problem 3 is also not that bad:
11 and 13 are prime numbers, so we can't break this down further
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for 2 (a) and (b), recall how we divide fractions.
also recall that a negative divided by a negative is a positive and that any number can be thought of as itself over 1, so you can think of 13 as if that makes it easier for you
for 2(c):
.....cross multiply
......simplify
..............divide both sides by 9
The way you did it makes it seem so easy!
Seeing your method, I can arrive at the same solutions. How did you post the fractions (to appear the way they do) on this thread? I couldn't figure that out, either.
On the second one, how did you figure out 11 and 13 would go into 143? Did you just happen to know that? I tried breaking it down for a while, but never came up with anything.
In awe,
~V~
oh? how so? which question?
I use LaTex, see hereSeeing your method, I can arrive at the same solutions. How did you post the fractions (to appear the way they do) on this thread? I couldn't figure that out, either.
well, i thought of the first few primes i knew and made some educated guesses that paid off.On the second one, how did you figure out 11 and 13 would go into 143? Did you just happen to know that? I tried breaking it down for a while, but never came up with anything.
the first few primes are: 2,3,5,7,11,13,17,...
obviously 2 and 5 were out of the question.
3 was out, because for a number to be divisible by 3, the sum of it's digits must be divisible by 3
i tried 7 it didn't work.
i knew 11 would work. since any three digit number in which the middle digit is the sum of the two digits on the ends is divisible by 11. since 1 + 3 = 4, 143 is divisible by 11. so i divided it by 11 and realized the result was 13, another prime number. so, the prime factorization ended there, since i only had primes, i couldn't divide into anything anymore
you shouldn't beIn awe,
~V~
For a, b, and c (um, question two I think; the first one you did), the way you wrote and then explained it made a lot of sense to me. What seems obvious to others seems to easily escape me. Particularly true in math.
What came off as an educated guess to you would be rocket science to me. I'm DEFINITELY going to remember your prime number trick. I use the 2, 3, 5, and 10 tricks already, but didn't know about the prime number thing you've got going on. Way cool!
Arigato,
Gracias,
Danka,
Thanks,
~V~
ok, glad to have helped.
you don't have to know all those divisibility rules, trial and error would have gotten you through it, we did not have to try that many numbers. just list the prime numbers and try them 1 by 1 (10 is not prime by the way ). chances are, for questions like these you won't need to get up to really large prime numbers, one of the small ones should work.What came off as an educated guess to you would be rocket science to me. I'm DEFINITELY going to remember your prime number trick. I use the 2, 3, 5, and 10 tricks already, but didn't know about the prime number thing you've got going on. Way cool!
i believe it's "Danke"...I know, i'm taking a German class this semesterDanka