(5/2 + 1/3) divided by 5/2 = ? BECAREFUL! Many will make this MISTAKE!

How to solve complex fraction math problems.
TabletClass Math Academy
Help with Middle and High School Math
Test Prep for High School Math, College Math, Teacher Certification Math and More!
All Courses - TCMathAcademy.com/
✓Help with Middle and High School Math (Public/Private Schools)
✓High School & College Math Test Prep
✓Teacher Certification Math Test Prep
✓Homeschool Math Program and Courses for Pre-Algebra, Algebra 1, Geometry, Algebra 2 and Pre-Calculus.
Popular Math Courses:
Math Foundations
tabletclass-academy.teachable...
Pre-Algebra
tabletclass-academy.teachable...
Algebra
tabletclass-academy.teachable...
Geometry
tabletclass-academy.teachable...
Algebra 2
tabletclass-academy.teachable...
Pre-Calculus
tabletclass-academy.teachable...

[@chestermarcol3831]

Why not just rewrite the problem as 5/2 /5/2 + 1/3/5/2 reduced to 1 + 1/3 x 2/5 reduces to 1 2/15 and reduce that to 17/15 that seems a lot shorter to me.

[@ginny5937]

I enjoy your videos because I'm 79 years old and solving these problems stimulates the old gray matter. Plus, your voice is soothing and I love it when you say, "Don't panic!". 😊

[@markanderson6707]

I think there are a lot of old-timers watching. (b1949)

[@jannetteberends8730]

I’m 70, and it’s so much fun to solve the problems.

[@theDemocraticway]

I’m kinda old and slow but back in the day preferred to see the answer as a mixed number rather than an improper fraction. In 15 seconds of looking at that , my answer was a mixed number number 1 2/15

[@luisPcordeiro]

me too.

[@christysatfield8302]

I did this problem the same way, however what I said to myself was 1+ 1/3x2/5= 1 2/15. Will I always come out with the correct answer doing it that way?

[@brettgofgosky1911]

​@@christysatfield8302you are right, this dude was taught by someone with only one oar in the water or maybe by joe biden😮😅

[@brettgofgosky1911]

​@@christysatfield8302here is a math problem for you. Many college professors have given up. Ready, A pair of shoes and a dress costs $110. The dress costs $100 more than the shoes. How much did the shoes cost?

[@kathyradford7187]

Agreed

[@xlwatcher8885]

if you know fractions, immediately make this problem 1 + 1/3 / 5/2. Which is 1/15 * 2 or 2/15. Add 1, immediately rename the 1 as 15/15, add to 2/15, to get correct answer of 17/15. Approx 5 seconds. If you don't understand the concept of division being multiplication of reciprocal, check out a previous video to learn that. it's a big, important topic.

[@detroittigersandotherbaseb7220]

I got 17/15 but I found the common denominators of 15/6 +2/6 for (17/6)/(5/2). When dividing fractions, you invert and multiply for (17/6) * (2/5) for 34/30 or 17/15

[@erniedichiarafromminecraft7990]

When I first look at a problem like this it was simple to break into two fractions simplify the first and multiply the second like you did took me about 7 seconds to do the problem in my head

[@barbarasnetiker3452]

So why would you leave the answer as 17/15, instead of reducing it even further to 1 2/15 (1 and 2/15)?

[@jennifergrebner6994]

17/15 IS fully reduced, because in order to reduce a fraction, you need to be able to divide the top and bottom by the same number. 17 & 15 cannot be divided by the same number, so it cannot be reduced. The reason math teachers will often choose to leave the number as an improper fraction rather than changing it to a mixed number is that so often the number will need to be plugged back into something in order to finish answering the question. If you changed into a mixed number, you'd have to change it back into an improper fraction in order to plug it in.

[@TheLakingc]

I am over 75 and have not done this since 1993! I did this one correctly, but the quadratic problem needed review. I am having fun. I bought some math books for fun, but just forgot about them! So, this is a fun reminder.

[@doubledee9675]

I'm over 75 also (!) but it's 60 years since I finished secondary school and the last time I did maths. But some things never leave you and solving this was easy..

[@bigdog3628]

(5/2 + 1/3) / 5/2 is the same as (5/2 * 2/5) + (1/3 * 2/5) which is 1 + 2/15. 15 is the denominator so 15/15 + 2/15 is 17/15. (remember: [x + y] / x is the same as x/x + y/x this means 1 + y/x.)

[@timalexander4205]

67 year old here who uses your questions to keep my math skills up to speed. MBA and BA in econ, so I used math throughout my career. Yet, basic math still keeps me sharp in retirement. Thanks for these.

[@kathyradford7187]

I'm gonna start doing this, too.

[@terrytysinger6022]

Young whipper snapper; I'm doing the same at 70. He does make some sneaky tricky 😃

[@KW-gb9cd]

I multiplied the top and bottom by 2/5, turning the denominator into 1 and the numerator into 1 + 2/15, thus giving 1 2/15.

[@iowapanner2223]

Same here, except somehow I messed up my 2/5 x 1/3. Embarrassing. I'll play the old guy card on that one.

[@wernerviehhauser94]

Yup.

[@devonwilson5776]

Greetings. Without rewriting that which is given the answer is 17/15 or 1 2/15. The top portion, above the line, works out to 17/6. You will now divide 17/6 by 5/2 which is the same thing as multiplying 17/6 by 2/5. Following that we would cancel the common factor 2 in the numerator and denominator to get 17 times 1 in the numerator divided by 3 X 5 in the denominator resulting in 17 over 15 = 17/15.

[@th5841]

Easy: This can be simplified by splitting it into two fractions. The left fraction is 5/2 over 5/2, which is 1 the right fraction is 1/3 over 5/2. You multiply the upper and under part with 2 and devide them with 5. 1*2 over 3*5 devided by 5*2/2*5 (which is 1). Result 1 and 2/15.

[@apmcd47]

This is how I did it too.

[@argonwheatbelly637]

17/15, or if you prefer mixed, 1 and 2/15. Did this in about six seconds.

[@ernstpattynama6361]

So did I ! I kid you not !

[@mortenthorpe]

Yeah, about the same… the algorithm took me about 3 seconds

[@mortenthorpe]

2 generic steps to this algorithm… 1. Division by a fraction equals multiplication by its inverse, 2. Exploding compound fraction into subparts of its elements… (a+b)/c = (a/c) + (b/c)…

[@user-dn5bi4si5w]

What a shmart fellow.

[@raelsackey104]

They mislead people in the title, because they include parentheses where they don’t exist, that would change the way you do the problem.

[@barbou2you]

Thank you, it took me 12 years in school and another 68 years to really enjoy math! I was surprised how much I did retain just to get started!

[@jerry2357]

Multiply top and bottom by 2/5, giving 1+2/15. So 17/15. EDIT: There's no problem dealing with this as two terms, especially because the 5/2s cancel in the first term. (x+y)/x can be expressed as 1+y/x. My way means you don't need to consider LCDs at all, because 1 is obviously 15/15, meaning the fraction addition is just 15/15+2/15.

[@ginnyk891]

I did it the same way. I always look for the simplest way to solve the problem

[@DavidPilcher51]

I wish you would stop using a . as a multiplication symbol. If someone is struggling with maths already it’s even more confusing to see 3.2 as in three point two rather than 3x2

[@What_Sorroichio]

I forgot how to do this a long time ago,but when finding this video i remeber now.Thank you for making this video!! really helped me!!

[@grbenny]

As a retiree, 30 years with large retail chain, my orientation is retail math. A vendor wouldn’t quote cost of an item 17/15. 17/15 = 1.13, right? So is it wrong to convert all the fractions to decimals at the go? 5/2 = 2.5, 1/3 = .33. 2.5 + .33 = 2.83. 2.83/2.5 = 1.13 Isn’t this correct? For my purposes, it’s a lot faster and has fewer steps. 🤷‍♂️

[@nyc4max]

You could just split it into two divisions with 5/2 as the common denominator. Therefore it goes as follow: (5/2 / 5/2) + (1/3 / 5/2) = (5/2 * 2/5) + (1/3 * 2/5 ) = 10/10 + 2/15 = 1 + 2/15 = 1.2/15 =17/15 when converted to an improper fraction > 15 * 1 + 2 = 17/15. Period.

[@stevedietrich8936]

numerator simplifies to 17/6, then multiply by the inverse of the denominator, 2/5, resulting in 34/30, or 17/15.

[@geirs4117]

Why so complicated? Multiply above and below by 2/5 and you immediately get 1 and 2/15

[@johnm6011]

+1

[@waynelassiter2290]

I did basically the same. Converted the division to a multiplication by inverting the denominator. Then distributed the multiplication,and added

[@DayanandPandey-ns5qc]

Thanks sir a lot.

[@mingkee27]

This can be tricky, however, move the bottom to right side (corrected) (5/2 + 1/3) * 2/5 and ignore the right 2/5 for now Find LCM of the first two 15/6 + 2/6 >>> 15+2/6 >>> 17/6 Now multiply with 2/5 17/6 * 2/5 Answer is 34/30 or 17/15 When a/b divided by c/d, you can convert to a/b * d/c

[@Astrobrant2]

Is there any preference in math these days between an improper fraction and a mixed number. In my way of solving this, I get 1 2/15 (one and two fifteenths). Would that be acceptable?

[@annemcwilliams2577]

You make it so complicated. To divide fractions, Invert the divisor and cancel. So simple. Also, the word is 'problem', not 'prolm'

[@raya.pawley3563]

Thank you

[@kevinphanson]

You have a tendency to WAY overcomplicate simple math. Multiply top and bottom by 2/5. bottom becomes 1. multiply 2/5 through (5/2 + 1/3) to get 1 + 2/15 = 17/15. Very simple.

[@catherinewoodsellerbeckhor7560]

71 still able, love your challenges, my maths teachers would be proud!

[@Iceland874]

67 and still working in finance and on a financial modeling certification and CPA exam. Earned mba and ms in my 50s. I get about 90% of your problems correct. My mistake with some is jumping in without thinking them through first.

[@johnnygeneric161]

I get practically all of your problems correct. I'm an engineer with 43 years of experience. But it is ALWAYS good to go over the basics and keep your math chops working. Now, if I could just my daughter to watch these....

[@christysatfield8302]

Good for you.

[@luisPcordeiro]

question I'm using parenthesis below to make it clear in simple text format the original expression. Isn't (2+7)/7 just the same as the sum of 2/7 + 7/7? Thus, this is not the same as crossing canceling of course! We are not canceling, but producing a "1" that is summed to the final result and not multiplied by one. Sorry if my tech language is not accurate :) An alternative way to solve this, although I understand the video is also teaching more interesting stuff. The expression on the video could also be represented as (5/2)/(5/2) + (1/3)/(5/2) = 1 + (1/3)/(5/2) = 1 + (1/3).(2/5) = 1 + 2/15 = making it a mixed number of 1(2/15) or 17/15

[@detroittigersandotherbaseb7220]

I found the common denominators of 15/6 +2/6 for (17/6)/(5/2). When dividing fractions, you invert and multiply for (17/6) * (2/5) for 34/30 or 17/15

[@laurindapace2164]

I understand things ,Thanks?

[@mathewhorodner2000]

Just find the least common denominator for each. Multiply each fraction by 6. You get (15 + 2)/15 = 17/15.

[@erzefranz3470]

17/15 in about 10 seconds, in my head. dividing by 5/2 = mult by 2/5. Used the distributive law to multiply each part of the sum.5/2 & 2/5 = 1; 1/382/5 = 2/15. 1+2/15 = 17/15.

[@omarjette3859]

OOPS the 1/382/5 should read 1/3*2/5 🙂

[@SkeeterHawkins]

I find it much less complicated to simply find the common denominator of 6 and combine the two fractions in the numerator which is 17/6 and then multiply this fraction by the inverse of the denominator, 2/5. This simple multiplication yields 17/15...which to me is far simpler than involving all the cancelling that you explained. HOWEVER, I do realize the value of being able to solve math problems using a variety of methods. WELL DONE!

[@alanhilder1883]

Haven't watched yet but you were similar to my method, no cancelling needed.

[@kaileim970]

I didn't cross cancel or reduce and came up with a raw 34/30. At 66, nice to know I still got it!

[@olenfersoi8887]

I agree with you, though it is appropriate to reduce the answer by removing factor of 2 from numerator & denominator. In fact, this very teacher's "bowtie" method would result in that answer, to be reduced.

[@jamesbalderson3931]

easiest way I know to do this it to split the top and just say its 5/2 over 5/2 plus 1/3 over 5/2. 5/2 over 5/2 = 1 and cross multiply the other 1/3 over 5/2(2/5) to get 2/15 so you now have 1+2/15 or 15/15+2/15=17/15. this took no time to figure out in my head.

[@padraicbrown6718]

I got 17/15 but want to make sure I didn't screw up. So, I did (15/6 + 2/6) / 15/6 = 17/6 / 15/6 -> is it appropriate to "cancel out the sixes" here? to get 17 / 15 or was I just lucky? The calculator seems to agree with me, but I want to make sure what I did was sound.

[@thenetsurferboy]

Just bring 2/5 to the top line outside the bracket as is normal to divide 8 seconds mental for me It is really only yea 3 primary

[@YECRED22]

Thank you! Great tips!😊

[@jeff-cd1gw]

this is a simple one. First make the 5 a 4 and the 2 a 12 cross out the 4 and add the 7 after you take three from the 11 but before you multiple the one by one. subtract the 8 and presto you have an answer.

[@mathewhorodner2000]

Just find the least common denominator for each. Multiply each fraction by 6. You get (15 + 2)/15 = 17/15.

[@antonioforte7510]

The answer is 17 / 15

[@jt9458]

Instead of a finding a LCD and just multiply 2/5(5/2+1/3) to get 1+2/15=17/15

[@olenfersoi8887]

What is fascinating is to read the comments, with people using entirely different procedures & still coming up with the right answer...

[@terezap5756]

You are an excellent math teacher 👍👏👍

[@hardwood7955]

grade level please????

[@84com83]

do you say fraxion or fraktion?

[@jerilynn871]

how did you know to flip the 2/5?

[@christysatfield8302]

A fraction divided by a fraction: always becomes a multiplication problem where you flip the digits in the denominator and multiply the two fractions. I don’t know why it works but it’s a math rule of the “universe”.

[@MrMousley]

This is what I would do .... 5/2 + 1/3 / 5/2 15/6 + 2/6 / 5/2 17/6 / 5/2 17/6 x 2/5 17x2 / 6x5 17/3x5 17/15 I hope that's it .. and the fact that there are two 5/2s means there is a short cut !

[@detroittigersandotherbaseb7220]

That's what I did. I found the common denominators of 15/6 +2/6 for (17/6)/(5/2). When dividing fractions, you invert and multiply for (17/6) * (2/5) for 34/30 or 17/15

[@cadfael4598]

So if you are a PEMDAS guy, why do you do the fractional addition before the cross multiplication? Surely 5/2/5/2 = 5/2 * 2/5 = null

[@christysatfield8302]

Actually equals 1 😘

[@thenetsurferboy]

Because using BOMDAS you get rid of Brackets first

[@pmw3839]

That’s what I thought too. Division should be done before addition according to PEMDAS and BODMAS. There are no parentheses or brackets in this problem. So it should be: 5/2+1/3 / 5/2= 5/2 / 5/2 + 1/3 / 5/2= 1 + 1/3 x 2/5 = 1 + 2/15

[@lsw1944]

I think your explanations are rather convoluted and difficult to understand. There are easier ways of explaining this but you always take the long way around.

[@cobrellie]

Exactly … way to convoluted … just stretching the video out to long

[@StephenBoothUK]

Longer video = more adverts = more money Also, if it seems convoluted that leads to two possible conclusions in the viewers mind. Either the creator is a poor teacher or the viewer doesn’t have enough of a maths background to understand. The creator states repeatedly that he has decades of experience as a math teacher (presumably he, like many North Americans who constitute a little over 4.285% of the world’s population, thinks the name of the subject is mathematic) so one might think he must be a good teacher, which I could class based on decades of experience as a student (I’m always doing some sort of course either directly for work or as a side interest in my own time) as assuming facts not in evidence, so that only leaves the viewer does not have enough of a maths background which will drive a proportion to buy his premium courses on the website he plugs. I think the solution is to keep plugging away, watch videos from other maths KZbinrs and use a range of resources to expand your knowledge till you can cut through the waffle, obfuscation and misdirection to understand the fundamentals. This is actually very useful as in life in general you will encounter a lot of waffle, obfuscation and misdirection. Personally, I’m refreshing my maths skills as, at age 53, I’m finding things I learned in school but never used after school are becoming relevant again due to changes at work so I need to reopen those pathways in my brain that did those things. One of the things I’m doing to help me, following the principle that the best way to learn something is to try to teach someone else, is write what I’m refreshing up as a textbook, but it’s very much a slow going back burner type thing. I’m also realising that my maths teachers were really bad at teaching, although I’m sure that they would argue that they were good at teaching but when you have a class of 35 pupils you can’t meet everyone’s learning needs. Perhaps rather than streaming kids by ability we should stream them by learning style?

[@hulamei3117]

​@@cobrellieirritating

[@johncipolla8335]

When I as aki d I found the test questions so much harder than the lectures.

[@CarlWinter-oy8uf]

Answer-? its so much cross multiplying and dividing and inverting and re-inverting --now I am so lost --it takes So long and so many operations I have become confused!

[@ajsaus4825]

17:15

[@Martin-tn5lm]

Thanks so much.🙏

[@stevecox8979]

Hmmm I think the actual answer should be 1 2/15, you should resolve the answer down to the lowest form. But this may be me be picky the value is the same.

[@susanm1109]

When I took a precalculus class last year our instructor preferred that we leave answers as improper fractions rather than changing them to mixed fractions.

[@stevecox8979]

Interesting. OK, I was taught this method for UK O Levels back in the 80s. It has very possibly changed. We would have been marked down for not doing it the way I did, however I accept the value is the same, things change, and it may even been a localisation variation. I work in a school, not as teaching staff, but I will find out how they currently teach it. I'm very curious! Thank you for you reply it was very appreciated! :) @@susanm1109

[@christysatfield8302]

This opinion is probably a function of when you were first taught fractions. I probably learned fractions about 1960. I’m an “old math” girl🤣 who’s trying to learn a new way of doing math.

[@kathyradford7187]

I cant believe i got it right. I did it the first way. I remembered the cross multiplication but couldn't remember the 2 x 3 part.

[@TruthFrequencyNews]

What hurts my brain most is when showing me problems with wrong answers and wrong processes. Why do you showing improper ways first? Showing the right answer first but then showing multitudinous wrong or erroneous processes is frustrating. When teaching another to drive, you show the correct way first, right?

[@Jono2905]

As some other comments below, i am 71 and in 10 seconds get to 17/15 in my head. Why does it take such a long involved video to get to the same answer? Is it because children are not being taught properly in the first place?

[@alcorgarcia619]

1+(1/3 * 2/5) = 1 2/15 = 17/15

[@jerilynn871]

im back in college this fall and struggling with everything math 😢 from these fractions to basic algebra.

[@christysatfield8302]

Find a good programmed text: a short unit will be explained, then you’ll work some problems following the method you were just taught and finally, the correct answer will be given in the back of the book. I studied from a programmed text for algebra and geometry and Aced the math part of a test I had to take to get my credential in CA. I learned to love math then after hating algebra in high school. I’ve been following along with this math teacher and am having fun doing it. If you have to, listen to his lessons > once 🤓.

[@MaydayAggro]

Never had a problem with math. My dad was a math professor.

[@thenetsurferboy]

There is no such word as math. It is maths, short for mathematics

[@MaydayAggro]

@@thenetsurferboy lol. Ok.

[@Winkkin]

Was able to do it in my head in about 8 seconds.

[@dohanddonuts5716]

I feel that the most important equation in life is cross multiply and divide. It can figure so many things out. I've done a few of your equations and done quite well... please no word problems.

[@Wilkins_Micawber]

This problem could be expressed using BODMAS. (5 over 2 plus 1 over 3) divided by 5 over 2.

[@detroittigersandotherbaseb7220]

No. Since we don't use BODMAS. I found the common denominators of 15/6 +2/6 for (17/6)/(5/2). When dividing fractions, you invert and multiply for (17/6) * (2/5) for 34/30 or 17/15

[@craignewell5728]

There are no bracket so division should be first@@detroittigersandotherbaseb7220

[@jamesalexander7540]

I just split the problem into a/a + b/a

[@richardmelville5973]

By inspection, the answer is 1 and 2 fifteenths. Just multiply top and bottom by 2/5. Many of your solutions are supremely convoluted.

[@nuffroom863]

17/15 In my head and my stopwatch calls 5 seconds.

[@DayanandPandey-ns5qc]

Ans. 17/15

[@delroymorgan3480]

17/15 2:36 2:52

[@erastusikiki3217]

5/2 +1/3/ 5/2 = Answer 17/15.

[@terrybarrett2368]

I'm glad we use the metric system

[@kevinphanson]

this has nothing to do with any system of measurement. This is just common fractions. Same all over the world.

[@Bunkerdwarfputin]

@@kevinphanson You obviously don't understand the metric system.

[@tonyperring]

I didn't leave the answer as an improper fraction but answered 1&2/15

[@seibertmccormick184]

Well, I didn't figure it out in 5 seconds, like some others claim. It took me maybe a minute. But I got the same answer as everybody else: 17/15.

[@bigdog3628]

it takes practice. My old math teacher would do "buzz in" style math questions. (think something like family feud where the host asks a question and the fastest person to buzz in and answer correctly wins). After the first month of this most of the students where answering within a few seconds. Something like this example isn't too much harder. Just know the rules and spit it out like you're breathing.

[@craignewell5728]

2/2 is 1 not zero. so that becomes 1. 7/2 =3.5 1+3.5 = 4.5 correct answer. Division first not addition. Not a good example

[@harrymatabal8448]

Yes if that's what you want ok

[@dayvrob]

I am 76yo and my final answer is 17/15 or changed to a mixed number is 1 and 2/15

[@mathewhorodner2000]

I learned in school that improper fractions are your friends :- )

[@84com83]

do you know how to pronounce "pro:m" correctly?

[@brianburnside5949]

This is the same problem as 2/5(5/2+1/3). This then equates to 1 + 2/15. I try to be as lazy as possible.

[@Geoff_G]

It is ironic that in attempting to write "be careful" you made a mistake and missed the space between the words.

[@andrewmccartneyy6981]

Surely the final answer should be 1 and 2/15

[@kennethwright870]

1+2/15

[@Sailor376also]

1.1

[@mossesmadjemite2289]

4/3

[@tytn9978]

Another one I solved in my head within 15 seconds!

[@christysatfield8302]

Aren’t you just so proud.

[@mathewhorodner2000]

@@christysatfield8302 lol

[@larrydickenson8922]

Shouldn’t take almost 24 minutes to figure this out. 34/30 or 1 and 2/15 in my head.

[@cindyhammack68]

1/3

[@ozfire7]

Answer 1+2/15=17/15

[@jefferyfarr6542]

17/15

[@rodfulford4306]

1 2/15

[@Cladman3001]

No not me, I will always get it correct. Never got lower than an A in all math course through high school and college.

[@mathewhorodner2000]

I got a B in Advanced Placement Calculus

[@user-ri6rn7ti5h]

11/8

[@domenikahila8585]

17/6×2/5= 34/30

[@domenikahila8585]

17/15

[@olenfersoi8887]

Why not do the division problem using the "bowtie" procedur, resulting in 34 over 30, and THEN reduce it by taking out the factor of 2??? I think in algebra, as opposed to simple arithmatic, that is how it would be done.

[@topkatz58]

17/6 × 2/5 = 17/15

[@SteveSearle]

Why did you make it so complicated?

[@nicoleb3636]

I get 1 + 2/15 = 17/15.

[@user-tb9fk1jd4q]

2/15

[@cujorucujoru-pm2gl]

Why did you do this?! The most important lesson you had in this video was one of the last things you have shown. First multiply the reciprocal: (5/2+1/3) X 2/5 Multiple the parts of the sum: 5/2 X 2/5= 1 1/3 X 2/5= 2/15 Combine new parts of sum: 1+ 2/15 or 1 2/15 Why was this drawn out? You said to not jump into a question, but overthinking a simple task is more dangerous.

[@tamasmaksza6450]

I convert to decimal every chance I get.....

[@jackievanburen9301]

67 and got the same answer more easily in my head.

[@jackievanburen9301]

I watch because, though while in college I tutored algebra 1, 2 and chemistry, I taught 3rd and 4th afterwards for 27 years. This helps me to refresh.

[@garyalabama]

I think it is easiest just to bring up the 5/2 out of the denominator and multiply the numerator by 2/5.

[@seanaudette8389]

Math teacher, what is your opinion on common core? I personally hate it and i will never allow my kids to do it.