My only question about your answer is? 'Why did you leave it in an improper fraction?' I only ask because I was always taught to reduce, reduce, reduce, and never leave it as an improper fraction. Thus I would have ended with 3 7/12. Note the space between the 3 and the 7! I was taught that if a mixed number was in the question then try to end with the best reduced mixed number.
@@kathykoeven Problem is Kathy you can't even solve a problem like that it's too confusing. It's not written clearly in mathematical language that universally understood. I will give you an example but the example will be a sentence in English. A scissors trims a large lawn mower lawn singly with blades. Now you tell me what this sentence says does it make sense to you I have a mathematical mind that was put together not only in mathematics classes but in physics classes I have a master's degree in physics the mathematics I have taught and learned can only be communicated one way not the way this man is trying to do this it's ludicrous
This problem was alot easier IMHO if you separate 2 3/4 to 2+3/4. Then you could say 3/4+5/6+2 = 3 7/12. When he revealed the answer my initial reaction was "why the heck would you have an improper fraction???"
One concept you left out is that when you multiply a number by one you don’t change the value. So you can multiply 3/3 times one of the fractions and it does not change the fraction.
When I was in school, which was over 30 years ago, it was a requirement to change your answer from an improper fraction into a mixed number, or else it would be an incomplete answer even though 43/12 is equal to 3 7/12.
I was just about to comment that I like to reduce it even further to 3 and 7/12. I think it's better when reduced in this fashion, because in that form it's plain and obvious that you have 3 plus part of a whole. That's not clear from 43/12.
Where did you go to school? I learned this nearly 70 years ago and 43/12 was a perfectly good answer. In fact it was preferred to the equivalent form 3 and 7/12 because it is much easier to work with. For example half of 43/12 is simply 43/24 but half of 3 and 7/12 requires multiple steps.
@@rogeraffleck8677 Well, it all depends on your use case for the answer. Of course, if one is going to take the answer and proceed to do further calculations, then 43/12 is preferred. If one wants to just present the answer as final data, however, I think 3 and 7/12 is much clearer. In fact, I prefer 3.5833... for reporting.
Here's a slightly different approach. First I find 1/2 of 5/3 to get 5/6. Then use LCD to change11/4 to 33/12 and 5/6 to 10/12.. Ans: 43/-12 or 3 7/12. Love the "bow tie" thing.
I went to school as a child in Ontario, Canada. I was taught this way. I had a stroke 7 years ago and I'm 71; love to do these to see how far I've slipped. I got this one right. Thanks for doing these.
Turn-based computer strategy games are helpful too, I find. The older ones are hardest, and being turn-based, there is no pressure to react, just time to respond after careful consideration. Puzzle games and logic challenging games are good to keep as sharp as you can too. And, of course, this. I try to do them in my head while looking at the thumbnail before opening the vid and posting my answer. Then I see if I was right.
I just love (NOT) the comments from people who are apparently good at mathematics & assume everyone else should be too. Speaking as a "poor soul" that appreciates his teaching, it would be great if the mathematical geniuses who are watching these even though they apparently do not NEED the instruction would just go away.
Hi, I like your content, ... Using PEMDAS most of us should be able to do fractions like this in 30 seconds in our head. 3 7/12 seems pretty obvious to older generations like mine. This was grade 6 math in our day.
I am thrilled! I got another one right! When I was in school, centuries ago,, we were not taught PEMDAS. i remember being confused about the order of the four operations. It was frustrating to remember when and where to do what. PEMDAS and your further rules are so clear and simple! I’m loving it! It’s fun!
@@craiggoodwin9704 Isn’t he a great teacher? I wish my teachers had been so encouraging and clear. I remember rules in math, but not PEMDOS combined with such clear explanations of addition/subtraction, multiplication/division rules for LCD AND Bowtie. It was all confusing to me then. His teaching has cleared that up. It’s fun now, though too late for school years. What a difference it could have made in the outcome! Sorry you didn’t get it this time … When I miss the answer, I do the problem over and over ‘til I get it. This technology we use now is really something. We can freeze time, go back, anything. Thank you for your kind encouragement! You’re like the teacher - You’re an encourager! 😊
@@littlebrookreader949 I would have loved to have had him for all but only one year when I had an incredible teacher who was as calm as he is. I was so happy for great grades in Algebra I, but beyond 3rd grade through 8th was a nightmare, and in 10th grade, I dropped Algebra II because I was drowning.
Process multiplication first (PEMDAS) 1/2 * 5/3 = 5/6 Now you need the LCM 4,2,3 >>> 12 Then 3/4 is 9/12 (ignore the integer for now); 5/6 is 10/12 9+10/12 >>> 19/12 or 1 7/12 Add the integer back 2+1 >>> 3 7/12
Something that really helped me understand why you can multiply a number like 11/4 by 3/3, without changing it, is realizing that you’re only multiply by 1. You can always multiply by 1 without changing anything. 3/3 and 2/2 are both just 1 in a different form.
I totally agree and it was a break through moment for me. I have to give it the math teachers. They explain the same information year after year without leaving steps out, thinking they already covered that step!
I did this in my head and changed the improper fractions to mixed numbers as I went along. For example, I dropped the 2 and added 3/4 to 5/6 using LCD getting 19/12 by adding 9/12 to 10/12, then subtracted 12 from 19 to get 7 which becomes the numerator at 7/12 plus the remaining 12/12 becoming 1-7/12. I then added that back to the 2 I dropped before for 3-7/12 or 43/12. I know this seems like a convoluted way to do it, but it took WAY longer to type this out than it did to actually do the problem this way in my head.
This is the way. I did the same, except instead of LCD I just multiplied the numerators by the other denominator to get 2+18/24 + 20/24 = 2+38/24 =2+ 1+14/24 = 3 7/12
I just came across your channel by accident. Math was certainly not on my mind! I HATE math. I actually got an F in math in 8th grade 😮. I just say I have a math disability. Lol. My brain shuts down if a number or math issue is thrown at me. Amongst my A’s and B’s in all my other subjects along comes the D’s in math. Following you do math problems is fascinating. I never heard of any of those abbreviations and they help so much. I so wish I had teachers like you! It’s interesting to learn from you here on UA-cam. Never in all my life did I ever think math could be interesting and non-intimidating! I’m gonna watch your channel everyday and learn some math - not because I have to but because I want to. Maybe being 70 years old has something to due with it……. A lifetime of struggling with numbers! 😢
I converted it to decimal instead of fractions and did this one in my head in 15 seconds or less. Why make math harder that it needs to be? Cool video.
I converted the fractions into decimals and calculated it in my head and got 3.58. That's pretty close since 12 goes into 43 a little over 3 and a half times (43/12 = 3 7/12). My thought processes were: .5 X 1.66 = .83; 2.75 + .83 = 3.58 Edit: To be more accurate (carry out the decimal to more than two digits) I would continue the 3's, thus, 3.5833333... 7 ÷ 12 = 3.5833333... 3 X 12 = 36 36 + 7= 43
@@patsavage1245 We didn't. NASA has been scamming the American people for decades. They hired a Hollywood producer to fake everything! Only the brainwashed cannot see it!
I would do it like this (and then I'll see what you did) 2 3/4 + 1/2 x 3/5 Remember BODMAS Multiply first 1/2 x 3/5 = 5/6 Why 5/6 ? because it's 1 x 5 on top and 2 x 3 underneath So now we have 2 3/4 + 5/6 which is 11/4 + 5/6 which is 66/24 + 20/24 which is 86/24 which is 43/12 which is 3 7/12
I just took the 2, sat it down in a chair, gave it a book and a cognac, and went back to the rest of the problem. Mixed fractions sometimes suggest a path to a final solution. By removing the 2 you have some math that you can do in your head.
PLEASE STOP saying “anyways”. It is “anyway”. It is OK in another meaning, but not here. I am surprised that an academic doesn’t know this. Anyway, I love your tutorials and have learned and recalled so much from my school days. Thanks very much!
First thing is 1/2 x 5/3 which is 5/6, I’m pretty sure. Then you turn the mixed number into an improper fraction. And that is 11/4. And just speaking of improper fraction, I was taught to save simplifying for final step of problem solving. Then you take the improper fraction from the mixed number and add it to the 5/6. So you take 33/12, which is 11\4 with a common denominator of 12 and figure out the other fractions. Then you’re left with 33/12 + 5/6. LCD is 12. So then you’re left with 33/12 +
Studying daily is exciting and I didn't enjoy the value of that when I was young. Terminology is so important for me. Proper, improper, mixed fractions, numerator, denominator ratio, per and to mean a lot to me today as a result of studying
I hated math in school but I really like how you explain things. It’s been many years since I’ve gone to school but I just happened to stumble upon this channel. I’m really enjoying it. I never thought that would be possible. My first thought with this math problem was to convert it to decimals. Would that work?
Greetings. We will first concern ourselves with 1/2×5/3 to get 5/6. Now we will add 2 3/4 or 11/4 to 5/6 to get 43/12 after finding the LCM of 12. The answer is 43/12 or 3 7/12, (3 and 7/12)
I may be wrong, but I started by calculating the 2 highest denominators 2 3/4 + 1/2 × 5/3 33/12 + 1/2 × 20/12 (then 1/2 of 20/12 which is 10/12) which makes 33/12 + 10/12 Which is 43/12 or 3 7/12 It's the way my brain works 😊
An easier way to me would be multiple each fraction by the denominator of opposite fraction example 6x11 and 6x4=66/24 then 4x5 and 4x6=20/24 added together =86/24 reduced to 43/12 = 3 and 7/12 walla 🤓You’re math lessons are very helpful to me I enjoy them!
Youre an amazing teacher. Youve taught me alot in just 3 days. This video though, is confusing for a person like me struggling with fractions. You seemed to be all over the place with this math problem.
Thank you for mentioning about extra works. I think if the teachers don't want the students do extra works ,then they should tell students ahead exactly what they should do is enough . It's so unfair to the students when the teachers don't make it very clearly, they spend more time for extra works but get lesser points instead .
You're the expert and I'm only 75 but i have to disagree with not reducing the improper fraction to a mixed number. Because if the student cannot do that part properly and gets the wrong answer then they deserve to have it marked as incorrect. The students need to be able to work the problem to it's conclusion.
To solve this math problem, use PEMDAS rule by multiplying first and then do the adding part… 2 3/4 + *1/2 * 5/3* 2 3/4 + *5/6* Once that’s done, find the LCD of denominators 4 and 6 to add. 2 9/12 + 10/12 = 2 + 12/12 = 3 + 19/12 - 12/12 = 3 + 7/12 = 3 7/12
Start with the multiplication : 2¾ + (1/2)*(5/3) = 2¾ + (5/6) = 2+(9/12) + (10/12) = 2+(19/12) = 24/12+19/12 = 43/12 Can't be simplified as 43 is a prime number. LCD, or the reason that I memorized the prime numbers up to 100 in secondary school.
Did it in my head, looked your answer of 43/12 and was so confused for a sec, because I already calculated it as 3 7/12.... 1/2x5/3= 5/6 ; 3/4+5/6=18/24+20/24=38/24=1 14/24=1 7/12 ; 1 7/12+2=3 7/12 (3 7/12=43/12)
Fractions are multiplied by multiplying enumerators and denominators. Fractions are added by bringing thhemm to the sae denoinator and then adding the enumerators. If you know that,it is really easy: (1/2)*(5/3)=(1*5)/2*3)=5/6 2+3/4+5/6=24/12+9/12+10/12=(24+9+10)/12=43/12 Now, we can write this result as a su of a whole number and a fraction between 0 and 1: 43/12=(36+7)/12=36/12+7/12=3+7/12 So the final result is 3 7/12 I disagree, that it is always the easiest way to convert mixed numbers to fractions. I think, sometimes it may be easier to lookat the mixed number as sum of a whole number and a fraction.
Before watching the video, I would turn all three into integers, because they are simple fractions: 2.75 + .5 x 1.67 = 2.75 + .835 = 3.585 Convert back to fraction and done. :)
Before clicking I got 12 and 3/4 I had to right it on my screan though. I got my answer by turning them all into like fractions so I came up with 6/12 x 20/12 that I did first and I turned the 2 3/4 into 11/4 that turned into 33/12. After that I had 33/12 + 120/12 making 153/12 that brakes down to 12 and 9/12 that can be reduced to 12 and 3/4. Edit, I just realized we're I went wrong. I did the multiplication wrong. I have not done math with fractions since the mid 90's
Quick comment, at the beginning when you are explaining proper, improper, and mixed fractions, you drew a circle around the 3/2 and another around the 3 1/2. Then you talked about converting improper and mixed fractions and drew arrows that appears to indicate that 3/2 is converted to 3 1/2 and vice-versa. For your "literal" watchers, (NO! Not Buffy's Watcher) maybe use 1 1/2 instead.
So, why stop when you almost find the correct answer? Divide 43 by 12 and you get 3 and 7/12. That's the final answer. But why go so long? I saw immediately that both 4 and 3 have 12 as first common multiplication factor. So you get 2 and 9/12 + (1/2 of 20/12). Half of 20/12 is 10/12. So you get 2 and 9/12 + 10/12. Which is 2 and 19/12. 19/12 is 1 and 7/12. So you get 2 and 1 and 7/12, which is 3 and 7/12.
I love it that you check your work. My grrandkids can do the math, but dont know how to check or even estimate the answers. (Kindergarten in 1947 -- but I STILL love to refresh my math knowledge. Thank you!)
I took the 2 out of the equation temporarily leaving 3/4 + 1/2 x 5/3 then becomes 3/4 + 5/6 then 9/12 + 10/12 = 19/12 then 19/12 = 1 7/12 plus the 2 that I had set aside = 3 7/12. ✅
Before it started, I was able to add the fraction quite easily, but then you blew me out of the water by not doing that. No parenthesis so I assumed (yeah, I know better than to do that) that I could start by adding the first 2 fractions. Then you tossed that out with the bath water. Halfway through I could feel a headache coming on as I struggled to follow, and about 2/3 of the way through, I threw myself out the window with the bath water. That was so far above my pay grade. I flunked miserably.
Will this work also? (assuming x is the answer to the equation rather than the ? you used.) x can also be fraction(43,12). The equation 2(3/4)+(1/2) x (5/3) = x can be simplified to 19/6 = x. Since 43/12 is also equal to 19/6, then x can also be equal to fraction(43,12). In other words, the two fractions, fraction(43,12) and 19/6, are equivalent. They represent the same number. Therefore, x can be equal to either of them. ???? Thanks, and love your videos.
Why did you bring the 2 in the 2 and 3/4 into the fraction? It's much cleaner if you just deal with the 3/4 + 5/6 by itself = 18/24+20/24=38/24 or 1 and 14/24 - then add the 2 back in = 3 14/24, which is easy to simplify as 3 and 7/12... I looked ahead in the video and there's way more messy fractions being through about.
I’m 39 and my mind just calculate it in both ways. Totally forgot how I got the LCD but I just know it is 12 by looking at it… mathematic is about practice practice and practice then it will become part of you… 😂
Using the LCD is nice, saves some work, but really any common denominator will work just fine Really only relevant if you like trolling math teachers or need efficiency and just can think of a common denominator to use immediately I did quite a lot of that in middle and highschool, teachers didn't like that the work i showed was an occasional note, doing most of the work mentally (nowhere near as proficient in mental arithmetic as i was 15 years ago, but it's fun to reminisce)
Just curious. At all the schools in Cincinnati up to at least 1983 we were taught multiplication first then division, never anything about left to right. So I am just curious what city and state you teach in?
Personally I try to avoid fractions. In the UK, like most of the world we use metric measurements so for the most part, fractions can be avoided. I simply convert this to 2.75+0.5x1.66
The great disadvantage of not using fractions is, that you may get rounding errors. Some number (like 5/3 or 7/12 in this case) have no exact representation with a limited number of decimal places. So you have to use fractions to get the exact result in this case. Evenif you do not need the exact result or if you need the resullt in a decimal representation, it may be an advantage to keep the fractions as long as possible and only convert the final result to a decimal representation, because the rounding errors may be lower (you avoid rounding errors "on the way").
Fun video to follow. I made many mistakes and would given a mixed fraction at the end which would not have been 3 7/12 because I would have been wrong along the way. 😢😅
Due to the absense of parentheses to indicate the order of execution there are two answers. Therefore the problem is invalid (except to make this point). 65 or 59
No parentheses are required here. Mathematical notation has grammar rules that make this expression unambiguous. Nothing wrong with adding parentheses for clarity if you want to though.
It is easy to get wrong only if one relies on PEMDAS rather than using parentheses in writing the equation. It is irresponsibly lazy not to use parentheses in this.
I got 3.58 in my head off the rip. Which i knew was not correct but very close. Don't get me wrong, I do like the methodology your teaching, and understand many applications need to be that precise.
My only question about your answer is? 'Why did you leave it in an improper fraction?' I only ask because I was always taught to reduce, reduce, reduce, and never leave it as an improper fraction. Thus I would have ended with 3 7/12. Note the space between the 3 and the 7! I was taught that if a mixed number was in the question then try to end with the best reduced mixed number.
FYI, He answers that at the end.
@@kathykoeven
Problem is Kathy you can't even solve a problem like that it's too confusing. It's not written clearly in mathematical language that universally understood. I will give you an example but the example will be a sentence in English.
A scissors trims a large lawn mower lawn singly with blades.
Now you tell me what this sentence says does it make sense to you I have a mathematical mind that was put together not only in mathematics classes but in physics classes I have a master's degree in physics the mathematics I have taught and learned can only be communicated one way not the way this man is trying to do this it's ludicrous
This problem was alot easier IMHO if you separate 2 3/4 to 2+3/4. Then you could say 3/4+5/6+2 = 3 7/12. When he revealed the answer my initial reaction was "why the heck would you have an improper fraction???"
Unless they ask you to, or the answer is in improper fraction if it’s multiple choice
One concept you left out is that when you multiply a number by one you don’t change the value. So you can multiply 3/3 times one of the fractions and it does not change the fraction.
2 3/4 + (1/2 *5/3)
2 3/4 + (5/6)
I rather change the 2 3/4 to a mixed number fraction = 11/4
11/4 + 5/6
Find LCD = 12
33/12 + 10/12 = 43/12
=43/12 (final answer)
I totally agree. Leaving an improper fraction is a big no no! This guy is a terrible teacher and really makes his presentations way too long too!
I did it exactly the same way, but changed my final answer to 3 7/12.
I find his explanation very confusing and long
Thanks for what you are doing. I am an 84 year old retired junior high/middle school math teacher.
When I was in school, which was over 30 years ago, it was a requirement to change your answer from an improper fraction into a mixed number, or else it would be an incomplete answer even though 43/12 is equal to 3 7/12.
I was just about to comment that I like to reduce it even further to 3 and 7/12. I think it's better when reduced in this fashion, because in that form it's plain and obvious that you have 3 plus part of a whole. That's not clear from 43/12.
Where did you go to school? I learned this nearly 70 years ago and 43/12 was a perfectly good answer. In fact it was preferred to the equivalent form 3 and 7/12 because it is much easier to work with. For example half of 43/12 is simply 43/24 but half of 3 and 7/12 requires multiple steps.
@@rogeraffleck8677 Well, it all depends on your use case for the answer. Of course, if one is going to take the answer and proceed to do further calculations, then 43/12 is preferred. If one wants to just present the answer as final data, however, I think 3 and 7/12 is much clearer. In fact, I prefer 3.5833... for reporting.
I was taught to simplify. 43/12 is a improper fraction, so therefore can be simplified.
In my school I had to brake ot down to a mix number and reduce it to the smallest number possible
Here's a slightly different approach. First I find 1/2 of 5/3 to get 5/6. Then use LCD to change11/4 to 33/12 and 5/6 to 10/12.. Ans: 43/-12 or 3 7/12. Love the "bow tie" thing.
Muahahahah.. I did the same.. Drinking beer at 2am watching math videos. Solving from the thumbnail and then taking victory lap on video
Also did it *just* this way. The LCD makes things simple... as an old teacher once said "Add apples to apples; it's less sticky than jam"
I worked it out the same way . . .
@@TaaxiCaab That's awesome. It's the exact same thing I did but it's only 11:30 pm my time now and I'm only three beers deep. Lol.
I did it the same way and got the same answer!!!!
I went to school as a child in Ontario, Canada. I was taught this way. I had a stroke 7 years ago and I'm 71; love to do these to see how far I've slipped. I got this one right. Thanks for doing these.
Turn-based computer strategy games are helpful too, I find. The older ones are hardest, and being turn-based, there is no pressure to react, just time to respond after careful consideration. Puzzle games and logic challenging games are good to keep as sharp as you can too.
And, of course, this. I try to do them in my head while looking at the thumbnail before opening the vid and posting my answer.
Then I see if I was right.
I just love (NOT) the comments from people who are apparently good at mathematics & assume everyone else should be too. Speaking as a "poor soul" that appreciates his teaching, it would be great if the mathematical geniuses who are watching these even though they apparently do not NEED the instruction would just go away.
😅😅
Hi, I like your content, ... Using PEMDAS most of us should be able to do fractions like this in 30 seconds in our head. 3 7/12 seems pretty obvious to older generations like mine. This was grade 6 math in our day.
Yes, it was. And this was ever so easy! Indeed, without writing anything down and in 30 seconds. Guess we were lucky to still get taught anything.
@Livingongrace I got 3 and 7/12 in my head as well. Half of 20/12 is easy. When he said the answer was 43/12 I hesitated briefly but yeah, I'm old!
I was so confused watching this video because he makes it soooo complicated. I still don't know that he actually came to an answer, lol
Definitely 6th Class Arithmetics when I was there in 1972. Often in "mental arithmetic" (no pencil and paper).
I am thrilled! I got another one right! When I was in school, centuries ago,, we were not taught PEMDAS. i remember being confused about the order of the four operations. It was frustrating to remember when and where to do what. PEMDAS and your further rules are so clear and simple! I’m loving it! It’s fun!
Congrats. You did better than I. Maybe we'll both get the next one! 🙃🙂🙂
@@craiggoodwin9704 Isn’t he a great teacher? I wish my teachers had been so encouraging and clear. I remember rules in math, but not PEMDOS combined with such clear explanations of addition/subtraction, multiplication/division rules for LCD AND Bowtie. It was all confusing to me then. His teaching has cleared that up. It’s fun now, though too late for school years. What a difference it could have made in the outcome! Sorry you didn’t get it this time … When I miss the answer, I do the problem over and over ‘til I get it. This technology we use now is really something. We can freeze time, go back, anything. Thank you for your kind encouragement! You’re like the teacher - You’re an encourager! 😊
@@craiggoodwin9704 I just looked at your motorcycle! WOW! Looks great! Live free!
@@littlebrookreader949 I would have loved to have had him for all but only one year when I had an incredible teacher who was as calm as he is. I was so happy for great grades in Algebra I, but beyond 3rd grade through 8th was a nightmare, and in 10th grade, I dropped Algebra II because I was drowning.
My nephew told me once, aunt I have a smart phone, a tablet, a laptop to do my math homework. What did you use back then ? I answered : my brain 😂
I find that it is quicker to cross multiply to get a common denominator and then reduce at the end. E.g. 86/24 = 43/12
I got the same answer
Can’t believe I got it right
Process multiplication first (PEMDAS)
1/2 * 5/3 = 5/6
Now you need the LCM
4,2,3 >>> 12
Then 3/4 is 9/12 (ignore the integer for now); 5/6 is 10/12
9+10/12 >>> 19/12 or 1 7/12
Add the integer back
2+1 >>> 3 7/12
That's exactly the way I did this in my head.
Something that really helped me understand why you can multiply a number like 11/4 by 3/3, without changing it, is realizing that you’re only multiply by 1. You can always multiply by 1 without changing anything. 3/3 and 2/2 are both just 1 in a different form.
I totally agree and it was a break through moment for me. I have to give it the math teachers. They explain the same information year after year without leaving steps out, thinking they already covered that step!
I did this in my head and changed the improper fractions to mixed numbers as I went along. For example, I dropped the 2 and added 3/4 to 5/6 using LCD getting 19/12 by adding 9/12 to 10/12, then subtracted 12 from 19 to get 7 which becomes the numerator at 7/12 plus the remaining 12/12 becoming 1-7/12. I then added that back to the 2 I dropped before for 3-7/12 or 43/12. I know this seems like a convoluted way to do it, but it took WAY longer to type this out than it did to actually do the problem this way in my head.
This is the way. I did the same, except instead of LCD I just multiplied the numerators by the other denominator to get 2+18/24 + 20/24 = 2+38/24 =2+ 1+14/24 = 3 7/12
I just came across your channel by accident. Math was certainly not on my mind! I HATE math. I actually got an F in math in 8th grade 😮. I just say I have a math disability. Lol. My brain shuts down if a number or math issue is thrown at me. Amongst my A’s and B’s in all my other subjects along comes the D’s in math. Following you do math problems is fascinating. I never heard of any of those abbreviations and they help so much. I so wish I had teachers like you! It’s interesting to learn from you here on UA-cam. Never in all my life did I ever think math could be interesting and non-intimidating! I’m gonna watch your channel everyday and learn some math - not because I have to but because I want to. Maybe being 70 years old has something to due with it……. A lifetime of struggling with numbers! 😢
I converted it to decimal instead of fractions and did this one in my head in 15 seconds or less. Why make math harder that it needs to be? Cool video.
exactly lololol
Not all fraction can be solid decimals as some are infinite decimal numbers so some are better done as fractions
@@thomashart5081 you just said a double negative...which meant the opposite of what you you thought you said lol
@@jfloyo11 sorry pain with the spellcheck
Exactly.
2 3/4+1/2×5/3=?
3/6 x 10/6 = 13/6
2 9/12 + 26/12 = 2 35/12 or 3 7/12
I converted the fractions into decimals and calculated it in my head and got 3.58.
That's pretty close since 12 goes into 43 a little over 3 and a half times (43/12 = 3 7/12).
My thought processes were: .5 X 1.66 = .83; 2.75 + .83 = 3.58
Edit: To be more accurate (carry out the decimal to more than two digits) I would continue the 3's, thus, 3.5833333...
7 ÷ 12 = 3.5833333...
3 X 12 = 36
36 + 7= 43
I'm 71. I don't use fractions.
@@patsavage1245 and I am 67, so I use both, but if complex, I resort to decimals.
@@libertypastor1307 Why should you have to? Only in America. They still like acres, hectares, 14/5ths etc. It baffles me how they got to the moon.
@@patsavage1245 We didn't. NASA has been scamming the American people for decades. They hired a Hollywood producer to fake everything!
Only the brainwashed cannot see it!
@@patsavage1245 14/5ths? You mean 2.8? Or do you prefer 2,8?
I was taught the rule called BODMAS in high school,Brackets,of signs,Division,Multiplication,Addition,subtraction.
We were taught BPMA (Bracket, Power, Multiply, Add).
You're right up there with *Bill Nye, the Science Guy!* We'll call you, *John Zimmerman, the Numb3r's Guy!*
I would do it like this (and then I'll see what you did)
2 3/4 + 1/2 x 3/5
Remember BODMAS Multiply first 1/2 x 3/5 = 5/6
Why 5/6 ? because it's 1 x 5 on top and 2 x 3 underneath
So now we have 2 3/4 + 5/6 which is 11/4 + 5/6
which is 66/24 + 20/24 which is 86/24
which is 43/12 which is 3 7/12
👍👍 Man, if only UA-cam, and more specifically, this channel, existed back in the day lol.
I just took the 2, sat it down in a chair, gave it a book and a cognac, and went back to the rest of the problem.
Mixed fractions sometimes suggest a path to a final solution. By removing the 2 you have some math that you can do in your head.
Haha, I like that.
PLEASE STOP saying “anyways”. It is “anyway”. It is OK in another meaning, but not here. I am surprised that an academic doesn’t know this.
Anyway, I love your tutorials and have learned and recalled so much from my school days. Thanks very much!
I was not taught math this way! I’m absolutely loving your videos!
First thing is 1/2 x 5/3 which is 5/6, I’m pretty sure. Then you turn the mixed number into an improper fraction. And that is 11/4. And just speaking of improper fraction, I was taught to save simplifying for final step of problem solving. Then you take the improper fraction from the mixed number and add it to the 5/6. So you take 33/12, which is 11\4 with a common denominator of 12 and figure out the other fractions. Then you’re left with 33/12 + 5/6. LCD is 12. So then you’re left with 33/12 +
Studying daily is exciting and I didn't enjoy the value of that when I was young. Terminology is so important for me. Proper, improper, mixed fractions, numerator, denominator ratio, per and to mean a lot to me today as a result of studying
I hated math in school but I really like how you explain things. It’s been many years since I’ve gone to school but I just happened to stumble upon this channel. I’m really enjoying it. I never thought that would be possible.
My first thought with this math problem was to convert it to decimals. Would that work?
Math is so much more fun as an adult 😁
In my country, we teach this subject in the 6th grade. I'm surprised how he prepared a 23-minute video for such a simple question.😮
Unnecessary complicated method. 70 years ago in 6th grade, if we didn't get the solution in 2-3 min.time... we flanked.
Greetings. We will first concern ourselves with 1/2×5/3 to get 5/6. Now we will add 2 3/4 or 11/4 to 5/6 to get 43/12 after finding the LCM of 12. The answer is 43/12 or
3 7/12, (3 and 7/12)
I may be wrong, but I started by calculating the 2 highest denominators
2 3/4 + 1/2 × 5/3
33/12 + 1/2 × 20/12 (then 1/2 of 20/12 which is 10/12)
which makes
33/12 + 10/12
Which is 43/12 or 3 7/12
It's the way my brain works 😊
An easier way to me would be multiple each fraction by the denominator of opposite fraction example 6x11 and 6x4=66/24 then 4x5 and 4x6=20/24 added together =86/24 reduced to 43/12 = 3 and 7/12 walla 🤓You’re math lessons are very helpful to me I enjoy them!
If I had been taught by you i might evenhave enjoyed maths. I am nearly 78 and have never seen this before!
3 7/12
Multiplication first, then convert to the lowest common denominator (12) and add.
Wow I'm finally getting it. This teacher is good
Youre an amazing teacher. Youve taught me alot in just 3 days. This video though, is confusing for a person like me struggling with fractions. You seemed to be all over the place with this math problem.
Thank you for mentioning about extra works. I think if the teachers don't want the students do extra works ,then they should tell students ahead exactly what they should do is enough . It's so unfair to the students when the teachers don't make it very clearly, they spend more time for extra works but get lesser points instead .
You're the expert and I'm only 75 but i have to disagree with not reducing the improper fraction to a mixed number. Because if the student cannot do that part properly and gets the wrong answer then they deserve to have it marked as incorrect. The students need to be able to work the problem to it's conclusion.
43/12 is the conclusion. You can convert it to a mixed number if you want to but that's not an important or necessary step.
To solve this math problem, use PEMDAS rule by multiplying first and then do the adding part…
2 3/4 + *1/2 * 5/3*
2 3/4 + *5/6*
Once that’s done, find the LCD of denominators 4 and 6 to add.
2 9/12 + 10/12
= 2 + 12/12
= 3 + 19/12 - 12/12
= 3 + 7/12 = 3 7/12
WE where taught order of operations was bedmas brackets exponents division multiplication add subtract
Start with the multiplication : 2¾ + (1/2)*(5/3) = 2¾ + (5/6) = 2+(9/12) + (10/12) = 2+(19/12) = 24/12+19/12 = 43/12 Can't be simplified as 43 is a prime number.
LCD, or the reason that I memorized the prime numbers up to 100 in secondary school.
Mixed fractions could be mistaken for 2*(3/4) so I would always write it as an improper fraction to begin with.
Goes to show the importance of brackets to show what is required
11/4+2/4×5/3
13/4×5/3
65/12 or
11/4+10/12
(33+10)/12
44/12
2.3/4+1/2×5/3, = 11/4+1/2×5/3 = 11/4+5/6, 4 and 6 ka lcm 12 , 11/4+5/6= 33+10/12, = 43/12 = 3.7/12 answer
The first thing? Convert 2 3/4 to 11/4. Then multiply, so you can reduce it to 11/4 + 5/6. Which is (33 +10)/12. Or 43/12. Or 3 7/12.
michaelgleason Nobody likes a showoff!
I wish you had been in my math class 76 years ago!!
Did it in my head, looked your answer of 43/12 and was so confused for a sec, because I already calculated it as 3 7/12....
1/2x5/3= 5/6 ; 3/4+5/6=18/24+20/24=38/24=1 14/24=1 7/12 ; 1 7/12+2=3 7/12 (3 7/12=43/12)
2 3/4 + 1/2 × 5/3 = 2 3/4 ( 1×5/2×3)= 2 3/4 + 5/6 = 11/4 + 5/6 = 33 +10 /12 = 43/12 =3 7/12
Fractions are multiplied by multiplying enumerators and denominators. Fractions are added by bringing thhemm to the sae denoinator and then adding the enumerators. If you know that,it is really easy:
(1/2)*(5/3)=(1*5)/2*3)=5/6
2+3/4+5/6=24/12+9/12+10/12=(24+9+10)/12=43/12
Now, we can write this result as a su of a whole number and a fraction between 0 and 1:
43/12=(36+7)/12=36/12+7/12=3+7/12
So the final result is 3 7/12
I disagree, that it is always the easiest way to convert mixed numbers to fractions.
I think, sometimes it may be easier to lookat the mixed number as sum of a whole number and a fraction.
Wow. I think he worked a different problem - what is the greatest level of complexity one can achieve in working this simple math problem?
3 7/12, solved by mental math. Love these brain exercises.
Got the same , in head , expressed as three and seven twelfths . Almost said two and nineteen twelfths .
Ditto
What happened to the Bow Tie theory-sure seems to be easier than this round about
I need to rest.🤯 I've learned more in the last 2 hours watching your videos than I tried to learn in high school.
I've got a headache 😢
I enjoy your videos! More! More!
Before watching the video, I would turn all three into integers, because they are simple fractions:
2.75 + .5 x 1.67 = 2.75 + .835 = 3.585
Convert back to fraction and done. :)
Before clicking I got 12 and 3/4 I had to right it on my screan though. I got my answer by turning them all into like fractions so I came up with 6/12 x 20/12 that I did first and I turned the 2 3/4 into 11/4 that turned into 33/12. After that I had 33/12 + 120/12 making 153/12 that brakes down to 12 and 9/12 that can be reduced to 12 and 3/4.
Edit, I just realized we're I went wrong. I did the multiplication wrong. I have not done math with fractions since the mid 90's
It's easy to get wrong, but it's easy to get right, when you know how.
Quick comment, at the beginning when you are explaining proper, improper, and mixed fractions, you drew a circle around the 3/2 and another around the 3 1/2. Then you talked about converting improper and mixed fractions and drew arrows that appears to indicate that 3/2 is converted to 3 1/2 and vice-versa. For your "literal" watchers, (NO! Not Buffy's Watcher) maybe use 1 1/2 instead.
So, why stop when you almost find the correct answer? Divide 43 by 12 and you get 3 and 7/12. That's the final answer.
But why go so long? I saw immediately that both 4 and 3 have 12 as first common multiplication factor. So you get 2 and 9/12 + (1/2 of 20/12). Half of 20/12 is 10/12. So you get 2 and 9/12 + 10/12. Which is 2 and 19/12. 19/12 is 1 and 7/12.
So you get 2 and 1 and 7/12, which is 3 and 7/12.
I love it that you check your work. My grrandkids can do the math, but dont know how to check or even estimate the answers. (Kindergarten in 1947 -- but I STILL love to refresh my math knowledge. Thank you!)
I took the 2 out of the equation temporarily leaving 3/4 + 1/2 x 5/3 then becomes 3/4 + 5/6 then 9/12 + 10/12 = 19/12 then 19/12 = 1 7/12 plus the 2 that I had set aside = 3 7/12. ✅
That's how I was thought maths
Before it started, I was able to add the fraction quite easily, but then you blew me out of the water by not doing that. No parenthesis so I assumed (yeah, I know better than to do that) that I could start by adding the first 2 fractions. Then you tossed that out with the bath water. Halfway through I could feel a headache coming on as I struggled to follow, and about 2/3 of the way through, I threw myself out the window with the bath water. That was so far above my pay grade. I flunked miserably.
Will this work also? (assuming x is the answer to the equation rather than the ? you used.)
x can also be fraction(43,12).
The equation 2(3/4)+(1/2) x (5/3) = x can be simplified to 19/6 = x. Since 43/12 is also equal to 19/6, then x can also be equal to fraction(43,12).
In other words, the two fractions, fraction(43,12) and 19/6, are equivalent. They represent the same number.
Therefore, x can be equal to either of them.
????
Thanks, and love your videos.
43/12 is not equal to 19/6.
Why did you bring the 2 in the 2 and 3/4 into the fraction? It's much cleaner if you just deal with the 3/4 + 5/6 by itself = 18/24+20/24=38/24 or 1 and 14/24 - then add the 2 back in = 3 14/24, which is easy to simplify as 3 and 7/12... I looked ahead in the video and there's way more messy fractions being through about.
I’m 39 and my mind just calculate it in both ways. Totally forgot how I got the LCD but I just know it is 12 by looking at it… mathematic is about practice practice and practice then it will become part of you… 😂
Using the LCD is nice, saves some work, but really any common denominator will work just fine
Really only relevant if you like trolling math teachers or need efficiency and just can think of a common denominator to use immediately
I did quite a lot of that in middle and highschool, teachers didn't like that the work i showed was an occasional note, doing most of the work mentally (nowhere near as proficient in mental arithmetic as i was 15 years ago, but it's fun to reminisce)
2 3/4 is 6/4, isn't it? Should this be written 2 + 3/4 + 1/2 x 5/3?
Just curious. At all the schools in Cincinnati up to at least 1983 we were taught multiplication first then division, never anything about left to right. So I am just curious what city and state you teach in?
Yes..thank you
Thanks!
You just inspired me to get my TI 36 Pro out and arrive @ 43/12 or 3.58333333333333333333333>>>>>>
Personally I try to avoid fractions. In the UK, like most of the world we use metric measurements so for the most part, fractions can be avoided. I simply convert this to 2.75+0.5x1.66
The great disadvantage of not using fractions is, that you may get rounding errors. Some number (like 5/3 or 7/12 in this case) have no exact representation with a limited number of decimal places. So you have to use fractions to get the exact result in this case.
Evenif you do not need the exact result or if you need the resullt in a decimal representation, it may be an advantage to keep the fractions as long as possible and only convert the final result to a decimal representation, because the rounding errors may be lower (you avoid rounding errors "on the way").
43/12 or 3 7/12
Fun video to follow. I made many mistakes and would given a mixed fraction at the end which would not have been 3 7/12 because I would have been wrong along the way. 😢😅
I wish I had had you for a math teacher. I didn't do well in high school and didn't graduate college cause I couldn't pass algebra. 😢
When my 8 year old daughter asks, "Daddy, may I watch UA-cam," I'm sending her to this channel
The final proper answer is 43 divided by 12 which equals 3 and 7 twelfths!
.5x1.666=.833+2.75=3.588
Every math teacher I have ever had wanted it as 3 7/12
Due to the absense of parentheses to indicate the order of execution there are two answers. Therefore the problem is invalid (except to make this point).
65 or 59
No parentheses are required here. Mathematical notation has grammar rules that make this expression unambiguous.
Nothing wrong with adding parentheses for clarity if you want to though.
Convert to decimal and get 3.58, same as 43/12
3.5833333333333333333 real world correct answer.
Three whole number and seventh twelfths. I love to work Maths😊😊
Can you make these shorter, please?
about 4 7/12s
whoops i added
Taught to never leave it in an improper fraction.
It is easy to get wrong only if one relies on PEMDAS rather than using parentheses in writing the equation. It is irresponsibly lazy not to use parentheses in this.
Wouldn't be much use as a tool to teach the grammar rules then though, would it.
Try giving a clear answer eg 43/12 =3 7/12
I think it's not finished. You could take 43÷13 to reduce it.
First thing is order of operations
Got it right in my head.
I HATE adding and subtracting fractions! It's so much easier to multiply and divide.
I got 3 and 7/12ths in 15 seconds - a retired engineer who went to school over 50 years ago.
What real life situation/occupation involves this math ?
Cooking and carpentry also if you are laying pipes
I got 3.58 in my head off the rip. Which i knew was not correct but very close. Don't get me wrong, I do like the methodology your teaching, and understand many applications need to be that precise.
it easy to use parentheses
11/4 and 5/6 multiply 11x 6 and 5 x 4 so its 66/24 and 20/24 = 86/24
It's misleading, (2+3/4) is noted as 2*3/4
10/3=3 1/3