Math people, please help me understand this

Because Geometry is all angles and Geography is all contours.

 

@Iskandar, @Incognitus, @Patman, @Mixt, help!

Did I do this right? We're on the dimensional analysis right now, and by itself it isn't a problem, but in word problem form, ugh! I looked at the book for the answer after trying it, but I don't really understand.

The former is supposedly better, but I don't know why. According to my work, it looks like the latter would be the better deal?

 

Unfortunately, he doesn't allow calculators.

However, if it's just a matter of the bigger number being the better deal, I can just look at it and say that 8/125 is better than 3/49. Although I may need to show my work, which would be where finding a common denominator would come in handy. Problem is with numbers like these, I have to do a factor tree since the common denominators don't just jump out at me, and I'm still confused on that whole concept, especially when it involves finding the common denominator for three or more fractions with unusual numbers--again, where the common numbers don't just pop out at you. The common denominators for 3/12 + 9/24 + 8/48 are easy, but when it's something like 8/125 + 3/49, forget thinking about it.

This is about as far as I remember, and I don't even know if that's right:

 

Unless there's more than one prime factorization, where you use the number with the higher exponent, and if there are two sets of numbers with the same exponents, such as 3^2 and 4^2, then you would use the higher number, IIRC:



Or do you use both?

 

So many practices I don't agree with or don't think are necessary, but I'm not your teacher so that isn't my call.

If there are multiple copies of the same prime, you use the one with the highest exponent. It does not matter if multiple primes have the same exponent (might be noteworthy if you are planning on taking a square root or something, but doesn't change the process)

So in the picture you would use 3^2 from 36 and 2^4 from 48 making the top circle your LCD.

 

Wat ?
Lol, never needed any of those. Have a nice day.

 

Holy mother of pearl is that a lot of steps. I almost couldn't figure out what you were doing. The easiest way to do this, in my opinion, instead of all that unnecessary work (guess that varies by person and how they were taught math) would just be deciding on one form on units and stick with it. I ended up getting the answers by doing this for the 5lbs and $12.50
5lb X 16 = 80 oz
$12.50 = 1250 cents

right there you have units that match the second number without anything complicated, with a number being 80/1250, which can reduce to 8/125. Unless you have to make the other number match the first too, but that seems like a lot of work you shouldn't have to do if you're just trying to find the answer.

I'm also going to be perfectly honest and admit I'm not even sure how you got the second number to lbs and dollars, but conversions where never my strong suit in chemistry and I would always mess the numbers up.

 

Yeah, I think I made more work for myself. I could have either converted the first one to match the second or vice-versa to see which one's cheaper.