to the point, man. Your vids are 5 times longer than they need to be. Content is good, but - GET - TO - THE - POINT.
Well we have to beg for likes and subscriptions for 2 minutes first!
Totally agree. Good vid but this isn't worthy of 17 minutes. This is like the video that discussed how to solve division of fractions such as: 3/8 divided by 1/4. I can tell you how to do that in 1 minute if I'm being slow, this guy took 17 minutes. You flip the 1/4 and turn it into a multiplication problem. Now it's converted to: 3/8 * 4 = 12/8 = 3/2 = 1-1/2 = 1.5 (depending on what form you want your answer in).
@@davenone7312
Yes, there is that.
Is he paid by the hour?
@@Skank_and_Gutterboy some people learn slower I think he is trying to cover the full spectrum of learning speeds. You could always speed up the video if it’s too slow for you. Your learning speed is not the standard in the world.
Learning truly is all about teaching! I had a good teacher for Beg. Algebra and got a B. Then I had a not so great teacher for Adv. Algebra and got a D. Took Geometry the next year with the first teacher again and got a B again. I felt really miserable about the D but cheered up a bit after I realized that it wasn't totally my fault.
Learned this “hack” more than 60 years ago in public school before learning the LCD method.
Not that long ago, but also, before lcd "kleinste gemene deler" in Dutch
Taught this hack for 35 years but after the LCD method had been taught first.
Thank you very much po ❤️😊😅😊😅😊😊
I wish I had known this 55 years ago. I might have even come to enjoy math instead of dread it. I’ll remember this for my grandchildren.
Thanks for your videos. I was a newbie to this method of cross multiplying.
This is not a hack...it's BASIC math that we were all taught back when teachers actually taught real math!
YES! That is how I was taught LCD's in the 1960's - they called it cross-multiplying then.
I think people called it sissors
Scissors, cross multiplying, chop stick, bread sticks, crossing streams, clashing lightsabers, jousting slongs, crossing sausages…. What ever you call it, it basic math!
@@mrfonz8034 how long have you been alive
I graduated in 2000 and I always remember to cross multiply and divide..... that's what our math teacher taught us it was called
I learned this hack about 75 years ago in elementary school.
That was when school was about teaching math and other useful disciplines and not gender pronouns, critical race theory and various other pieces of useless garbage..
Fractions only apply to cooking how a days. It was reduced when the Dow changed from fractions to decimal.
🤣🤣🤣
Very interesting. I enjoyed this and I subscribed to your channel. Your presentation was great. Thank you.
Yep, remembering this from Owings Mills Elementary! TY
17 min. long, could have covered this in 2 min. If you know anything about mathematics, this is not a hack, by any means. In fact, most schools teach this method!
You're right. I appreciate the content, but he is way too wordy. blah blah blah....
Exactly, this is not a hack or a trick, the math is sound and this is how it's taught. All you're doing is multiplying your fractions by 1 (which is what a fraction like 3/3 or 12/12 equals) to get a common denominator. Then you just add the new numerators and reduce as necessary. Piece of cake, calling it a "hack" or "trick" is wrong. Among kids, I remember hacks and tricks being passed around that were wrong and would usually give you the wrong answer (or you'd fall ass-backwards into the right answer but they would lead you to bad concepts). This method is not like that, it's the right way to do it.
I hope those who teach it also teach there students common courtesies like not being rude to people who are trying to help people who are not as knowledgeable.
@@susancook9228
No doubt!
@@susancook9228 you are absolutely right. I appreciate the length he took to explain the process. There will always be little people also known as haters who have to hate. Shame on them!!😡
I love maths but i still have some difficulties but with these videos i will understand thank you
That’s interesting. When you master the bow tie method, you can advance to the double Windsor method.
😂😂😂
Don't let this man know about the ascot method.
🤣 I’m so gullible! I fell for this and actually looked up the “double windsor” method! 🤣😂
@@kanay_norie my corny joke was not in vain 😉
@@88woodbikes4 😂🤣😆
That helps a lot to those students have struggling to answer the fraction answering.
The way I always do it. What a hack😂
Thanx for the review. Now i remember why i never liked math enough to go in to algerbra. Double talk by the teachers n malicious students who caught on how to dumb down others. Thanx for not being a malicious teacher.
My god, you are 2:26 and haven't even started... get on with it!
I wish more than ever I had you for my math teacher throughout high school. I would have enjoyed it and made straight A's
This is the standard way of doing it. The first one he showed us is an explanation of how the standard method works.
I wish I knew this SO many years ago. Thank you!
W O W. LOVE THE WAY YOU TEACH.
I UNDERSTAND THIS WAY BETTER THAN I DID BEFORE...THANK YOU SO
MUCH...😁😃🤯😂
Good video and hack!
Wondering though,…why not just ignore the whole number of the mixed fraction and simply apply the hack on the fractions…and then bring the whole number over?
3 1/8 + 2/5
Rewrite as 3 and 1/8 + 2/5… which becomes 21/40 and bring over the 3
Final answer = 3 21/40
Beauty of this is it avoids converting a mixed fraction to improper and then back to a mixed fraction.
Still a great video, thanks!
While he was doing the introduction I already solved the equation
An ego is not a good thing.
Wow! What a genius! 😂😂😂 Except for the fact that that's ain't an equation 😂😂
same; did it in my head
Well done, Einstein
For the problem @ 13:00, Can we just use the fractions ( without the whole number - 3 ) and arrive at the simplified answer of 3 and 21/40?
Correct. Think of the mixed number 3-1/8 (read: "Three and one-eighths". Sorry, the notation for mixed number uses a hyphen; it's not the subtraction symbol) as 3 + 1/8. (since 3-1/8 **is** 1/8 more than 3; convince yourself of this on the number line).
Then: (3-1/8) + 2/5 = (3 + 1/8) + 2/5 = 3 + (1/8 + 2/5) = 3 + 21/40 = 3-21/40 (Three and twenty-one fortieths).
Stopped at 6:14 when it became clear this was just the normal way of adding and subtracting fractions and wasn't a hack in the slightest.
I really like this you work in an elementary school with the fourth grade and we're calling that the butterfly method it is amazing
Really ? This was taught to us in the 2nd grade, in 1962. Just goes to show how far backwards our education system has gone in all these years. Thanks to teaching to the lowest level in the class instead of pushing everyone to achieve a higher level. Thanks a lot, " no child left behind ".
Then you were at a rare school. Generally third grade introduced times tables, even back in the olden golden days. You weren’t adding and subtracting fractions before learning basic multiplication. This is not a “no child left behind” problem, it’s a misremembering of your precious youth. Oh, and I polled multiple people who would have been in second grade a few years before and after 1962, representing both coasts and the heartland. Pretty consistent curriculum.
@@shaalijones3484 Amazing how some people think they know what someone else experienced in life. I do not claim to have gone to exceptional school, but we did have some exceptional teachers. Yes, we did learned our multiplication tables in second grade, which I struggled with. My older brother and sister took turns drilling me with our own flashcards. Pretty arrogant of you to think you have any idea of what was taught to others. I actually still have my school books from then. My parents bought a set for me since I was having so much difficulty with it at that time.
hahahaha!
Still, the older generation needs to be refreshed from time to time, while the newer generations need to simply learn some basics, and the more techniques they learn, the better the brain works and something in it clicks when there is an irregularity, and a flaw is seen, even when the brain hasn't consciously "computed" it, as yet.
Like gamblers who spend their time learning and practicing card tricks. Not for the amusement of the audience, but to keep their brain nimble.
We don't have as many Nimble Brains these days as we had in the 1940's and 50's - much less the 1880's-1940.
Numbers are stable blocks of measures, totally equidistant from eachother. The more someone handles them in the brain, like a juggler, The sense in the Brain of the Balance and Regularity will help the workman "FEEL" as well as anything else, whether everything is properly fitting together, clean and tight.
You may think this is something that goes without saying, but having worked with a few hundred kids on their math skills, I can tell you that over the decades, their sense of the "right feel" of the math they are working on has gone drastically downhill. And it is reflected in the deteriorating politics of our day.
My baby sister was only 3 1/2 yrs younger than me, but all the parent outrage at the "NEW MATH" that started in Elementary school in her grade, not the class above hers, worked to distort a wide variety of LOGIC in the schools and thus to the next generations of politicians and voters as this "Fun House of Mirrors" was forced into that and the following generations, until the students in many schools could NOT TOLERATE sound mathematical teaching or anything else that depended on a hefty grasp of Logic.
Now look at the MATH of last year's Election and tell us all how so many Millions of peoples world wide cannot figure out how badly distorted from Reality the Election Counts in dozens of nations are so messed up. They have no SENSE in their Brain Function of the Logic of the Numbers - it simply does not compute, they are overwhelmed.
I call BS here. Adding fractions not part of Grade 2 arithmetic.
This is amazing! Wish they taughted this when I was in school.
Did they not taughted English either?
As soon as you said "hack", I looked for a faster method. Dreamed up this method before I got 40 seconds in. This should be a two minute video.
I did the math in bout 30 seconds
When calculating the equivalent resistance of resistors in parallel requires: first add the Reciprocals of all parallel resistors and then take Reciprocsl of answer..
ie 1/[(1/R1 + 1/R2)]
your 'hack' is commonly employed here
@5:16 thank me later.
what is your best way to simplify the large numbers
It shouldn't take over 5 minutes to even start showing the technique. At current view count, you've wasted over 1.53 years of collective human life.
Every video he puts out might be someone's first time viewing him-of course he should be allowed to introduce himself and the products he offers for sale each time! too dumb to know how to fast scan with the youtube progress bar?
This was a great review, luckily I was taught the "Bow tie method" in the 4th grade. Thanks! :D
This isn't a trick or a hack, it is an alternative approach and nothing more.
Yeah, I thought there was some cool new method I didn't know about.
@@OmaBike Everything is a nickel now-a-days....plastic people with plastic thoughts....but hey parts of me are plastic now.
Maybe not, but the title got you here didn’t it?
@@atamagashock Deception isn't calculatable though is it?
@@ChadLuciano it’s not that deep lmao
Thanks, I loved the bow tie method. 🎀 This is the first time I have seen it.
Hack?? Really????What's so special about this. Been doing this for years !!!!
I’m curious. Is there a different way?
Yeah. It's the same method, just few steps are skipped.
For Thousands of years, in fact.
It is still a Hack, and there are STILL huge numbers of people who do not know it.
It being an OLD HACK, or a brand new hack, doesn't change its importance, or its clarity.
And now, thousands of years later, too many Americans are tolerating and even celebrating a Destructive Ignorance of Simple Logic.
It was different when I went to high school. I forgot a lot. But when I see it I remember. No algebra 2 for me worked too hard with Algebra 1...love this video..