9/16 - 3/20 = ? Subtract the Fractions, FULL Step-by-Step solution so anyone can understand!
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- Опубликовано: 5 сен 2024
- How to subtract fractions by finding the LCD (Lowest Common Denominator).
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I like the fact that you explain everything step-by-step, anyone that says oh it's easy do it in your head.. to long to explain, learned this in 4th grade, etc.. well, then this probably isn't the video for you. So, for those of us who enjoy the step by step instructions , stop making those who don't get it feel dumb. They are here to learn, this isn't trivia night at the bar. Math doesn't come easy for everyone.
Thank you!!!!!!!
i always feel like they’re preaching to the choir. also there’s too much written together - it needs to be separated. i like math, algebra and geometry, but i don’t remember everything (i’m 78 :). some things i have to think through and others i need to relearn.
thanks for the effort, people, but like more in between steps are needed :) 🌷🌱
I like this pace.
33/80
Even if you do know, some times, it's good to get a refresher.
I love this channel. Keeps the brain energized. My wife didn't even know channels like this exsist. Glad this one does.
WHERE WERE YOU 60 YEARS AGO!
I'm 69 and was always horrible at not only math but school in general!
Thanks for the incredible video!
Lol! Me too! I'm 72. In those days I would have rather been outside chopping down trees, or driving a frontend Loader or a bulldozer! School was not for me at all! I actually hated going there!
16=4x4, 20=4x5; 4 being the common factor in both. Multiple the top and bottom term of the 1st first fraction by the uncommon factor of the second (9x5; 16x5 -> 45/80) and the top and bottom terms of the 2nd fraction by the uncommon factor of the first (3x4; 20x4 -> 12/80). LCD is 80. Answer is 33/80
Wrong! The correct answer is 0.4125. 33/80 is an incomplete mathematical statement because the answer you state is an operation that hasn't yet been worked out. I did this quickly by reducing the fractions and subtracting one from the other, et voila! Simple.
@@rustyknott-W.D Fractions are not "incomplete mathematical statements" but rather the most complete statement of any number that is transcendental, which is the overwhelmingly vast majority of all numbers. 33/80 just happens to be one of the very few numbers that is algebraic and thus has a finite decimal equivalent.
Further, since the question was concerned with operations between fractions the expected solution would necessarily be fractional within the context of the problem; and, since 33/80 = 0.4125 saying one is incorrect and the other correct is nonsensical.
Pi is the expression of a fraction. Pi is infinitesimal, for sure but at some point you have to clip it because the extension of the decimal becomes so small as to be superfluous. I'm talking about making numbers work for you, not the esoterics of math. It's like talking about how many angels can dance on the head of a pin: useless. I worked in mathematics for 30 years solving real world problems and we NEVER did operations like this because you can't use something like 33/80 without reducing it.@@khy6330
You are right that the correct form of answer when calculating a fractional problem is a fraction, but a fraction is a rational number.
The term "rational" comes from the word "ratio" which is what a fraction is, a ratio between two numbers.
This what I thought, bujt dude got into the breakdown of prime factors for LCD & I got lost ASAP! LOL Glad u saw what I saw to solve it.
There are people here that don’t understand the concept of LCD and how to find it They are here to Learn Don’t disrespect them I find these problems easy I know this I am here to support those who don’t People are at different levels of math Some are at the basic level some are pretty darn advanced …Like advance
Algebra ,Geometry, Trigonometry, and Calculus I use to be decent in Calculus not any more far from it My knowledge is at Algebra. 2 or a little higher This is good enough for myself to tutor kids in math Basic math Pre-Algebra Algebra 2 I can tutor Geometry but I need to know where the student is I have to know what proofs and Theorems they have have learned I can’t give them a proof they haven’t already proven or a Theorem they have not gotten I need their book.
I graduated from high school in 1959, but I have forgotten much of this stuff, which I was good at then. Your videos have been very helpful. I remember order of operations now, but I don't think they taught us PEMDAS back then.
I was born in 1959, and I don't recall being taught PEMDAS. That said I slept through or skipped most math classes, so maybe I just missed it.
I usually slept through English and Civics (Today called social studies) Math I have always loved.@@panpiper
Me too. Jr hi in '50s
Slightly later born in 1955 and a different country for us it was BODMAS Brackets rather than parenthesis
@@grahamheath3799 For me, that was PEDMAS.
Love your videos. When I know the subject, I think, "That's so easy!" When I don't, I'm glad to see each step to find what I need to know. Thanks a lot!
I like that you explain everything step by step. If someone says get to the point, they already know how to the problem. For those people that don't understand how to do the problem, they need a complete description. Thanks for all you do!
Quite simple if you understand our base ten system and "even" numbers being multiples of 2.
1. The lowest common denominator must end in a 0.
2. Factor both denominators into 2 factors: 16 = 4 x 4, and 25 = 4 x 5.
3. Notice 5 is the only odd number and anything evenly divisible by 16 is divisible by 4.
4. Multiply 5 x 16 = 80. This is the lowest common denominator.
By inspection, remembering the lcd must end in 0, you can see that 70, 60 50 40, 0r 30 are not divisible by both 16 and 20.
Another shortcut is to notice that 5 is the smallest number that will result in a number ending in 0, i.e. 80. Then it is easy to see that 20 is divisible by 20. Ergo, 80 is the lcd.
I've been wanting to learn this for a long time
Great video 👍❤
I'm so grateful that you take the time to break it down like you do.
You're a great teacher. When people ask "why do you take so long?" You can tell em its for people like me that don't know how to do it and want to learn .
I wish I could reply that to every negative comment but we both know that would be impossible .😂
Thanks again
Appreciate your detailed explanation. Thank you.
I kinda got it now. A little. Finding the LCD...and times the top fraction equal to it's own. 9×5=45 & 3×4=12 over 80. 45-12=33/80. Thank you. I'm trying to learn it. Like you said small steps.
I wish my math teachers were this thorough, They tended to skip over minor details and I didnt make the connections.
I'm glad my teachers weren't
Finally gave into my hatred of fractions and worked it out! The LCD is 680. The answer to 3 over 40 plus 5 over 85 is 91 over 680!
Love this channel. I have always forget the basics. This is great. Thanks a million.
This is a simple one to do in your head.
1) Multiply 16 x 20 = 320
2) Half of 320 is 160 - which is a common denominator, but not the lowest.
3) Half of 160 is 80. Both numbers are divisible by 80 and nothing < 80 works.
4) Answer - 80.
That's the way I instantly saw it too due to rote learning. But my brain also attempts to factorize everything to discover primes whether I like it or not. It's just what 5 and 2 are 🙂
I’m obsessed with this channel. It’s not enough that I work as an accountant doing analysis in Excel for 8-10 hours a day and teach music. Music is mathematical and financial analysis and modeling involves a lot of math too.
Chess is math also, like the x and y axis. The knight moves like a slope, rise over the run. 🤔
Oh my...and you still find time to cook and clean?
Finally a video that does not start with. “many will get this wrong”
The LCD (lowest common denominator) is 80. To find the LCD, write the prime factors of 16 which are, 2×2×2×2. Then, write the prime factors of 20 which are, 2×2×5. Take the larger group of prime factors of 2, then multiply them by one of the prime factors of 20, which is 5. Then multiply 2×2×2×2×5 which is 16×5 = 80. 80 is the LCD. Divide the denominator 16 into the 80. Multiply the answer which is 5, times the numerator 9. The new fraction is 45/80. Use the same procedure for the other fraction, which is now, 12/80. The new subtraction problem is 45/80 - 12/80. The answer to this problem is, 33/80.
Or just multiply the denominators and then simplify
@@wlonsdale1
Hi Walt,
Thank you for replying to my comment. I really appreciate it. As a math tutor, I wrote my comment as if I was tutoring a student in basic math. However, you are 100% correct with your comment. Have a great 2023!
Wouldn't it have been far simpler to divide 9 by 15, then divide 3 by 20 and subtract the latter from the former? You come up with the same answer, which is 0.4125. 33/80= 0.4125, by the way.
@@wlonsdale1This. It is the easiest and simplest solution and works every. single. time. It is also the easiest to teach and learn.
@@rustyknott-W.Dlol. Not without a calculator.
You don't need the LCD. A CD works just fine...320 or 160 for example.
I haven't listened to your explanation yet but I used what I remembered of something you taught a few days ago about factoring. That gave the LCD. So one building block almost consolidated into the building. If I listen to the rest of what you say, it might stick. [edit] I just listened to the rest. As per previous comments, these are building blocks. One piece of awareness adds to the greater whole. This was arithmetic. Arithmetic leads to mathematics and I appreciate being led down (or up) that path once again. Cheers.
Your explanation is longer than his video 😅😅😅😅😅
Your channel is a GREAT refresher for my math.
I remember those times when my teachers had us find the LCD of some large numbers, like one including 83 and the other 97 as prime factors, or something similar... And, peoples wonder why I know all of the primes up to 109.
We also had to find the Largest Common Divider of a bunch of numbers. Useful when simplifying fractions made of large numbers.
Direct approach : (9/16)x20 + (3/20)*16 > 180/320 + 48/320 > (18+48)/320 (320 is the common denominator at this point).
Only then we divide the expression (each of the three terms) as many times as possible, we soon reach after dividing by 4 (or twice, by 2), yielding (45+12)/80
You started with the division so you had more steps, my method stops when it can't divided any one value in the expression without yielding a decimal.
I reckon that your demonstration is pedagogic and for doing by hand. I relearned something myself, I had forgotten about the factors, Thanks for that.
My version seems more efficient algorithmically, and the machine won't mind the big numbers on the denominator. But soon AI will probably do it differently !
Save the factoring, the lcd has to have a zero in the 1s place and there is only 1 number that when multiply by 6 will result in a zero in the one's place and that number is 5 as in 6x5=30. Knowing your multiplication tables makes problems like this easy.
Yes an even number was my first thought, too. No need for factor trees!!!
I was part of a terrible experiment in the early 60s when they decided to introduce the concepts of teaching math title 'New Math' this was around my multiplication/division/fractions world... I was struggling already... memorizing multiplication tables was easy. However, fractions weren't at 1st. I'm just getting it the BOOM next semester, all different. The worst part was we had a strange system then, and we were kinda half 4th graders at the start of the 5th when summer rolled in. Large school districts, so they split curriculum. So your helping me rediscover my lost Math brilliance 😅. Actually I'm enjoying learning instead of dreading. PEDMAS/BODMAS have settled in and I'm able to do some in the head! For myself that's quite a jump for a old kid!😊
That was fun! I did this one in my head; it took me about 80 seconds.
When reducing a number to it's prime factors, it is a very useful practice TO CIRCLE THE PRIME FACTORS because it reduces any confusion one might have when regarding the many numbers involved. Thank you for showing us this technique. 👍
keep in mind ANY common denominator will yield the correct expression for any operation ...the idea of having to use the least is only to save you time and effort ..So when you multiply 16 x 20 the product is 320 ..this is not a LCD however it is a workable CD to get the right answer...If i divide 320 by 2 = 160 also a workable CD ..not the least but will also work to get the right answer...now divide 160 by 2 =80 and 80 is a CD and is also is the LCD
Maybe it's a fluke but i did the cross multiplication you showed in other videos: (20 x 9) - (16 x 3) divided by (16 x 20) = 180 - 48 divided by 320 = 132/320. I divided both numbers by 2 until i couldn't anymore and got the same result.
I annoyed my teacher by doing that. If the LCD wasn't immediately obvious, I'd multiply each fraction by the other denominator(s) without caring whether it is the lowest, just common. Then factored the result. I find it is often easier to compute with the larger number than bothering to reduce it before the end.
An example where this works well is 1/3 + 1/4 + 1/5 The LCD isn't immediately obvious so I convert it to
(1x4x5)/(3x4x5) + (1x3x5)/(3x4x5) + (1x3x4)/(3x4x5) or
20/(3x4x5) + 15/(3x4x5) + 12/(3x4x5) equals
(20+15+12)/(3x4x5)
or
47/60
I then try to factor the result. What number will both the numerator and denominator divide by? In this case, only 1, so 47/60 is the proper answer. if both were even, I'd repeatedly halve the numerator and denominator. I'd then check 3,5,7,11.
I needed to refresh myself on fractions and your videos are fantastic 👌
I wish resources like this had existed when I was in HS.
High teach students who are unable to go to school in multiple subjects at multiple grade levels. I'm not a stem Person, But these videos really help me know how to explain different concepts. Thank you
Only one thing I wasn't clear on and I don't know if any other commenters mentioned this, but why do you pick the prime number with the highest exponent to find the LCD?
In creating this text I think I figured it out. Two squared here is the divisor for the 16* 20 number. That's why the two squared drops out. That is?
😅
with the highest exponent to calculate the LCD?
glad to have watched this. Yeah, it seemed convoluted to my feeble brain, but my original method with a much huger denominator was overwhelming, so I hope I can remember how this goes! Please do more of these! Thank you.
In my head, before watching the video:
9/16-3/20=(180-48)/(16*20)=132/320
Even numbers, so successive cancelling by 2 givess: 132/320=66/160=33/80
Remaining prime factors: numerator 3*11, denominator 2*2*2*2*5
There are no remaining prime factors in common between numerator and denominator, so this is the simplest form of this fraction.
The LCD must be 80.
I haven't watched the video yet. I was a good but unspectacular mathematician at school 45 years ago, and got a B in O-level maths, and I think that the answer is 33/80.
I got there by figuring out that 80 is the lowest number divisible by both 16 and 20, which I guess is what is meant by "lowest common denominator."
Then my workings go as follows:
(i)16x5 = 80 and 9x5=45;
(ii)20x4=80 and 3x4=12;
(iii) lastly, 45-12=33. QED.
This took about me about a minute.
I’m a parking line painter - I layout and paint the lines in parking lots. I’m given a blueprint that is drawn to a scale -say, 1” = 10’.
Sometimes I get a drawing that has been reprinted on a smaller paper in which case the legend is not true. (Ex: 1” does NOT equal 10”), so I break out my ruler to find say, the width of a parking space. So the space may measure 3/4” so I need to convert it to feet to mark my painted line placement. This is an algebra problem. What’s the formula?
I think this video touches on the sort of problems I face in the field with drawing that are not to scale.
Great teacher!
Factor 16 and 20. Use 2 to the fourth power times five
Your LCD is 80. Answer is 33 over 80.
80
5 x 16 = 80
4 x 20 = 80
I find it hard to follow him too, but his writing and procedure is very orderly for the most part. So if you think he's too chatty, try to focus more on his notes.
I have absolute no problem finding the solution for this, but I don't always calculate with the LCD. But the most important thing is you are able to find the solution
IF you have found the solution you have found the LCD. So what do you mean?
@@uni-byte If I understand well, you have to find the lowest deminominator first, and then you solve the problem
You can always multiply the denominators to find the solution
9/16 - 3/20 = 180/320 - 48/320 = 132/320 = 33/80.
But here it's easy to find the LCD = 80.
45/80 - 12/80 = 33/80
@@batavuskoga To express the result correctly, n the end you will find the LCD. That's what I'm trying to say.
Actually did it in my head in about 40 secs!
Me too. I thought it was easy. Everybody else seems to have complicated processes to get the answer.
I went to grade and middle school in the 60's. I suspect you too?
Am in UK so not sure what age you would go to grade school but I am 65 now if that helps!@@franks2910
No the factor trees were just complete waste of time! You either multiply by 2 or 3 to get the common denominator! I did use a paper and pencil but got it in less than a minute!
I learned a lot! Thank you!
It might be a good idea to show that we're multiplying each fraction by 1 as 5/5 or as 4/4. This is why we have to multiply the numerator by the 5 or the 4.
I didn't wait for his method and just tried something: Multiply the numerator and denominator of each fraction by the other fraction's denominator (same as multiplying each fraction by 1), which gives (180/320) - (48/320) = 132/320. Then divide the numerator and denominator respectively by 2 until you get an odd number in either the numerator or denominator: (132/2) / (320/2) = 66/160. (66/2) / (160/2) = 33/80. But this method working in this case doesn't mean it would work in all cases, so I'm going to try it on some examples with odd numbers in the numerator or denominator.
Without watching the video or reading other comments:
⁹/₁₆ - ³/₂₀ =
⁴⁵/₈₀ - ¹²/₈₀ =
³³/₈₀
This result cannot reduced because:
33 = 3 ⸳ 11
80 = 2 ⸳ 2 ⸳ 2 ⸳ 2 ⸳ 5
Best regards
Marcus 😎
This really is very simple. The LCD has to end in zero since one denominator is 20. With the other denominator being 16, the only number that can make a 6 become a zero is 5. So 5 x 16= 80 and 4 x 20 = 80.
How do I turn a 60 into an 80? Easy, multiply it by 4. That will 320 please. 23:56.
I do have to say, though, you explain the math well. Some of my math teachers of old just couldn't get to everyone. Thank you.
LCD means lowest common denominator or least common multiple
To explain I would tell a student trial and error.
16 and20
16*2 =32
16*3 = 48
16*4= 64
16*5 = 80 bingo ! Even number ending in 0 (like 20)
So LCD is 80! Done without factor trees!
Got it! Thanks for the math instruction!
Good refresher. I knew to factor to primes but what to do next I was a bit uncertain.
No calculator in my day Slide ruler Advance math math 4 (trig) math 5 ( pre-Calculus) kids had them but they were very expensive Like around 200 dollars This was back in the school year 1975-1976 When I went to college the Ti 31 came out and it cost only 30 dollars That was the fall of 77 However we were not allowed to use them on tests This was at the college I went to in the Fall of 77 SR 31 was a nice little scientific calculator Some people from my age should remember it I still have it
20 is nice round number. So let's take look at 16, multiply that by 10. 160, now 160/20 is 8. So we can get to 9*10-8*3= 90-24 = 66, divide by obvious 2. Can we divide 80 by 3, no digits don't sum to 3, 11 is out as well. Ergo 33/80. Easy enough to do in head.
At 14:10 he finally “gets into it.”
Hmm, almost worked this out in my head but needed a piece of paper to keep track half way through. That said, went about it using what you call the bow-tie method then simplified down.
(9/16) - (3/20)=?
Well;
16x20=16x2x10=32x10=320
9x20=9x2x10=18x10=180
3x16=3x2x8=6x8=48
So;
(9/16) - (3/20) = (180/320) - (48/320) = (90/160) - (24/160) = (45/80) - (12/80) = 33/80
Does it all end in 0 and/or 5 = divide everything by 5
Digits add up to 3, 6 or 9 = divide everything by 3 (example; 99's digits add up to 18 then 18's digits add up to 9, so divide by 3 giving 33.)
Everything an even number = divide it all by 2
Repeat.
Hope you don't hit something divisible by 7 or another higher prime number as those are harder to spot.
Have to admit I don't recall the prime factoring from my schooling at all. Probably got taught it, but totally don't remember it, so I'm glad I watched this.
Love your channel, keep up the good work. Btw, what blackboard software are you using?
I agree with the LCD but on some or many calculators they use LCM least common Multipul...
I got the answer correct. Took me less than 20 seconds. My problem with this explanation is it's incredibly convoluted.
It's
simple...start multiplying the smallest denominator of the two in question. Until you get to the first number the highest denominator can be divided into equally. There's your cd.
I got the right answer in my head. (I wouldn't have been able to do so without actually 'seeing' the problem written.) Can't tell you how I knew to do it exactly though.
Did it in my head, but it was well worth the watch anyway.
This one can be done with the bow tie hack and without a calculator: 180 (20 times 9) -48 (16 times 3) /320 (16 times 20) = 132/320. Simplify at the end dividing the N and the D by 4 and you get 33/80.
But I get the point. One need to know the long method to find the LCD if the numbers are bigger and IF the problem needs to be solved WITHOUT the calculator.
This equation had just low enough numbers to be solved mentally with the hack in my humble opinion.
Yes, but then you have to reduce the answer anyway.
@@royreber526 I think I acknowledged that in my answer, no? ;)
Speak less, solve right away
I also just go straight for easiest .. 16*20=320=~CD. no need lowest
(9*20)-(3*16)=180-48=132/320 then reduced it by half TWICE! =66/160 OR 33/80😂🎉 can't reduce any more
To make fraction subtractable, multiply each (top&bottom)by the others denominator, SUBTRACT AWAY, then reduce as far as you can.😊
Nobody in the comments did it like mine, ..😢😢 but I did it in 30 secs with no calc AND no pencil ✏️ or paper 📜😮😮
Is there a proof that shows the LCD is the product of the highest prime factor?
Just out of interest, is the answer to the sum at 21:18 29,969/5,408,776 ?
Good luck doing a prime factorisation of 20182 (hint: 10091 is prime, but you need to check that), so computing the LCM of 1608 and 20182 via their prime factorisations is a pain. Generally going via the gcd is a better algorithm.
Can't you just multiply the denominators? Then, multiply each numerator by the result divided by each numerator? Then, reduce the resulting fraction to it's lowest denominator possible?
It’s hard to follow when you go off topic all the time. I liked your site at first but now it drives me crazy waiting for you to get to the point.
Lowest Common Denominator ( LCD) is 80 and answer is 33/80 I.e 45/80 - 12/80 = 33/80
Did it in my head in a few seconds.!!
12:00
Least Common Denominator is not the lowest common multiple
I might as well just pluff my way through this test..
This guy is doing just fine!
I'm really keen in following your lessons but the discussion is lengthy and at times , in my mind irrelevant.
Thank you for sharing. 💚
Yeah, mine was long division! I love fractions! ❤
33/80
I'm doing these in my head so by making their that's possible but I'm pretty sure the answer to this one is 33 / 80.
LCD - lower common de
4 x 4 = 16, 4 x 5 = 20. LCD = 5 x 16 = 80 which is divisible by 20.
Like your lessons
I did it in my head. I just kept increasing 20 until I found the right number: 20, 40., 60! Sixty, that's it. After that, it continued to be easy
Many years ago students did use calculators. It was called the Ababcus.
(9*5-3*4)/80=33/80
Hello everyone,
basically, the tutor determines the least common multiple of 16 and 20 through prime factorization. There is another way in which the greatest common divisor is first determined and then the smallest common multiple is determined from this.
gcd
20 : 16 = 1 R 4
16 : 4 = 4 R 0
gcd(16, 20) = 4
lcm(16, 20) = x
4x = 16 ⸳ 20
x = (16 ⸳ 20)/4
x = 4 ⸳ 20
x = 80
qed
best regards
Marcus 😎
the lcd is the least common denominator,my answer is 33/80
9/16 - 3/20
40/80 - 12/80 =28/80= 7/20
I like your videos, but you're just a little too chatty. Just get to the mechanics and be done with it.
With Mathematics you can’t be quick or direct with any shortcuts. John states in most, if not all of his videos that he is a Math teacher. Which requires an explanation in as much as possible. That requires concentrated explanations. Just some food for thought.
Using pencil and paper I had the answer in three minutes into the video. .5625 minus .150 equals .4125. 33 divided by 80 equals .4215.
Good stuff, but you don't need the least common denominator to be able to add or subtract, you just need any common denominator. It's OK if you have fractions in the numerator or denominator. You can take care of them later.
Let's use 20 as a common denominator.
16 is four parts to 20's five parts, so 16 time 5/4 equals 20.
Take 9/16. Multiply top and bottom by 5/4, yielding 45/4 divided by 20.
Now the problem is (45/4)/20 - 3/20.
The three from 3/20, expressed in quarters, is 12/4. So, the math on the numerators is 45/4 - 12/4 yielding 33/4.
The mental math became 45 - 12 = 33. The rest is just mechanical manipulation.
Remembering our common denominator is 20, and the 33 we got is actually 33/4 the answer is (33/4)/20. You probably want to kill off the fraction in the top.
If you have a complex numerator, multiply top and bottom by the top's denominator to get rid of the fraction in the numerator.
(33/4)/20 equals ((33/4)*4) / (20*4)
(33/4)/20 becomes 33/80.
The Least Common Denominator (LCD) is 80. 20x16 =320 is the Most Common Denominator. 320/2=160 also works. 160/2=80 works too. 80/2=40 does not work, so 80 is the LCD. Easy peasy.
did it in my head in less than 2 minutes.
Wouldn't it be easier to multiply the two denominators? Then reduce them.
Got it!😊
What's so great about finding the LCD? Just multiply the other term by the denominator. So find (9/16 * 20/20) - (3/20 * 16/16). Then reduce.
Got it
33/80? The lowest common denominator is found by multiplying the denominators by amounts where they end up at the same number
"16 and 20 have infinite multiples in common". Not so, your lowest common multiple is 80 which solves the problem, but eventually as they approach infinity they will stop having common multiples. Maybe sooner than we think. QED, that statement is not correct.
45-12
----
80
33
-
80