Thank you. You are the FIRST TEACHER that made ANY sense to me. In third grade I moved and my new school was very advanced in fractions. My old school had not started fractions. I got LOST in the dust and was “behind” for the rest of my education. I tried to get help. I maybe had a mind block because of the word stupid. Attended 9, yes NINE different schools. I now finally know fractions.
I'm sorry you had to go through moving so much. 😔 everything like leaving friends behind each time. Then the math issue where no one checked in your knowledge. I'm glad you got it now. 👍
It would be nice if you explained WHY these techniques work. Rather than just what to do and how to do it. It would be interesting, and possibly help some of us remember the technique better. My memory isn’t great, but when I understand why something works, it sticks in my mind more. But thank you for the refresher. It is very helpful and easy to watch.
a/b ÷ c/d = a/b × d/c = ad/bc 2/5 ÷ 1/4 = 2/ 5 × 4/1 = 8/5 = 1 3/5 ; 1.6. Learned this in 4th grade, back in 1967. Some things just stay with you. I really like how this guy explains how to solve step-by-step.
Thank you for the refresher course in basic math. Just following, remembering and applying the different rules is exciting now that a graded paper is out of the way. How I wish all math teachers are as positive like you sir. Growing up in the Philippines and learning all the rules was a real challenge. Then to be channeled into a degree (Geology) without mastering mathematical concepts was frustrating. I am so thankful I was lucky enough to enlist in the navy, and not to disappoint my hardworking parents for not earning a degree. Again though, my lack of really understanding math concepts was a struggle in my Statistics, Finance and College Math classes when I decided to finally earn a degree after waiting until advancement to E-7. Earning an Associate in Science helped me earned my naval commission (CWO then LDO) and a Bachelor's in Business Administration, (after retirement with 30+ years) was to appreciate my parents' wish. So, my bottom line in Math?, (Algebra, Geometry, etc..), fun and understandable given the right teacher. Thank you sir!
If you put this problem as a word problem and were cutting fabric which is measured by the yard, I would divide 36 by 5 which equals 7.2”. 7.2” time 2 is 14.4”, and 1/4 of that is 3.6”. This number is 10% of one yard as a yard is 36”. This is life in the real world. Translated into cutting fabric, you have instead of dividing a cut fabric which was only 14.4” long, you have now a piece of 57.6”. If you were selling leather by the roll and giving away product when the customer wanted you to cut a remnant of 14.4” long in quarters, you would not keep your job for very long. Or if you had cut a pumpkin pie into 5 slices and 2 slices remained, you’d cut each slice in two to make four pieces. Each slice would then be 1/10th of the pie. Anything you want 1/4 of, you cannot get a bigger portion than you started with. Your answer is bigger than what you began with. Math is practical unless it isn’t. If you had turned this problem into geometric shapes, you’d see my point.
I'm 80 years of age and enjoying re-learning the skills you are teaching so well. I have a question, I'm really interested in getting a board like yours that I can do problems on. What software/pen/stylus do you use. It appears simple and very functional. I've researched this but all appear a bit more complex than yours and at my age I prefer simplicity. Thanks for your help.
I love the review of these basic math skills. So important. I wish I had the interest in math I have at 69 when I was 10. I am always playing with numbers in my mind.
If students always get tripped up turning their improper fraction into a mixed number, that's just proof of how much they really need to be made to do it. Are they just going to go through life never having the skill of turning an improper fraction into a mixed number because the math teacher doesn't want to insist they learn it, so they can get higher test scores and the math teacher looks like a better teacher than he/she really is?
It does seem incomplete (leaving the answer as an improper, top-heavy, fraction). Saving time, and avoiding error, seem weak reasons; if those are the only reasons.
Thanks for the review of fractions. :) And thanks for reminding me about my university calculus teacher that would explain the process and then go over all the ways that students make mistakes. The other thing that he would stress is look at the numbers before and estimate what the answer should be. In your second example 2/5 / 1/4 -- the answer should be how many times does 1/4 go into just under a 1/2, well a little less than twice - so 8/5 is in the range that you should expect. Thanks again.
Before you mentioned that you were in the Marine Corps, I sort of figured you were well - educated (beyond college.) Don't get me wrong, please. A college degree is wonderful, but, the discipline of a Military Career puts one "over - the - top" to me. I, myself, was in the Army, but, I was unable to complete BCT because of a knee injury. My MOS was to be (as it was known to be back in the early 2000's) a Patriot Missile Systems Operator/Maintainer because of my electronics knowledge. But, now, I'm happily married to my husband and we have a very sweet Polydactyl Tuxedo Cat named Cindy Lou. She's just a kitten in her picture above. TY for this refresher course in dividing fractions, though. That is a mathematical operation which isn't used every day, so, it's quite a good idea to have a "refresher" in it, sometimes. Also, TYSM for your service to our country. GOD BLESS YOU AND YOURS !!! 🙏👍 BTW, I believe if I'd had you as a teacher in school or a professor in college, I would've been much better in the algebra/geometry/trigonometry classes I took. As it was, I just "eeked" by, then. LOL !!! Take care !
I graduated with my bachelors degree 20 years ago but I still love to do math kind of as a hobby. I had to start at pre-algebra and work my way up to college algebra for my art degree (go figure). I loved it even though I would never use it as an artist. Thanks for your videos.
Wanted to say thank you; first for your service, second for this site. (For what it's worth, my best math teachers were always marines...tough to say being retired Air Force ;) ). We currently have our grandchildren living with us and even though I have an advanced degree, it wasn't in math. Being able to bone up on concepts I haven't used in a while (consciously) is really helping with tutoring them. I want them to have the kind of help not available to me growing up...something that teaches them math is a field to be excited about, no matter the grade (or age). Of course I subscribed, for now the only other way I can say thank you. Semper Fi Marine!
The last math class I had was College Calculus in Spring 1970 (The May Days of Kent State). Since I got a "D" --it was the last math class and I switched majors that June!! This was a nice refresher of the basics!! Thanks.
Things are only easy if you are familiar with and understand them. The ideas behind fractions are actually quite abstract -- especially for kids. I've even seen videos, where math teachers admitted they didn't fully understand them until they were adults (and had been teaching for a while).
That's because, I think, arithmetic is taught rather than algebra, which explains how arithmetic actually works. "Invert and multiply" to divide by a fraction. That's a rule of arithmetic, but WHY? Algebra provides the clear explanation. Arithmetic is just a limited and rather crabbed corner of algebra, and mathematics.
Remember that division and multiplication are the inverse of each other. So it is not difficult at all to divide fractions. For example 3/4 : 5/7 = 3/4 x 7/5 = 21/20 or 1 1/20.
Taught math for 35 years…always required fractions to be reduced. Improper fraction. Divide bottom number into top number , remainder goes over bottom number to make new mixed number.
When dividing a fraction by another fraction, you multiply by the reciprocal, thus you end up with 2/5 * 4/1 = 8/5. Done! Maybe if you explained WHY multiplying by the reciprocal works, then we'd have something.
Why it works. 1/2 ÷ 1/4 = (1÷2) ÷ (1÷4) = (.5) ÷ (.25) = 50 ÷ 25 = 2 1/2 ÷ 1/4 = 1/2 * 4/1 = (1*4) / (2*1) = 4/2 = 2 So doing long division (the equation is 3 division problems) results in the same answer as the short cut of multiplying by the reciprocal.
The flipping works because a fraction is in itself a division problem. If you have 1/2 ÷ 1/4, it's the same as (1 divided by 2 ) ÷ (1 divided by 4) , which becomes .5 ÷ .25 or point five divided by point two five in long division. Then the answer is 2, because 25 goes into 50 twice. 1/2 ÷ 1/4 1/2 * 4/1 = 1*4 ÷ 2*1 = 4/2 = 2
When I was little my dad helped me learn fractions and when he told me to invert and multiply I said but why do you invert and he said I don’t know just do it. This reminds me of my dad who has passed away.
Hay dos maneras de hacerlo: Una) Multiplicando en cruz 2/5:1/4=8/5 Dos) Producto de extremos partido por producto de medios: 2/5/1/4= 2x4/5x1= 8/5 Más concuerdo con su explicación, amigo. Ya que es muy dinámica y operativa. Saludos.
Thanks. This was a great video and feel I have learnt a lot here. My old maths teacher tried to teach things simply, but this is much simpler for me to understand. Thanks again.😀
Yeah, I am 51 yrs old. I have gone back to school twice and both times and a third if I go back again. Basic math for me John. But then I have never been the sharpest knife in the drawer. 😁
I learned to make the dividend fraction a numerator and the divisor fraction a denominator of a larger fraction. Then multiply the very top numeral by the very bottom (outer numbers) to become the numerator of the answer. And multiply the two inner numbers to become the denominator of the answer.
Division of fractions. REVERSE THE SIGN( ÷) TO (× )AND INVERSE THE FRACTION. 70 years old and I still remember it. Thank you to my Math teacher.💞💛💞💚💞💙💞🤍
phew I guess I didn't forget my math from 50+ years ago Our teacher taught us to (dividing fractions-cross multiply) multiply the 1st numerator 2 by the 2nd denominator 4 = final numerator 8 then multiply 1st denominator 5 by 2nd numerator 1 gives final denominator 5 : so 2/5 / 1/4 2x4 and 5x1 resulting in 8/5 (easier when you're looking at it (LOL)) Was a bad day so you cheered me up! Thank you! :) Now if I can just use this sin square theta plus cos square theta = 1 to any real use.. hmmm,,,. (LOL) P.S. I liked Math, it just didn't seem to like me! (LOL) :)
Every teacher I had that taught operations with fractions want the final answer in mixed number. They don't want the final answer in improper fractions.
That makes things simple but I have a question about the last problem. If the answer is 35/4 which is 8 3/4 how can that be correct ? That would be much larger than the original number being divided.
I haven’t worked with fractions in more than 50 years. I thought when dividing fractions you take the second fraction and invert it so you make 1/4 into 4/1. Then you multiply. 2 x 4 = 8. 5 x 1 = 5. So the answer is 8/5.
Who thought all these rules out? This isn't a lesson in logic; it's a display of creative licence as in "flipping". Teachers should say, "nothing makes sense; just learn the rules that no-one knows how they came into existence. It's just a great big, fat game where someone made up the rules along the way to suit themselves."
Exactly !! What I don't understand is this. A fraction is a part of a whole number ( it has already been divided and is relative to the whole). So if you divide a fraction by another fraction how do you end up with a whole number or whole number + a fraction that is greater than the number being divided ? That is illogical. It makes sense to invert a fraction when dividing a whole number by a whole number, like 4 divided by 2 , you invert the 2/1 to 1/2 and arrive at the correct answer of 2. Any word problem would fit with that rule. So what started out as a truth became transformed into a deception. How ? By dividing fractions by fractions. They changed the rules to fit their abstract reality, and then end up with a greater amount after dividing, while at the same time equating division with multiplication, which, again, does not fit with reality. For example, if you have a pie and cut it in 1/2 and now want to divide that 1/2 of the pie in 1/2 again, common sense says you will have 1/4 of a piece of pie. You can arrive at that answer by multiplying 1/2x 1/2 =1/4. KISS ( Keep it simple stupid ). According to their rules you divide 1/2 by 1/2 you by inverting (reciprocal ) the 1/2 on the right to 2/1 , in which case 1/2 x2/1 = 1 whole pie. It does not fit reality. Math should not be able to bend the rules to suit some agenda, as you said. My guess is that their agenda more than likely came about with the advent of fractional reserve banking, using debt based fiat currency created out of thin air, not asset backed, and can never be repaid because it is debt based. It was during this time that the math rules changed where you get into the realm of fractions and negative numbers and abstract pseudo math problems which don't fit with reality. How I would take the equation on this post , is to multiply 2/5 x1/4 =2/20=1/10. Now the next step is to see if this would work in a word problem based on reality. Let 1 whole number (1), represent $100.00 (100%) . Now take 40% (2/5) of $100.00 which would be $40.00 and then take 1/4 or 25% of the $40.00 ( or 40. x.25=10.00 ) which would be 10.00 dollars . That works in reality.
So wish I would have had you rather than the drunk math teacher I had some 30+ years ago...Seriously, he was hungover every day. You actually make math not suck.
This is easy. That line between the 2 and the 5 and the line between the 1 and the 4 are division signs. So basically all you have to do is 2 ÷ 5 ÷ 1 ÷ 4 = 1/10 or .1 You can have an unlimited number of fractions lined up each divided by the next and just replace all those horizontal lines with division signs and work it out as long as there are no other signs involved.
Thanks, me too. I’m smart in physics & chemistry, it’s a shame that I always thought I couldn’t do math & grandma had always said I was stupid in math since kindy because I will bring home 70-80% on everything else 55% in math. I always did the calculations in physics & chemistry with excitement but math on its own I had developed idea that it was “dishonest, schemes & didn’t like it or understood it”. This is likely because I was afraid to ask the teacher how he numerated or generated certain numbers (the formulas & patterns how do you confirm it is true & that it is the only truth, these were questions I had as a kid) because I wanted to understand the meaning of formulas instead of just accepting & working with it. Many math teachers were not friendly or approachable at all. Whereby in chemistry I’m able to follow how numbers (chemical levels combine & generate the figures) which makes it exciting to solve or predict outcomes. This stupid thing stuck with me & I was afraid to pursue medicine. Because math was waiting for me, it didn’t have meaning & if it did, the teacher didn’t know it, or couldn’t explain it, he gives a pattern or formular accept it & work with it, there is no real meaning as there is in physics. Looking back I changed school too often because of broken home & mostly I had tried to adapt to the math on my own without any extra classes because of the sadness & fear it brought to me I hated it & never did homework or extra study on it. I realised if you missed the early years of math expecially kingdargateen up to year 4/5, you will probably never grasp the concepts but now I watched your videos & immediately I’m starting to love math. I’m 25years, & shame I didn’t pursue medicine I was very intelligent. I wish I knew that my destiny was tied to it, instead of running away from it, I wouldn’t have wasted time to study any of the other things I studied at university. Plus my uncle is an engineer, my cousin is a nurse, I’m the youngest and we grew up together, they were all dumber than me, better in mathematics ofcourse it saddens me how I did not choose medicine because of this stupid idea of “seeking meaning behind formulas”. At a point my uncle use to say if I were to register at his school, they would put me in class with the seniors & I would have still been a top student back in primary school but again, we separated due to broken home
I remember, back in my day, if we turned in an improper fraction, even if it was correct, it was wrong. We had to post all answers as mixed numbers, it was part of reduction. I also remember the day one of my co-workers and I did long-division on a white board and all of our younger peers looked at us like we were speaking in tongues. They had never seen long-division and couldn't do division as fast or accurately as we did. I miss maths class.
I have a 13 yr old grandson who is good in school. I just would like to know how to continue to stress the importance of math and keep his enthusiasm for math; as the math gets harder and harder.
What's the policy on when to convert an improper fraction (or mixed number) answer to a decimal answer? Or does that depend on the teacher and/or subject??? Back in the old days (my days actually) which was before calculators were invented it made sense to leave answers as fractions, but today with calculators and everything digital it doesn't take much time to convert to decimal. Example - You calculate the amperage to be 4/5 amps and the meter shows 0.79 amps.
There is a reason 8/5 is called an "IMPROPER FRACTION", but the form is optional in really life depending on how the solution will be used. Most kids today will be lucky if they can get the solution to read 1.6 on a calculator.
Does anyone know or remember the Keep, Switch, Flip rule when dividing fractions. I'm 62 and that was a standard for us to memorize when dividing fractions? Keep the first number the same, switch division to multiplication, and flip the last.
Students would benefit to realize that their deficiency is in arithmetic, not in mathematics. The glorification of a basic element of practical education into what is a scholarly pursuit is a disservice to the student. He or she ought to be confronted with the understanding that their lack of accomplishment - if that is the case - is in a very basic area, not in something elevated that one does not necessarily need to learn. Those who teach arithmetic should not be deluding themselves into thinking that they are "math" teachers.
Or just cheat with a Calculator... (2/5ths = .4) (1/4th =.25) (.4 ÷ .25 = 1.6) (1.6 decimal to fraction = 8/5ths) Saved me 16:00 minutes. Clicked you a like.
Thank you. You are the FIRST TEACHER that made ANY sense to me. In third grade I moved and my new school was very advanced in fractions. My old school had not started fractions. I got LOST in the dust and was “behind” for the rest of my education. I tried to get help. I maybe had a mind block because of the word stupid. Attended 9, yes NINE different schools. I now finally know fractions.
a good teacher makes everything easy and a bad teacher makes everything more mysterious
This happen to me.
I'm sorry you had to go through moving so much. 😔 everything like leaving friends behind each time. Then the math issue where no one checked in your knowledge. I'm glad you got it now. 👍
That was fun. I'm 70 yrs old. In college I had math though calculus. It's amazing how much one can "loose" over time. Lol
Me too.
It would be nice if you explained WHY these techniques work. Rather than just what to do and how to do it. It would be interesting, and possibly help some of us remember the technique better. My memory isn’t great, but when I understand why something works, it sticks in my mind more.
But thank you for the refresher. It is very helpful and easy to watch.
Your an excellent teacher. You even retrained me of some 60 years ago. Things had become a little cloudy, thank you young man, you rock.🤟
You’re
@@rontopp Wish I was a smart a.. like you. I think his statement was understoood.
@@robertlindh1439 If you’re teaching math, you might as well teach English as well….
a/b ÷ c/d = a/b × d/c = ad/bc
2/5 ÷ 1/4 = 2/ 5 × 4/1 = 8/5 = 1 3/5 ; 1.6.
Learned this in 4th grade, back in 1967. Some things just stay with you.
I really like how this guy explains how to solve step-by-step.
Keep, Change, Flip Keep the 1st fraction, Change divide to multiply, Flip the second fraction. 2/5 ÷ 1/4 = 2/5 x 4/1 = 8/5 = 1 3/5 I enjoy your videos
He said: "don't reduce 8/5 but to check if 1 3/5 is correct just multiply 1 3/5 = 8/5. LOL
Thank you for the refresher course in basic math. Just following, remembering and applying the different rules is exciting now that a graded paper is out of the way. How I wish all math teachers are as positive like you sir.
Growing up in the Philippines and learning all the rules was a real challenge. Then to be channeled into a degree (Geology) without mastering mathematical concepts was frustrating. I am so thankful I was lucky enough to enlist in the navy, and not to disappoint my hardworking parents for not earning a degree.
Again though, my lack of really understanding math concepts was a struggle in my Statistics, Finance and College Math classes when I decided to finally earn a degree after waiting until advancement to E-7. Earning an Associate in Science helped me earned my naval commission (CWO then LDO) and a Bachelor's in Business Administration, (after retirement with 30+ years) was to appreciate my parents' wish.
So, my bottom line in Math?, (Algebra, Geometry, etc..), fun and understandable given the right teacher. Thank you sir!
If you put this problem as a word problem and were cutting fabric which is measured by the yard, I would divide 36 by 5 which equals 7.2”. 7.2” time 2 is 14.4”, and 1/4 of that is 3.6”. This number is 10% of one yard as a yard is 36”. This is life in the real world. Translated into cutting fabric, you have instead of dividing a cut fabric which was only 14.4” long, you have now a piece of 57.6”. If you were selling leather by the roll and giving away product when the customer wanted you to cut a remnant of 14.4” long in quarters, you would not keep your job for very long.
Or if you had cut a pumpkin pie into 5 slices and 2 slices remained, you’d cut each slice in two to make four pieces. Each slice would then be 1/10th of the pie. Anything you want 1/4 of, you cannot get a bigger portion than you started with. Your answer is bigger than what you began with.
Math is practical unless it isn’t. If you had turned this problem into geometric shapes, you’d see my point.
I'm 80 years of age and enjoying re-learning the skills you are teaching so well. I have a question, I'm really interested in getting a board like yours that I can do problems on. What software/pen/stylus do you use. It appears simple and very functional. I've researched this but all appear a bit more complex than yours and at my age I prefer simplicity. Thanks for your help.
I love the review of these basic math skills. So important. I wish I had the interest in math I have at 69 when I was 10. I am always playing with numbers in my mind.
Thanks, 76 years old and I forgot most of this. It came back quickly.
Me too! 76 also. Good refresher! Thanks!
77yrs old.
Thank you for all of your amazing content! This is what the Internet should be about! All the best to you!
I’m 70 and I love this. I could get the answer, but I couldn’t tell you the steps. 👍👍. (I knew that!).
If students always get tripped up turning their improper fraction into a mixed number, that's just proof of how much they really need to be made to do it. Are they just going to go through life never having the skill of turning an improper fraction into a mixed number because the math teacher doesn't want to insist they learn it, so they can get higher test scores and the math teacher looks like a better teacher than he/she really is?
It does seem incomplete (leaving the answer as an improper, top-heavy, fraction). Saving time, and avoiding error, seem weak reasons; if those are the only reasons.
Thanks for the review of fractions. :) And thanks for reminding me about my university calculus teacher that would explain the process and then go over all the ways that students make mistakes. The other thing that he would stress is look at the numbers before and estimate what the answer should be. In your second example 2/5 / 1/4 -- the answer should be how many times does 1/4 go into just under a 1/2, well a little less than twice - so 8/5 is in the range that you should expect.
Thanks again.
Before you mentioned that you were in the Marine Corps, I sort of figured you were well - educated (beyond college.) Don't get me wrong, please. A college degree is wonderful, but, the discipline of a Military Career puts one "over - the - top" to me. I, myself, was in the Army, but, I was unable to complete BCT because of a knee injury. My MOS was to be (as it was known to be back in the early 2000's) a Patriot Missile Systems Operator/Maintainer because of my electronics knowledge. But, now, I'm happily married to my husband and we have a very sweet Polydactyl Tuxedo Cat named Cindy Lou. She's just a kitten in her picture above. TY for this refresher course in dividing fractions, though. That is a mathematical operation which isn't used every day, so, it's quite a good idea to have a "refresher" in it, sometimes. Also, TYSM for your service to our country. GOD BLESS YOU AND YOURS !!! 🙏👍 BTW, I believe if I'd had you as a teacher in school or a professor in college, I would've been much better in the algebra/geometry/trigonometry classes I took. As it was, I just "eeked" by, then. LOL !!! Take care !
I made 2/5 into 8/20 & 1/4 into 5/20, then 5 goes into 8, 1 3/5 and 20 goes into 20, 1, so 1 3/5 over 1 = 1 3/5. Did anyone else solve it this way?
Yep answer is 1 3/5
I did.
Just flip and multiply 2/5 by 4/1
8/5 or 1.6 or 1⅗. The same number in 3 different forms.
I didn’t watch his video, but I just multiplied by 4, so just one step needed.
I graduated with my bachelors degree 20 years ago but I still love to do math kind of as a hobby. I had to start at pre-algebra and work my way up to college algebra for my art degree (go figure). I loved it even though I would never use it as an artist. Thanks for your videos.
I get homeschool books on clearance at the Christian bookstore for fun🙂
For a humanities student you must have pretty good math skills. They're better than mine for sure. :D
This makes my brain feel so good! I've always been 'afraid' of math!
65 years old and I learned something today! Math and algebra were never my strong points.
🤣🤣🤣
Well done for learning at 65 years old! You're amazing! I hope I'll have the same curiosity about the world at that age as you do.
Wanted to say thank you; first for your service, second for this site. (For what it's worth, my best math teachers were always marines...tough to say being retired Air Force ;) ). We currently have our grandchildren living with us and even though I have an advanced degree, it wasn't in math. Being able to bone up on concepts I haven't used in a while (consciously) is really helping with tutoring them. I want them to have the kind of help not available to me growing up...something that teaches them math is a field to be excited about, no matter the grade (or age). Of course I subscribed, for now the only other way I can say thank you. Semper Fi Marine!
The last math class I had was College Calculus in Spring 1970 (The May Days of Kent State). Since I got a "D" --it was the last math class and I switched majors that June!! This was a nice refresher of the basics!! Thanks.
Things are only easy if you are familiar with and understand them. The ideas behind fractions are actually quite abstract -- especially for kids. I've even seen videos, where math teachers admitted they didn't fully understand them until they were adults (and had been teaching for a while).
That's because, I think, arithmetic is taught rather than algebra, which explains how arithmetic actually works.
"Invert and multiply" to divide by a fraction. That's a rule of arithmetic, but WHY?
Algebra provides the clear explanation.
Arithmetic is just a limited and rather crabbed corner of algebra, and mathematics.
Remember that division and multiplication are the inverse of each other. So it is not difficult at all to divide fractions. For example 3/4 : 5/7 = 3/4 x 7/5 = 21/20 or 1 1/20.
Yes I'm in the right tablet class in 20222 and I feel good to know I can get the help I need to get my ged.💪🏾💪🏾💪🏾💯💯🥳🥳🥳🥳
Taught math for 35 years…always required fractions to be reduced. Improper fraction. Divide bottom number into top number , remainder goes over bottom number to make new mixed number.
Enjoying this once again had it done in my head and converted to a decimal in about 20 seconds.
I learned "Stay, Change, Flip" in school about 100 years ago.
I’m getting rusty at 65 years of age. Thanks for the refresher!!
It's a smart move to learn math in order to sharpen your mind!
Very good problem, combining absolute values and quadratic equations, and having extraneous solutions that have to be discarded.
Math teacher can’t pronounce reciprocal. The simple answer we were taught is invert and multiply. I have remembered this for 60 years!
When dividing a fraction by another fraction, you multiply by the reciprocal, thus you end up with 2/5 * 4/1 = 8/5. Done! Maybe if you explained WHY multiplying by the reciprocal works, then we'd have something.
Why it works.
1/2 ÷ 1/4 =
(1÷2) ÷ (1÷4) =
(.5) ÷ (.25) =
50 ÷ 25 =
2
1/2 ÷ 1/4 =
1/2 * 4/1 =
(1*4) / (2*1) =
4/2 =
2
So doing long division (the equation is 3 division problems) results in the same answer as the short cut of multiplying by the reciprocal.
The flipping works because a fraction is in itself a division problem. If you have 1/2 ÷ 1/4, it's the same as (1 divided by 2 ) ÷ (1 divided by 4) , which becomes
.5 ÷ .25 or point five divided by point two five in long division. Then the answer is 2, because 25 goes into 50 twice.
1/2 ÷ 1/4
1/2 * 4/1 = 1*4 ÷ 2*1 = 4/2 = 2
Would be nice to see the proof of why taking the reciprocal of the divisor and multiplying works.
See my comment.
When I was little my dad helped me learn fractions and when he told me to invert and multiply I said but why do you invert and he said I don’t know just do it. This reminds me of my dad who has passed away.
Hay dos maneras de hacerlo:
Una) Multiplicando en cruz 2/5:1/4=8/5
Dos) Producto de extremos partido por producto de medios: 2/5/1/4= 2x4/5x1= 8/5
Más concuerdo con su explicación, amigo. Ya que es muy dinámica y operativa. Saludos.
Thanks. This was a great video and feel I have learnt a lot here. My old maths teacher tried to teach things simply, but this is much simpler for me to understand. Thanks again.😀
Yeah, I am 51 yrs old. I have gone back to school twice and both times and a third if I go back again. Basic math for me John. But then I have never been the sharpest knife in the drawer. 😁
I learned to make the dividend fraction a numerator and the divisor fraction a denominator of a larger fraction. Then multiply the very top numeral by the very bottom (outer numbers) to become the numerator of the answer. And multiply the two inner numbers to become the denominator of the answer.
Too many damn rules for me. Best video I have watched instead of listening to gossip. Thanks
Thank you!
I have aphasia and Comprehension reading and math, now understand it. Thank you again.
Division of fractions.
REVERSE THE SIGN( ÷) TO (× )AND INVERSE THE FRACTION. 70 years old and I still remember it. Thank you to my Math teacher.💞💛💞💚💞💙💞🤍
We used to call it 'cross-multiply' here in New Zealand :D Thanks for the refresher course :D
Thank you Professor, I was able to understand this crisp clear. Thanks for educating us.
phew I guess I didn't forget my math from 50+ years ago Our teacher taught us to (dividing fractions-cross multiply) multiply the 1st numerator 2 by the 2nd denominator 4 = final numerator 8 then multiply 1st denominator 5 by 2nd numerator 1 gives final denominator 5 : so 2/5 / 1/4 2x4 and 5x1 resulting in 8/5 (easier when you're looking at it (LOL)) Was a bad day so you cheered me up! Thank you! :) Now if I can just use this sin square theta plus cos square theta = 1 to any real use.. hmmm,,,. (LOL) P.S. I liked Math, it just didn't seem to like me! (LOL) :)
To divide by a fraction .. turn the fraction upsidedown and multiply
So divide by 1/4 becomes multiply by 4
2/5 becomes 4 x 2/5 = 8/5 = 1 3/5
Great Teacher ,so grateful for for this. I’m learning so much.
Every teacher I had that taught operations with fractions want the final answer in mixed number. They don't want the final answer in improper fractions.
I started grade school in 1959 and that is what we were taught.
Thank You for your service !!
Excellent presentation.. 🙏
first marine i ever knew of who could divide fractions!
We had the students do KCF (Keep - Change - Flip).
Works every time and only takes about 30 seconds to master.
I remember from school years that to divide fractions you cross multiply. Same as what you’re doing but different method, correct?
I’d convert them to decimals.
Invert and multiply 8/5
Correct Kenneth, less talk too!
In 4th or 5th grade we learned to invert and multiply so it’s 8 5ths
Lovely technique, this. Got 8/5 in about three seconds, but the video was pleasant.
Thank you sir, it was a very clear explanation. You are a great teacher! 👍
That makes things simple but I have a question about the last problem. If the answer is 35/4 which is 8 3/4 how can that be correct ? That would be much larger than the original number being divided.
He doesn't want you to be a "Hero" by simplifying cuz you could get the wrong answer ,instead of 8 3/4 you could get 8 1/4. LOL
Thank you so much . I would like to continue learning these basic skills but I knew some of them
17 minutes to say invert one fraction and multiply across. Answer is 8/5 or 1.6
Help please, I have forgotten the simplest fractions. I get how 2x5=10, and 3x4 =12. In simple instructions, how do we get 5/6?
10/12 10 ÷ 2/12 ÷ 2 = 5/6 ,hope you understand what I did.
(2/5)÷(2/4) = (2/5)×(4/1) = (2×4)/(5×1) =8/5
How about old school “invert and multiply”😂👍
Took 17 plus minutes to answer a very simple equation. I know you're trying to show all forms to solve and give an explanation but 17 minutes. Man!!!
I haven’t worked with fractions in more than 50 years. I thought when dividing fractions you take the second fraction and invert it so you make 1/4 into 4/1. Then you multiply.
2 x 4 = 8. 5 x 1 = 5.
So the answer is 8/5.
Thank you!!! GREAT REFRESHER
Who thought all these rules out? This isn't a lesson in logic; it's a display of creative licence as in "flipping". Teachers should say, "nothing makes sense; just learn the rules that no-one knows how they came into existence. It's just a great big, fat game where someone made up the rules along the way to suit themselves."
Exactly !! What I don't understand is this. A fraction is a part of a whole number ( it has already been divided and is relative to the whole). So if you divide a fraction by another fraction how do you end up with a whole number or whole number + a fraction that is greater than the number being divided ? That is illogical. It makes sense to invert a fraction when dividing a whole number by a whole number, like 4 divided by 2 , you invert the 2/1 to 1/2 and arrive at the correct answer of 2. Any word problem would fit with that rule. So what started out as a truth became transformed into a deception. How ? By dividing fractions by fractions. They changed the rules to fit their abstract reality, and then end up with a greater amount after dividing, while at the same time equating division with multiplication, which, again, does not fit with reality. For example, if you have a pie and cut it in 1/2 and now want to divide that 1/2 of the pie in 1/2 again, common sense says you will have 1/4 of a piece of pie. You can arrive at that answer by multiplying 1/2x 1/2 =1/4. KISS ( Keep it simple stupid ). According to their rules you divide 1/2 by 1/2 you by inverting (reciprocal ) the 1/2 on the right to 2/1 , in which case 1/2 x2/1 = 1 whole pie. It does not fit reality. Math should not be able to bend the rules to suit some agenda, as you said. My guess is that their agenda more than likely came about with the advent of fractional reserve banking, using debt based fiat currency created out of thin air, not asset backed, and can never be repaid because it is debt based. It was during this time that the math rules changed where you get into the realm of fractions and negative numbers and abstract pseudo math problems which don't fit with reality.
How I would take the equation on this post , is to multiply 2/5 x1/4 =2/20=1/10. Now the next step is to see if this would work in a word problem based on reality. Let 1 whole number (1), represent $100.00 (100%) . Now take 40% (2/5) of $100.00 which would be $40.00 and then take 1/4 or 25% of the $40.00 ( or 40. x.25=10.00 ) which would be 10.00 dollars . That works in reality.
You called it Math - that was enough for me!!
It took me 5 seconds to come up with 1.6. 😎👍
you are correct but to make it to fraction 0.6 = 6/10 ÷ 2 = 3/5 answer 1 3/5
I am enjoying the lessons thank you
For fun you can convert 2/5 to 8/20. So 8/20 divided by 1/4. Then divide numerators and denominators straight across. No need to invert and multiply.
So wish I would have had you rather than the drunk math teacher I had some 30+ years ago...Seriously, he was hungover every day. You actually make math not suck.
This is easy. That line between the 2 and the 5 and the line between the 1 and the 4 are division signs. So basically all you have to do is 2 ÷ 5 ÷ 1 ÷ 4 = 1/10 or .1 You can have an unlimited number of fractions lined up each divided by the next and just replace all those horizontal lines with division signs and work it out as long as there are no other signs involved.
Thanks, me too. I’m smart in physics & chemistry, it’s a shame that I always thought I couldn’t do math & grandma had always said I was stupid in math since kindy because I will bring home 70-80% on everything else 55% in math. I always did the calculations in physics & chemistry with excitement but math on its own I had developed idea that it was “dishonest, schemes & didn’t like it or understood it”. This is likely because I was afraid to ask the teacher how he numerated or generated certain numbers (the formulas & patterns how do you confirm it is true & that it is the only truth, these were questions I had as a kid) because I wanted to understand the meaning of formulas instead of just accepting & working with it. Many math teachers were not friendly or approachable at all. Whereby in chemistry I’m able to follow how numbers (chemical levels combine & generate the figures) which makes it exciting to solve or predict outcomes.
This stupid thing stuck with me & I was afraid to pursue medicine. Because math was waiting for me, it didn’t have meaning & if it did, the teacher didn’t know it, or couldn’t explain it, he gives a pattern or formular accept it & work with it, there is no real meaning as there is in physics. Looking back I changed school too often because of broken home & mostly I had tried to adapt to the math on my own without any extra classes because of the sadness & fear it brought to me I hated it & never did homework or extra study on it. I realised if you missed the early years of math expecially kingdargateen up to year 4/5, you will probably never grasp the concepts but now I watched your videos & immediately I’m starting to love math. I’m 25years, & shame I didn’t pursue medicine I was very intelligent. I wish I knew that my destiny was tied to it, instead of running away from it, I wouldn’t have wasted time to study any of the other things I studied at university. Plus my uncle is an engineer, my cousin is a nurse, I’m the youngest and we grew up together, they were all dumber than me, better in mathematics ofcourse it saddens me how I did not choose medicine because of this stupid idea of “seeking meaning behind formulas”. At a point my uncle use to say if I were to register at his school, they would put me in class with the seniors & I would have still been a top student back in primary school but again, we separated due to broken home
I remember, back in my day, if we turned in an improper fraction, even if it was correct, it was wrong. We had to post all answers as mixed numbers, it was part of reduction.
I also remember the day one of my co-workers and I did long-division on a white board and all of our younger peers looked at us like we were speaking in tongues. They had never seen long-division and couldn't do division as fast or accurately as we did.
I miss maths class.
Am a math teacher here in Philippines..
This makes complete sense
I have a 13 yr old grandson who is good in school. I just would like to know how to continue to stress the importance of math and keep his enthusiasm for math; as the math gets harder and harder.
I am finally noticing where I am going wrong. I am studying for my GED. It says in the GED book to put into mixed numbers at the end of the equation.
What's the policy on when to convert an improper fraction (or mixed number) answer to a decimal answer? Or does that depend on the teacher and/or subject???
Back in the old days (my days actually) which was before calculators were invented it made sense to leave answers as fractions, but today with calculators and everything digital it doesn't take much time to convert to decimal.
Example - You calculate the amperage to be 4/5 amps and the meter shows 0.79 amps.
I wish I had you as an instructor in the 80s.
There is a reason 8/5 is called an "IMPROPER FRACTION", but the form is optional in really life depending on how the solution will be used. Most kids today will be lucky if they can get the solution to read 1.6 on a calculator.
Does anyone know or remember the Keep, Switch, Flip rule when dividing fractions. I'm 62 and that was a standard for us to memorize when dividing fractions? Keep the first number the same, switch division to multiplication, and flip the last.
He helpED me with integers now integer with fractions SMART MAN 🤓
I need help with fractions with integers but this is not it but simyle it still helped the same
"V" for up and "V" for down:
2/5:1/4= 2 x 4/5 x 1= 8/5✓
Great teacher, thanks! I remember that! Wow!
Saw this and immediately thought HOW SWAY!? But in all seriousness, thanks!
Change the division to multiplication and invert the number..
Thanks a whole bunch really appreciate it
)76 years old remembering 8th grade. USMC 1964 -1968
Students would benefit to realize that their deficiency is in arithmetic, not in mathematics. The glorification of a basic element of practical education into what is a scholarly pursuit is a disservice to the student. He or she ought to be confronted with the understanding that their lack of accomplishment - if that is the case - is in a very basic area, not in something elevated that one does not necessarily need to learn. Those who teach arithmetic should not be deluding themselves into thinking that they are "math" teachers.
Thank you . Very informative.
1 3/5, because ÷1/4 is the same as ×4,
.•.2/5÷1/4=2/5×4=8/5=1 3/5 or 0.4÷0.25=0.4×4=1.6
A student from my church in Tahlequah, developed a RUclips video title "I will derive" you should take a look at that.
2/5 * 4/1 = 8/5 = 1 3/5
Thank you for sharing, humbly appreciate👍
In precalculus, my professor called division the act of "multiplying the reciporocal"
I would like to know more about compounded interest
Should the 35/4 be negative? The mixed number was negative right?
Re-CIP-ro-cal. Re-ci-pro-cal. You're saying it as "Re-CIP-o-cal" without the "PRO" in the middle.
Or just cheat with a Calculator... (2/5ths = .4) (1/4th =.25) (.4 ÷ .25 = 1.6) (1.6 decimal to fraction = 8/5ths) Saved me 16:00 minutes. Clicked you a like.