Hey math friends! If you’re enjoying this video, could you double-check that you’ve liked it and subscribed to the channel? It’s a simple equation: your support + my passion = more great content! Thanks for helping me keep this going - you’re the best!
Your teaching style is fantastic! It's great that you don't skip any steps, no matter how simple or obvious they might seem to be. I've always been of the opinion that a teacher should not make any assumptions about how "easy" or "obvious" something is and, instead, just explain everything. It's far better to over explain something than to not give enough explanation and leave the student confused.
@@MalengWan I don't recall any reference to Oxford or any implication that this was supposed to be university level maths. Could you point out where I missed those, please?
I love this channel. I'm in my 50s and just following along for fun. I forgot a LOT from my high school and college days like the quadratic equation. Thanks for posting these.
Thank you very much! I suddenly realize that in school, they taught us without explaining why. For example, when moving a term to the other side of an equation and simply changing its sign from positive to negative, they didn't tell us that what we're actually doing is subtracting the number from both sides of the equation. That makes it much more logical, of course! ❤
As a mathematics teacher myself, I believe it is a disservice to students for teachers to focus on narrow techniques instead of broad fundamentals. Being able to derive the narrow techniques is far more useful than memorizing them. There have been a few teachers that I have wondered whether they actually knew the whys versus just memorizing formulae.
My version - restate the fractions using least common denominator (6); thus 3x/6 plus 2x/6, add together to get 5x/6=10. Then multiply both sides by 6 to eliminate the denominator, resulting in 5x=60. Divide both sides by 5 to get x=12
I'm 70 and do these just to keep the mind sharp. I solved that problem as you did, just did it as multiplying each side by 6/5, combining the step. On the second I subtracted the 2x/5 from the left side first, and apparently kept from having such big numbers to deal with 20x/60 + 15x/60 - 24x/60 = 11; then 11x/60 = 11; multiply by 60/11 quickly gives the answer of 60.
As is pointed-out in the comments, you did not skip things, even 6 divided by 3 equals 2. This is why I understand how the equation works. I can understand by what mechanisms things are kept *equal* to each-other. Math teachers were like "This is obvious, so I skip"... man, if it was obvious to me, why would I need you to teach me anything in the first place... Love your work, queen! 💪
Clear and concise - a great refresher for solving equations for those of us who rarely use these types of problems but who want to retain the skills to do so should we ever need to.
You have an excellent way for teaching and declaring what you do in addition to the meaning of doing and how to think to reach into conversations, excellent!!!, i love you do
You would make a great high school math teacher because you explain things: 1) clearly and simply; 2) step-by-step; 3) succinctly, and 4) at a very easy pace for students to follow......BTW, you are one of the few teachers of math who smile and with a truly genuine. That goes a long way in making learning enjoyable.
Interesting at 07.30 in splitting the multiplication into to parts. I remember solving a maths problem at junior school in that way and my teacher said it was the wrong method. That has stuck with me for over 50 years: I knew I was right, the result was the same, but his proscribed method was different! I'm glad I've resolved that issue before I die!
I am 72...... haven't done much maths since I stopped teaching science about fifteen years ago. I love trying to do these myself first then follow your solutions to see if I got it right..... such good brain training for an oldie!
Really enjoying your videos, you do a fantastic job of talking thru every step and not skipping the tiny steps, thank you. What application/tools are you using for the math?
Great stuff! I really enjoy your simple but complete explanations. In the second example, I found it easier to subtract the 2x/5 from both sides at the beginning, getting all of the x's on one side early.
New subscriber here. I agree with all the | comments | after each of the 3 vids I've seen so far. The only I can add is that the use of color is fantastic, as a visual learner, it really helps me to focus on the term in play. Thank you Math Queen!
Many (many) years ago when my kids were young and asked for help with math homework, one thing I pushed them on over and over, which would usually bug them, was to double check, or check their work. That is, plug the solution back into the equation(s) and ensure it works out. I was kind of hoping you would do that here. You might consider including that to your video. (I fully agree with your solutions, but I did still plug them back in to double check - the confirmation feels valuable)
I'm just going to say I appreciate you solving an equation I can actually follow. The last few have been way over my head...then I feel silly when I hear how to get the solution.
I really enjoyed the way how you solved it. It seemed too easy. Jejeje! I learnt how you multiplied 60. 11. Thanks for sharing. Regards and blessings from 🇵🇦😊
I love love love your videos. I love that you put the problems in the thumbnail, bc I like to solve it my way and then watch you solve it your way and compare notes to see what I can do to solve it faster, which your videos are a much faster method than mine, not necessarily right or wrong, we both still got the same answer, but I tend to overthink and overcomplicate and your method helps me reduce that. For example: I changed the denominator first and then multiplied the denominator out for the first linear equation and the 2nd linear equation I found the LCD for 3 and 4 first, then changed the 11 to 55/5 and added it to 2x/5 as 55+2x/5 and then found the LCD for 12 and 5 being 60. So I still found the right answer, but ended up making waay more work for myself and your methods very much helps me reduce all that work. So thank you so much, I love your videos so much, it helps
Good job classifying as linear....some would say that it is rational because of the fractions. Multiplying denominators will always find a common denominator, just not always the least common denominator. I like giving the multiplier to the numerators then reduce as a single fraction...easier to see.
I think a better solution will be looking for the LCD and performing the mathematical process. It'll be the same as the video solution but will teach the learner more of performing mathematical process to simplify. x/2 + x/3 = 10 ; look for LCD which is 6, then simplify left side (3x + 2x)/6 = 10 ; cross-multipying, we get 5x = 60 x = 60/5 = 12
As someone who teaches mathematics, it depends upon the intent of the lesson. For efficiency, it is usually best to eliminate the fractions immediately by multiplying both sides of the equation by the factors that comprise the least common denominator as shown in the video. The only thing I would have shown differently is in the simplifying, as it is inefficient to first multiply and then divide, i.e. any products without x should be left factored for maximum efficiency. For the first problem, since the LCD=2*3 that would be 5x=10*2*3 thus x=2*2*3=12; and, the second equation would yield 11x=11*3*4*5 so x=3*4*5=60.
Well hmmm. I see your basis statement is a pure numeric statement which is True. Unfortunately, the problem given us contained symbolics, namely variable "X," and asked to solve for X. That poses a contradiction when you put the X terms back, because it yields a different answer. How'd you lose your symbolics? 😊 Well don't just remove them without using the proper rules for the type of equations involved. This lesson was about solving for X after finding a common denominator for each term, say the Least Commom Divisor among terms. Just a tech note: Given a pure numeric equation, it will contain there are no variables, and you're usually asked to simplify or reduce it until is become irreducible. Given a symbolic, usually we are asked to solve in terms of one or more variables. Like the number and type of roots. I'm not trying to bust you chops, but cut short a bad habit and save you future grief. I'd hate for this very correctable habit to lead to your slumped, tattered body in a gutter, muttering "math sucks," while swigging bottles of Woolite. 🥵😊♥️ Hang in there, we're supposed to help each other. Cheers
Many thanks Susanne, you are an excellent teacher. At the age of 84, I am pleased to announce that I nailed them both - the first one in my head. I am so glad that you skipped the words "lowest common denominator" (LCM), which I think is so out-dated - even for large denominators. In my opinion, it is far faster and more efficient to simply multiply the denominators, as you did, to find a number into which each denominator will divide. Unless the LCM is obvious by inspection, the commonly taught method of finding it is such an unnecessary waist of time and a step that could lead to unnecessary arithmetic errors.
Un calcolo semplicissimo da eseguire applicando le regole delle operazioni tra frazioni è stato trasformato in un procedimento complicato, non scorrevole, con eccessivi rimandi. Questo succede spesso in questo canale!
The first one I did cross multiply picking 6 as the denominated and then multiplying the top left half by 3 and the top right half by 2 and the removing the 6 by multiplying the rhs by 6 - I think this was how I was taught to do it but I could be wrong it’s like 36 years ago now 🤣
My way of solution ▶ x/2 + x/3 = 10 ⇒ 2*3= 6 we multiply both sides of the equation with 6, we get: 3x+ 2x= 60 5x= 60 ⇒ x= 12 b) x/3 + x/4 = 11 + 2x/5 ⇒ 3*4*5= 60 we multiplay both sides of the equation with 60, we get: 20x+ 15x= 60*11 + 24x 35x= 660 + 24x 11x= 660 ⇒ x= 60
Yeah that is the way it's taught but as a shortcut you can just multiply the denominators and multiply both sides by that number it will clear the fractions. She just changes the order of when you do things usually you add the fractions before you multiply instead you multiply first before you add because at that point it's integers with a variable.
The way I was taught to approach these was to first get all the x on one side, then get the fractions to a common denominator and the run through the calculation to get an answer so, for the first one: (X/2) + (X/3)=10 (3X/6) + (2X/6)=10 (5X/6)=10 Here we have a choice, we can notice that 10 is divisible by 5 to give 2 so X must be 2*6 or we can go the long way and multiply both sides by 6 the divide by 5 to give X=12. The second we just subtract the (2X/5) from each side, get all three fractions over 60 and then do the calculations. Again we have a choice of noticing that the figure on the right is the same as the multiplier on the left so X must equal the denominator or of going the long way and multiplying both sides by 60 then dividing by 11. Both approaches work, it’s just a case of preference and selecting which ever is easier for us and the problem.
this one I did on thumb nail so I think I am past the level 1. I would like to see tricks involving ratio proportion as well as more involving Log and differentiation
Multiply anything by 1 and you get the same value. So you can multiply the first term x/2 by 3/3 giving you 3x/6. Do the same to the second term but multiply x/3 by 2/2 giving you 2x/6. Now both terms have the same denominator and can be added. I think this method is more simple.
Bonjour, j'adore votre chaine. Mais sur cette vidéo je trouve que la réduction au même dénominateur est compliquée et peut entrainer des erreurs de calcul. Merci à vous. Hello, I love your channel. But on this video I find that the reduction to the same denominator is complicated and can lead to calculation errors. Thank you.
A few months ago I probably wouldn't have known what to do with such a problem (I haven't had a maths class since 1996), but I'm fairly confident I can do this now! OK, so: x/2 + x/3 = 10: 3x/6 + 2x/6 = 10: 5x/6 = 10: (10 x 6=) 60 = 5x: *x = 12*
In both examples, what if the denominators don't end up at 1? Also what happens if I cannot find a number that is divisible in each of the fractions? I often find I can follow the examples easily but once I get a problem in the real world that uses a slightly different pattern it fails 🤯
Before watching the video: (1) x = 2 * 3 * a. x/2 + x/3 = 10 = 5*a. a = 2. x = 12. (2) x = 3 * 4 * 5 * a. x/3+x/4 = 35 * a = 11 + 2*x/5 = 11 + 24*a. a = 1. x = 60.
Probably not the method but I got the same result. With x/2 being 50% and x/3 being 33% of x. Together they make 10 = 83% of x. Making a 100% of x = 12
But it is about knowing the formulaic process so that you can use that to solve the ones you can’t figure out in your head. Just because you can figure out the simple ones in your head doesn’t mean the formula is useless because eventually you will run into equations that aren’t that easy. Anyone can figure out the simple ones in their head, it is about knowing the process for the complex ones you will run into.
Once upon a time, when the dinosaurs still roamed the earth and computers were all mainframes, my junior high math teacher frequently admonished us to never say "cancel," but to use the term "divides out."
Technically, that teacher is correct. Admonishment seems too strong an approach. Did the teacher at least explain why divides out is the appropriate way to call it? Cancelling (which is akin to annihilation) leaves 0 as a multiplier as in x+(-x)=0*x, whereas, dividing out a common factor leaves 1 as a multiplier.
I could make a word problem out of it, but it would not exactly be practical. At a birthday party, there are ten children and some adults. Half of the attendees are boy children and a third of the attendees are girl children. How many people were at the party? The point of solving equations is practice, at this basic stage, not real world applications.
Yes, practice to be prepared to practice further mathematical concepts until they model real world situations beyond simple accounting. However, word problems such as the one I wrote give practice at solving real world problems, because all real world problems are expressed in words before logic is applied to solve them, regardless of whether they can be translated mathematically.
@ Why not just practice real world applications ? To answer your question, the answer to how many kids were at the party, is undefinable. I’m certain that this can be expressed as some sort of symbolic and meaningless equation.
@@LysanderLH I amended the word problem. Your statement was not correct though. The number of children was certainly defined; however, the problem was not well-defined, since it was impossible to determine how many people were at the party given how I initially wrote the problem.
Instead of multiplying by 6, to get rid of fractions, multiply by (2x3) it saves a step, it works really well if the two denominator's have no common denominators too.
This is what pisses me off about the way math is taught. Its the reason that I didn't get good grades in math. I can look at that very simple equation and immediately know that x equals 12. Instead I was forced to complicate it. Ridiculous. Show me a complex equation I can't solve in 2 seconds by looking at it please. I mean obviously I understand the process now but I think that the attempt to simplify math actually over complicates it.
As a mathematics teacher, I would indeed have given you more and more complex equations until you agreed that you needed better techniques than what you were doing. We start simple so that the practice is easy for all students. Yes, there are simpler ways, so that the complex methods you hated are overkill. What you seem to want is to be thrown into the deep end so that you either sink or swim and that no practice in the shallow end should be given you in advance.
There will come a pont when you simply can not calculate the result that way, perhaps due to complexity, and when that happens, you'll need to fall back onto proven principles and techniques. This video demonstrates ways to appraoch a specific example in a step by step way. Yeah, a lot of people can solve it in their head, as I did, but that's missing the point.
It's a little painful watching you solve for x. There's a fifth grade simpler way! Fifth grade math: make like denominators 3x/6 + 2x/6 = 10. Gather like terms. 5x/6 =10.... multiply by 6...5x =60. Divide by 5..x ,=12
Hey math friends! If you’re enjoying this video, could you double-check that you’ve liked it and subscribed to the channel? It’s a simple equation: your support + my passion = more great content! Thanks for helping me keep this going - you’re the best!
Your teaching style is fantastic! It's great that you don't skip any steps, no matter how simple or obvious they might seem to be. I've always been of the opinion that a teacher should not make any assumptions about how "easy" or "obvious" something is and, instead, just explain everything. It's far better to over explain something than to not give enough explanation and leave the student confused.
Even more so online, where feedback is much more cumbersome.
If the student is confused by a faster pace, maybe his place is NOT in the Oxford University ?
@@MalengWan I don't recall any reference to Oxford or any implication that this was supposed to be university level maths. Could you point out where I missed those, please?
I love this channel. I'm in my 50s and just following along for fun. I forgot a LOT from my high school and college days like the quadratic equation. Thanks for posting these.
I'm 60 years old I'm watching you from Turkey
Thank you very much!
I suddenly realize that in school, they taught us without explaining why.
For example, when moving a term to the other side of an equation and simply changing its sign from positive to negative, they didn't tell us that what we're actually doing is subtracting the number from both sides of the equation. That makes it much more logical, of course!
❤
As a mathematics teacher myself, I believe it is a disservice to students for teachers to focus on narrow techniques instead of broad fundamentals. Being able to derive the narrow techniques is far more useful than memorizing them. There have been a few teachers that I have wondered whether they actually knew the whys versus just memorizing formulae.
Very good point 👍
Me too!!
I don't remember getting an explanation in school
x(1/2+1/3)=10
x(3/6+2/6)=10
x(5/6)=10 | *6/5
x=6*10/5
x=12
How I did it too.
me too, from indonesia
4 ÷4=1 Too many steps. Good thing I finished high school before coming to America.
Thank you for showing your work
My version - restate the fractions using least common denominator (6); thus 3x/6 plus 2x/6, add together to get 5x/6=10. Then multiply both sides by 6 to eliminate the denominator, resulting in 5x=60. Divide both sides by 5 to get x=12
I'm 70 and do these just to keep the mind sharp. I solved that problem as you did, just did it as multiplying each side by 6/5, combining the step.
On the second I subtracted the 2x/5 from the left side first, and apparently kept from having such big numbers to deal with
20x/60 + 15x/60 - 24x/60 = 11; then 11x/60 = 11; multiply by 60/11 quickly gives the answer of 60.
As is pointed-out in the comments, you did not skip things, even 6 divided by 3 equals 2. This is why I understand how the equation works. I can understand by what mechanisms things are kept *equal* to each-other. Math teachers were like "This is obvious, so I skip"... man, if it was obvious to me, why would I need you to teach me anything in the first place... Love your work, queen! 💪
Clear and concise - a great refresher for solving equations for those of us who rarely use these types of problems but who want to retain the skills to do so should we ever need to.
Why would you ever need to ?
You have an excellent way for teaching and declaring what you do in addition to the meaning of doing and how to think to reach into conversations, excellent!!!, i love you do
You would make a great high school math teacher because you explain things: 1) clearly and simply; 2) step-by-step; 3) succinctly, and 4) at a very easy pace for students to follow......BTW, you are one of the few teachers of math who smile and with a truly genuine. That goes a long way in making learning enjoyable.
Interesting at 07.30 in splitting the multiplication into to parts. I remember solving a maths problem at junior school in that way and my teacher said it was the wrong method. That has stuck with me for over 50 years: I knew I was right, the result was the same, but his proscribed method was different! I'm glad I've resolved that issue before I die!
I am 72...... haven't done much maths since I stopped teaching science about fifteen years ago. I love trying to do these myself first then follow your solutions to see if I got it right..... such good brain training for an oldie!
These equations are not hard but your delivery is wonderful!
Love your tutorials Susanna, you explain things very clearly and methodically. Do you have a tutorial on factorials?
I’m so close to solving the Riemann Hypothesis! If I had a teacher like you back in the day I guarantee I’d have finished! Easily!
Really enjoying your videos, you do a fantastic job of talking thru every step and not skipping the tiny steps, thank you. What application/tools are you using for the math?
Great lessons and easy to binge watch them!
You’re an awesome teacher!
Great stuff! I really enjoy your simple but complete explanations. In the second example, I found it easier to subtract the 2x/5 from both sides at the beginning, getting all of the x's on one side early.
New subscriber here. I agree with all the | comments | after each of the 3 vids I've seen so far. The only I can add is that the use of color is fantastic, as a visual learner, it really helps me to focus on the term in play. Thank you Math Queen!
Many (many) years ago when my kids were young and asked for help with math homework, one thing I pushed them on over and over, which would usually bug them, was to double check, or check their work. That is, plug the solution back into the equation(s) and ensure it works out. I was kind of hoping you would do that here. You might consider including that to your video. (I fully agree with your solutions, but I did still plug them back in to double check - the confirmation feels valuable)
LOVE THESE! - takes me back to the good old school days.
...except that the teachers were usually not that thorough at explaining the fundamentals.
Or to the bad old school days.
I agree, you have a unique talent for explaining math in a very easy to understand format. Great stuff; thank you.
Wow, thank you so much for your kind words!
It's not really unique is it ?
Susanne you have made legend status in my house. Everyone loving your videos and teaching prowess.....Happy New Year.
I can listen to you forever…. Enchanting to the math mind 🥰
I'm just going to say I appreciate you solving an equation I can actually follow. The last few have been way over my head...then I feel silly when I hear how to get the solution.
I really enjoyed the way how you solved it. It seemed too easy. Jejeje! I learnt how you multiplied 60. 11. Thanks for sharing. Regards and blessings from 🇵🇦😊
I love love love your videos. I love that you put the problems in the thumbnail, bc I like to solve it my way and then watch you solve it your way and compare notes to see what I can do to solve it faster, which your videos are a much faster method than mine, not necessarily right or wrong, we both still got the same answer, but I tend to overthink and overcomplicate and your method helps me reduce that.
For example: I changed the denominator first and then multiplied the denominator out for the first linear equation and the 2nd linear equation I found the LCD for 3 and 4 first, then changed the 11 to 55/5 and added it to 2x/5 as 55+2x/5 and then found the LCD for 12 and 5 being 60. So I still found the right answer, but ended up making waay more work for myself and your methods very much helps me reduce all that work. So thank you so much, I love your videos so much, it helps
Good job classifying as linear....some would say that it is rational because of the fractions.
Multiplying denominators will always find a common denominator, just not always the least common denominator.
I like giving the multiplier to the numerators then reduce as a single fraction...easier to see.
Love these lessons! Thanks so much❤
I think a better solution will be looking for the LCD and performing the mathematical process. It'll be the same as the video solution but will teach the learner more of performing mathematical process to simplify.
x/2 + x/3 = 10 ; look for LCD which is 6, then simplify left side
(3x + 2x)/6 = 10 ; cross-multipying, we get
5x = 60
x = 60/5 = 12
As someone who teaches mathematics, it depends upon the intent of the lesson. For efficiency, it is usually best to eliminate the fractions immediately by multiplying both sides of the equation by the factors that comprise the least common denominator as shown in the video. The only thing I would have shown differently is in the simplifying, as it is inefficient to first multiply and then divide, i.e. any products without x should be left factored for maximum efficiency. For the first problem, since the LCD=2*3 that would be 5x=10*2*3 thus x=2*2*3=12; and, the second equation would yield 11x=11*3*4*5 so x=3*4*5=60.
Haha, I’m really early to this video. I’ve been enjoying your videos recently, so keep up die gut arbeit!
Great solutions my fellow Mathematician ❤ keep up
You're a very good teacher 👍
60/2 +60/3 = 50 therefore hence not = to 10 so equation not balanced. But my method gave me correct answer and it got verified balancing equation.
x/2 + x/3 = 60
3x + 2x = 60
5x = 60
x= 12
check = 12/2 + 12/3 = 10
6 + 4 = 10
therefore L.H.S = R.H.S
try make common denominator like normal fractions simplifications and then bring denominator to answer side and multiply.
Well hmmm.
I see your basis statement is a pure numeric statement which is True.
Unfortunately, the problem given us contained symbolics, namely variable "X," and asked to solve for X.
That poses a contradiction when you put the X terms back, because it yields a different answer.
How'd you lose your symbolics? 😊
Well don't just remove them without using the proper rules for the type of equations involved. This lesson was about solving for X after finding a common denominator for each term, say the Least Commom Divisor among terms.
Just a tech note: Given a pure numeric equation, it will contain there are no variables, and you're usually asked to simplify or reduce it until is become irreducible. Given a symbolic, usually we are asked to solve in terms of one or more variables. Like the number and type of roots.
I'm not trying to bust you chops, but cut short a bad habit and save you future grief. I'd hate for this very correctable habit to lead to your slumped, tattered body in a gutter, muttering "math sucks," while swigging bottles of Woolite. 🥵😊♥️
Hang in there, we're supposed to help each other.
Cheers
Im not saying im 100% correct but my answer made the equation balanced.
Many thanks Susanne, you are an excellent teacher.
At the age of 84, I am pleased to announce that I nailed them both - the first one in my head. I am so glad that you skipped the words "lowest common denominator" (LCM), which I think is so out-dated - even for large denominators. In my opinion, it is far faster and more efficient to simply multiply the denominators, as you did, to find a number into which each denominator will divide. Unless the LCM is obvious by inspection, the commonly taught method of finding it is such an unnecessary waist of time and a step that could lead to unnecessary arithmetic errors.
Un calcolo semplicissimo da eseguire applicando le regole delle operazioni tra frazioni è stato trasformato in un procedimento complicato, non scorrevole, con eccessivi rimandi.
Questo succede spesso in questo canale!
From calculus to linear equations. Whatever you neeed Susanne got it covered. 🥰
That's great to know bro.
Wonderful being a wee bit rusty on the ru,especially. Terrific teaching style.
Great explanation
The first one I did cross multiply picking 6 as the denominated and then multiplying the top left half by 3 and the top right half by 2 and the removing the 6 by multiplying the rhs by 6 - I think this was how I was taught to do it but I could be wrong it’s like 36 years ago now 🤣
Really appreciate the way wo explain the most "mathy" things . Do you plan to start with some Math courses (like college algebra , calculus )
12, of course. But I'll enjoy listening through your explanation. I just LOVE to hear myself described as one of your lovelies!
My way of solution ▶
x/2 + x/3 = 10
⇒
2*3= 6
we multiply both sides of the equation with 6, we get:
3x+ 2x= 60
5x= 60
⇒
x= 12
b) x/3 + x/4 = 11 + 2x/5
⇒
3*4*5= 60
we multiplay both sides of the equation with 60, we get:
20x+ 15x= 60*11 + 24x
35x= 660 + 24x
11x= 660
⇒
x= 60
I did the first one by multiplying the fractions by 3/3 and 2/2 to get common denominators and then just adding them
Yeah that is the way it's taught but as a shortcut you can just multiply the denominators and multiply both sides by that number it will clear the fractions.
She just changes the order of when you do things usually you add the fractions before you multiply instead you multiply first before you add because at that point it's integers with a variable.
What software do you use?
The way I was taught to approach these was to first get all the x on one side, then get the fractions to a common denominator and the run through the calculation to get an answer so, for the first one:
(X/2) + (X/3)=10
(3X/6) + (2X/6)=10
(5X/6)=10
Here we have a choice, we can notice that 10 is divisible by 5 to give 2 so X must be 2*6 or we can go the long way and multiply both sides by 6 the divide by 5 to give X=12.
The second we just subtract the (2X/5) from each side, get all three fractions over 60 and then do the calculations. Again we have a choice of noticing that the figure on the right is the same as the multiplier on the left so X must equal the denominator or of going the long way and multiplying both sides by 60 then dividing by 11.
Both approaches work, it’s just a case of preference and selecting which ever is easier for us and the problem.
this one I did on thumb nail so I think I am past the level 1.
I would like to see tricks involving ratio proportion as well as more involving Log and differentiation
The product of the two denominators is always A common denominator, but not necessarily the LCD. But, it’s a brutally efficient way forward.
Multiply anything by 1 and you get the same value. So you can multiply the first term x/2 by 3/3 giving you 3x/6. Do the same to the second term but multiply x/3 by 2/2 giving you 2x/6. Now both terms have the same denominator and can be added. I think this method is more simple.
That's how I did it.
Bonjour, j'adore votre chaine. Mais sur cette vidéo je trouve que la réduction au même dénominateur est compliquée et peut entrainer des erreurs de calcul. Merci à vous.
Hello, I love your channel. But on this video I find that the reduction to the same denominator is complicated and can lead to calculation errors. Thank you.
1st equation- multiply both sides by 6
6x/2+6x/3=6 × 10
3x+2x=60
5x=60
X=12
Check- 12/2 + 12/3 = 10
6+4=10 ♡
First equation: (3x + 2x) / 6 = 10 so 5x = 60 and x = 12
Second equation: (20x + 15x) / 60 = 11 + 24x / 60 so (35x -24x) / 60 = 11 or x = 60 . 11/11 = 60
I love the video
I suppose:
(3x + 2x)/6 = 10
3x + 2x = 60
5x = 60
x = 12
I hammered it out but I think it’s right.
Dankeschön ❤❤
I still got it. Math is the best!!!
Nice to brush the rust off the brain cells, thanks.
excellent
Solutions:
(1)
x/2 + x/3 = 10
3x/6 + 2x/6 = 10
5x/6 = 10 |*6/5
x = 12
(2)
x/3 + x/4 = 11 + 2x/5 |*5
20x/12 + 15x/12 = 55 + 2x |-2x
35x/12 - 24x/12 = 55
11x/12 = 55 |*12/11
x = 60
Well done! 😍
if I was taught like this....... I'm telling you ma'am I would have been professor by now.....🙂
Proof that I had ass teachers back in my day. I understand her easily. But struggles greatly learning the same stuff back in my day. Hmmm…
A few months ago I probably wouldn't have known what to do with such a problem (I haven't had a maths class since 1996), but I'm fairly confident I can do this now!
OK, so:
x/2 + x/3 = 10:
3x/6 + 2x/6 = 10:
5x/6 = 10:
(10 x 6=) 60 = 5x:
*x = 12*
Your English language is beautiful. I wish we here in the USA could speak as well as you do . I'm sure it's your second language. 😊
Thank you so much! I’m German and I try to get used to the different mathematical expressions. But I enjoy learning again as well.
1.
3x 2x
------- + ------- = 10
6 6
3x + 2x
------------ = 10
6
5x = 60
x = 12✅
2.
X + X - 2X
---------------- = 11
3 * 4 * 5
X + X - 2X = 11
----------------
60
20x + 15x - 24x
------------------------- = 11
60
35x - 24x = 660
11x = 660
X = 660/11
X = 60✅
x(7/12-2/5)=1
x(35/60-24/60)=1
x(11/60)=1 | *60/11
x=60/11
Hello lovely Suzanne ❤❤
Nice. I feel like we just cleaned up a mess.
One I can do! :)
Do you do all these steps for proving that that’s what the answer was?
X/3+X/4=11+(2X)/5 X=60
In both examples, what if the denominators don't end up at 1? Also what happens if I cannot find a number that is divisible in each of the fractions? I often find I can follow the examples easily but once I get a problem in the real world that uses a slightly different pattern it fails 🤯
Before watching the video:
(1) x = 2 * 3 * a. x/2 + x/3 = 10 = 5*a. a = 2. x = 12.
(2) x = 3 * 4 * 5 * a. x/3+x/4 = 35 * a = 11 + 2*x/5 = 11 + 24*a. a = 1. x = 60.
Elementary, my dear Watson but ... I follow you because I love your smile and the way you explain things.
10 = (3x) / 6 + (2x) / 6 = (5x) / 6
= (5/6)x. So, x = (6/5) * 10 = 12.
Probably not the method but I got the same result. With x/2 being 50% and x/3 being 33% of x. Together they make 10 = 83% of x. Making a 100% of x = 12
X/2+X/3=10 X=12 It’s in my head.
But it is about knowing the formulaic process so that you can use that to solve the ones you can’t figure out in your head.
Just because you can figure out the simple ones in your head doesn’t mean the formula is useless because eventually you will run into equations that aren’t that easy.
Anyone can figure out the simple ones in their head, it is about knowing the process for the complex ones you will run into.
@@maddevil7474The process would be the same, but it would likely be too much to hold onto in one's head in the more complex cases.
Once upon a time, when the dinosaurs still roamed the earth and computers were all mainframes, my junior high math teacher frequently admonished us to never say "cancel," but to use the term "divides out."
Technically, that teacher is correct. Admonishment seems too strong an approach. Did the teacher at least explain why divides out is the appropriate way to call it? Cancelling (which is akin to annihilation) leaves 0 as a multiplier as in x+(-x)=0*x, whereas, dividing out a common factor leaves 1 as a multiplier.
@@bryanalexander1839 Yes, he did!
On my short list of best junior high teachers I had.
Yes !!!!! Got it right !! Ha!!!
Hi. Can you show me a practical application for this equation? Where would it occur ?
I could make a word problem out of it, but it would not exactly be practical. At a birthday party, there are ten children and some adults. Half of the attendees are boy children and a third of the attendees are girl children. How many people were at the party? The point of solving equations is practice, at this basic stage, not real world applications.
@ practice for what though? practice for more practice?
Yes, practice to be prepared to practice further mathematical concepts until they model real world situations beyond simple accounting. However, word problems such as the one I wrote give practice at solving real world problems, because all real world problems are expressed in words before logic is applied to solve them, regardless of whether they can be translated mathematically.
@ Why not just practice real world applications ? To answer your question, the answer to how many kids were at the party, is undefinable. I’m certain that this can be expressed as some sort of symbolic and meaningless equation.
@@LysanderLH
I amended the word problem. Your statement was not correct though. The number of children was certainly defined; however, the problem was not well-defined, since it was impossible to determine how many people were at the party given how I initially wrote the problem.
12
The lowest common denominator is 6 so multiply everything by 6
3x +2x = 60
5x=60
X=12
If you were my teacher, I would have understood this
When is 1/8th = 3.5?
(3x+2x)/6=10
5x=60
x=12
Instead of multiplying by 6, to get rid of fractions, multiply by (2x3) it saves a step, it works really well if the two denominator's have no common denominators too.
Interesting coincidence that in Example 2 the LCD happened the be the value for x.
The answer is x=12. 12/2 +12/3=6+4=10.
12!
The first one instantly shouted 12.
Actually, x=12 appears to be the correct answer in my simple mind. 60 does not work in that equation…but I am no mathematician.
How about twelve.
X,2×+5=2
12.
Do you use a mouse to write 😮?
x=12?
This is what pisses me off about the way math is taught. Its the reason that I didn't get good grades in math. I can look at that very simple equation and immediately know that x equals 12. Instead I was forced to complicate it. Ridiculous. Show me a complex equation I can't solve in 2 seconds by looking at it please. I mean obviously I understand the process now but I think that the attempt to simplify math actually over complicates it.
As a mathematics teacher, I would indeed have given you more and more complex equations until you agreed that you needed better techniques than what you were doing. We start simple so that the practice is easy for all students. Yes, there are simpler ways, so that the complex methods you hated are overkill. What you seem to want is to be thrown into the deep end so that you either sink or swim and that no practice in the shallow end should be given you in advance.
There will come a pont when you simply can not calculate the result that way, perhaps due to complexity, and when that happens, you'll need to fall back onto proven principles and techniques. This video demonstrates ways to appraoch a specific example in a step by step way. Yeah, a lot of people can solve it in their head, as I did, but that's missing the point.
It's a little painful watching you solve for x. There's a fifth grade simpler way! Fifth grade math: make like denominators 3x/6 + 2x/6 = 10. Gather like terms. 5x/6 =10.... multiply by 6...5x =60. Divide by 5..x ,=12
x=12
feeling pretty good that I did the first one in my head just from the thumbnail.
Big deal.
IKR
12 in the head..