I work as a math teacher for 11th and 12th grade, and I have the same problem. It's incomprehensible to me, but since I don't teach the grades where you learn fractions, I can't say what went wrong before. All I know is that it is a huge hurdle in higher grades. How are you supposed to do derivatives if the basics are missing!

People prefer (and even back in the day preferred, at least where I went to school) to break them into psuedo percentages easily handled by the more straightforward and intuitive use of decimal points. In the grander scheme of hings, that people don;t do math at all anymore is understandable. When's the last time you worked out an azimuth and built a sundial, rather than glanced down at your digital watch? I told some kid to "work clockwise" and he looked at me like I had a penis growing out of my forehead.

Exotic fractions like those in he op rest firmly in the realm of academic arcanum. People do not find them applicable to their lives, and those things that are applicable are (and have always been) handled by the devices at our disposal. Chances are a previous generation was aghast at your/our inability to do or use some x that they felt was fundamental as well.

What are fractions?

(January 15, 2017 at 4:06 am)Firefighter01 Wrote: I own a business where employees need to now how to work out fractions and long multiplication to do their job efficiently. Here are my questions that I placed in their interview exam to determine if they know basic maths: 
1. 1/4 + 1/3 =
2. 1/4 x 1/3 =
3. 132 x 64 =

Only about 3 applicants over dozens that have sat the exam have answered all questions correctly. Most of them got the last one right, but they used their mobile phones.  I originally thought that the questions were too easy, but apparently they are now redundant? I don't know why teachers today don't teach fractions so that their students are competent in their usage, or is it a case that they aren't considered important enough to warrant any special attention?

It was either in 5th or 6th grade that problems like your #1 caused me to do some algebraic generalizing for the first time. After performing some number of straight forward problems of that sort it occurred to me the sum would always be sum of the denominators over their product, i.e.:  1/A + 1/B = (A + B)/AB.  Of course that just comes from generalizing the algorithm and not any deep insight into the meaning of fractions. 

Problems like you #2 should be trivial to anyone, at least algorithmically.  Unless of course lack of use and lack of insight into the algorithm's construction has just totally deserted you.  If one remembered only that multiplication by a unit fraction is the same as dividing by its numerator it wouldn't be too hard to work out an answer.  So  N • 1/3 = N ÷ 3 asks us to find just one third of N, the amount we started with.  We started with 1/4 so we only want a third of that.  If we imagine a cup measurer marked out in 1/4's with each fourth further divided by smaller lines into three equal sections, we'd wind up with 12 equal sections (of this smaller size) in the entire cup.  So our problem means how much of the entire cup is just one of those smaller sections and the answer becomes 1 of 12 equal parts, 1/12.

Operations with fractions were always taught between 2 and 3 years before students came to me.  Part of the failure of the american education system traditionally has been that we teach a shit load of things every year and then go on reteaching them since we never do any of it in enough depth to stick.  So I almost always had to work in some review too.  With the common core that was implemented just before I retired there is a chance this cycle will finally be broken. But then there are so many other things wrong with the education system as a whole that I wouldn't bet on it.  The only think I am positive about is that if we continually jump between one reform system and another forever students are screwed.

(January 15, 2017 at 8:45 am)Firefighter01 Wrote:

(January 15, 2017 at 5:47 am)downbeatplumb Wrote: When you say "hardly anyone" can you suggest a way to describe how many?

I'm only guessing, but I would say around 100 applicants. Try it yourself. It's surprising how many "educated" adults today don't know how to do simple maths without using Google.

But 100 out of how many and how would you portray that?

(January 15, 2017 at 4:06 am)Firefighter01 Wrote: I own a business where employees need to now how to work out fractions and long multiplication to do their job efficiently. Here are my questions that I placed in their interview exam to determine if they know basic maths: 
1. 1/4 + 1/3 =
2. 1/4 x 1/3 =
3. 132 x 64 =

Only about 3 applicants over dozens that have sat the exam have answered all questions correctly. Most of them got the last one right, but they used their mobile phones.  I originally thought that the questions were too easy, but apparently they are now redundant? I don't know why teachers today don't teach fractions so that their students are competent in their usage, or is it a case that they aren't considered important enough to warrant any special attention?

Where these young people just out of school, or older people, who may have forgot from lack of use? Just curious. I would think that those just out of school should remember enough to at least attempt it. Someone who hasn't done these things in ten years, I have a little more understanding.

Also, curious what type of job this was? Perhaps if you our having difficulty, you could test for the necessary aptitude, to do the problems, and those who could relatively quickly be shon how to do the problems.

Skills you don't use are really easy to forget. It's not exactly a skill that finds much use in everyday life, at least not for me. I'm surprised I still remember how.

(January 15, 2017 at 2:28 pm)Cthulhu Dreaming Wrote: Skills you don't use are really easy to forget. It's not exactly a skill that finds much use in everyday life, at least not for me.  I'm surprised I still remember how.

That gets at another weakness in the way math was traditionally taught.  Too procedural.  Just practice the algorithm without much comprehension for how it accomplishes what we're after or why it is a useful operation for particular questions.  Little wonder that so many adults feel so happy to deride the subject and avoid it wherever possible.

(January 15, 2017 at 10:54 am)Alex K Wrote: I work as a math teacher for 11th and 12th grade, and I have the same problem. It's incomprehensible to me, but since I don't teach the grades where you learn fractions, I can't say what went wrong before. All I know is that it is a huge hurdle in higher grades. How are you supposed to do derivatives if the basics are missing!

Easy! Don't go subatomic!

On a serious note, the wife can work out in a shoe sale exactly how much she is saving to the nearest cent, but the rest of the time, she adds up with her fingers...

(January 15, 2017 at 9:14 am)BrianSoddingBoru4 Wrote: But I do know that '132 x 64' doesn't involve fractions.

Wrong! Its 132/1 x 64/1