Geometry question.

[JohnnyReb]

Yes, it was on the sons geometry quiz. I know what he did now tell me what your answer would have been. I would have had the same answers as did the son and they would have been wrong.

Question:

Rewrite the fraction so that the numerator and denominator have the same units.....

1: 4 days/16 hrs

2: 25 minutes/2 hours

 

[thundley4]

1. 96 hrs/ 16hrs  or 4 days/(2/3day) = 6

2. 25 min/120 min or (5/12 hr)/2hrs = 5/24

[JohnnyReb]

1. 96 hrs/ 16hrs  or 4 days/(2/3day) = 6

2. 25 min/120 min or (5/12 hr)/2hrs = 5/24

That's the answer she was probably looking for...simplify the fraction...right....always simplify.

But that ain't exactly what she asked for and in the modern public school system you aren't supposed to assume, think or do more than is asked for...damned if you do and damned if you don't.

ETA: He took a geometry test 2 weeks ago today that he hasn't gotten a grade on yet...and she hasn't posted grades to the school site so he ain't lying....and his history teacher is even slower...and they are never allowed to keep or bring their test papers home with them....how in the hell am I supposed to help him if I don't know what he's getting wrong....grrrrrrr 

[NHSparky]

And since when the hell is that geometry?

This is more like 5th or 6th grade general math, tops.

[CG6468]

The teacher didn't ask for a solution to the problem. She/he asked merely to rewrite the fraction so the numerator and denominator have the same units.

[JohnnyReb]

And since when the hell is that geometry?

This is more like 5th or 6th grade general math, tops.

Those were the first questions on the test and absolutely my first thoughts also.

[NHSparky]

http://regentsprep.org/regents/math/geometry/FormulaSheetGeometry.pdf

This is closer to the speed of my 9th grade Geometry.

[JohnnyReb]

http://regentsprep.org/regents/math/geometry/FormulaSheetGeometry.pdf

This is closer to the speed of my 9th grade Geometry.

Can't do pdf with this computer.....

They certainly don't do geometry like they did 50 years ago.

...and the form of proofs they use now are nothing like we used.

Bill Ayers and the liberal school crowd should be put on trial.

[DumbAss Tanker]

I'm assuming these are two separate problems, as opposed to BOTH fractions having to have common denominators with each other?

To give them what they asked for, you'd basically pick the smallest time unit in each and multiply the other out to match, since you time units over a minute don't have a common base from one unit to the next higher and lower which makes factoring an impossible bitch, it would just be easiest to multiply out the higher units to reach the lowest common one.

If the assumption is wrong, I'd have to go with minutes on both as the lowest unit anywhere in either fraction.

So 4 days [X 24 hours/day] / 16 hours, = 96/16 hours, leaving it as an improper fraction which seems to be what's asked, though it reduces to 6 hours.

And 25 minutes / 2 hours [X60 minutes/hour] = 25/120 minutes, which reduces to 5/24 minutes.

---

Something I never really grasped adequately while I was screwing off in high school, but did learn and use heavily in Freshman physics and chemistry, it to treat the units of measurement algebraically, so instead of shortcutting throught the known to just say 25/2X60, you frame it all in terms where the units you don't want cancel out, which enables you to resolve from units and rates that aren't as intuitive and ingrained in daily life as time units are, like this (Using the time butt-simple time unit coversion of two hours into minutes for illustration):

  2 hours                       60 minutes         
--------------      X    ---------------  = 
      1                               hour                 

After identifying common units for factoring out like they were integers -

2 hours           60 minutes
---------       X     ---------- =
      1                   hour

setting it up to multiply through -
 
2 X 60 minutes
--------------- =
       1

final result is -

120 minutes

[zeitgeist]

And since when the hell is that geometry?

This is more like 5th or 6th grade general math, tops.

I can see this is going to be a popular response.  Geometry?  I think not.  And I would drop it a grade level at that. 


BTW The government was allowed to go back to math testing for certain apprenticable trades hiring.  I have found the best refresher for this new testing is 7-8 grade math. I won't tell you how many HS graduates can't even make it over that bar.   

This is a huge drop from thirty or so years ago when you at least had to be able to do algebra, geometry, and trig to get a decent score on the federal tests.   There were years  in the eighties and ninties when you could not give a 'math test' because it discriminated against women and minorities. 

[JohnnyReb]

I'm assuming these are two separate problems, as opposed to BOTH fractions having to have common denominators with each other?

To give them what they asked for, you'd basically pick the smallest time unit in each and multiply the other out to match, since you time units over a minute don't have a common base from one unit to the next higher and lower which makes factoring an impossible bitch, it would just be easiest to multiply out the higher units to reach the lowest common one.

If the assumption is wrong, I'd have to go with minutes on both as the lowest unit anywhere in either fraction.

So 4 days [X 24 hours/day] / 16 hours, = 96/16 hours, leaving it as an improper fraction which seems to be what's asked, though it reduces to 6 hours.

And 25 minutes / 2 hours [X60 minutes/hour] = 25/120 minutes, which reduces to 5/24 minutes.

---

Something I never really grasped adequately while I was screwing off in high school, but did learn and use heavily in Freshman physics and chemistry, it to treat the units of measurement algebraically, so instead of shortcutting throught the known to just say 25/2X60, you frame it all in terms where the units you don't want cancel out, which enables you to resolve from units and rates that aren't as intuitive and ingrained in daily life as time units are, like this (Using the time butt-simple time unit coversion of two hours into minutes for illustration):

  2 hours                       60 minutes         
--------------      X    ---------------  = 
      1                               hour                 

After identifying common units for factoring out like they were integers -

2 hours           60 minutes
---------       X     ---------- =
      1                   hour

setting it up to multiply through -
 
2 X 60 minutes
--------------- =
       1

final result is -

120 minutes

As you stated, the time units cancel out and you left with only the number 6 and a fraction 5/24 which is, like I told the son, probably the answer she was looking for but it's not the answer she asked for in my book.

If she had said "solve" or "simplify", I would say that the answers would be simply 6 for #1 and 5/24 for #2.

I think, therefore I could be wrong  , but they have been given problems with measurements in different units like one measurement being in mm's and the other in cm's or feet and inches. I think what the teacher was driving out was trying to get them to convert all measurements to the same units. He wrote his answers as follows....

96 hrs/16 hrs and 25 mins/120 mins

I told him to question the teacher today so we'll see what she says.

I'm an old ornery bastard aren't I....

    

[JohnnyReb]

. 


BTW The government was allowed to go back to math testing for certain apprenticable trades hiring.  I have found the best refresher for this new testing is 7-8 grade math. I won't tell you how many HS graduates can't even make it over that bar.   

This is a huge drop from thirty or so years ago when you at least had to be able to do algebra, geometry, and trig to get a decent score on the federal tests.     

I believe you. I believe every word of it.

Last year son was having trouble in algebra. Son and I are to much alike...don't need no damn help, I can do it all by myself types.

Well, he and mom keep the report cards from me until the third grading period....he had made an "F". The stuff hit the rotating device and it was on...crying, cussing, the whole 9 yards. I was going to help him wheather he liked it or not. That's when I discovered that he didn't have a good foundation in third/forth grade arithmatic. I remember saying something to the grammar school teachers about letting them use calculators and "NOT" requiring them to memorize the multiplication/division tables like we had to do back in the stone age. Teacher said, and I quote, "Oh, they'll pick it up as they go along." Well, it didn't stick to him. He didn't have a problem with algebra, he had aproblem with arithmatic. So here we were, him in the ninth grade learning the multiplication tables so he could quickly recognize certain numbers as squares and quare roots so he could factor equations and do other things.

Took 8 weeks(2 grading periods) to get him up to an "A" in algebra
He was proud of that "A". The teacher would list by name on the report cards all the students that had made "A's". They had gotten into some pretty tough stuff by that point in the year. About half of the "A" students had fallen off the list by then and he had finally gotten on it.

[zeitgeist]

I believe you. I believe every word of it.

Last year son was having trouble in algebra. Son and I are to much alike...don't need no damn help, I can do it all by myself types.

Well, he and mom keep the report cards from me until the third grading period....he had made an "F". The stuff hit the rotating device and it was on...crying, cussing, the whole 9 yards. I was going to help him wheather he liked it or not. That's when I discovered that he didn't have a good foundation in third/forth grade arithmatic. I remember saying something to the grammar school teachers about letting them use calculators and "NOT" requiring them to memorize the multiplication/division tables like we had to do back in the stone age. Teacher said, and I quote, "Oh, they'll pick it up as they go along." Well, it didn't stick to him. He didn't have a problem with algebra, he had aproblem with arithmatic. So here we were, him in the ninth grade learning the multiplication tables so he could quickly recognize certain numbers as squares and quare roots so he could factor equations and do other things.

Took 8 weeks(2 grading periods) to get him up to an "A" in algebra
He was proud of that "A". The teacher would list by name on the report cards all the students that had made "A's". They had gotten into some pretty tough stuff by that point in the year. About half of the "A" students had fallen off the list by then and he had finally gotten on it.

I have a great story about the fourth grade teacher and the "math wheel concept".  Safe to say she and I didn't see eye to eye on a lot of things.  It could have been the note which I marked up with red pen and sent back that did it, I am just not sure.  Anyway, I did not have much interaction with that teacher as she went on extended sick leave and retired. ( I am pretty sure I was not the cause of that but m/zeit didn't encourage me to interact much with the new teacher.)  I ended up sending the lad to summer school.  He was probably one of the only ones in his class who could actually make change in his head.  Funny as the dickens to see him spit out nickles, dimes and quartes.

[JohnnyReb]

"You can't have decimals in ratios."

What the hell has she been smoking?

[DumbAss Tanker]

"You can't have decimals in ratios."

What the hell has she been smoking?

Well, of course you can, it's just ugly and doesn't make a clean fraction.  Assuming they're rational numbers you normally multiply the the numerator and denominator by the same power of 10 so the decimal goes away.  I imagine what she means is 'You'd better not have decimals in your fraction in MY class, kid.'

[JohnnyReb]

Well, of course you can, it's just ugly and doesn't make a clean fraction.  Assuming they're rational numbers you normally multiply the the numerator and denominator by the same power of 10 so the decimal goes away.  I imagine what she means is 'You'd better not have decimals in your fraction in MY class, kid.'

I don't get where the subject of ratios even entered into the question? And no matter how you decide to do the first problem, there is no decimal. The second one, maybe so.

The teacher is from Puerta Rico. Wonder if that makes a difference?

[DumbAss Tanker]

I don't get where the subject of ratios even entered into the question? And no matter how you decide to do the first problem, there is no decimal. The second one, maybe so.

The teacher is from Puerta Rico. Wonder if that makes a difference?

Ratios and fractions are two different ways of looking at (And naming) the same mathematical thing.

[JohnnyReb]

I have emailed the teacher. We'll see what she says.

Now I know why I had transmission problems...all the gear ratios were in decimals.

[DumbAss Tanker]

I have emailed the teacher. We'll see what she says.

Now I know why I had transmission problems...all the gear ratios were in decimals.

Yeah, they just don't mesh right with .1 or .5 of a tooth somewhere on the wheel...

She does have a point, but gear ratios for instance are often not referred to by the total number of teeth, though that is the way they actually work.