SOLUTION: how do i figure out -1 2/3 divided by (-10) ... and i have another one i am having problems with -28 5/36 + 16 7/30

Question 904009: how do i figure out -1 2/3 divided by (-10) ...
and i have another one i am having problems with -28 5/36 + 16 7/30

Answer by AlgebraLady88(44) (Show Source): You can put this solution on YOUR website!
To start, I would recommend dividing by -1 for both numerator and denominator. This gets rid of the negative signs nicely. Then I would turn the mixed number numerator into an improper fraction. Let's work it out below:
(- 1 2/3 ) / -10
= (1 2/3) 10 (here, the negative signs are gone as we have divided by -1)
= (5/3) /10 (here, the mixed number numerator is now an improper fraction)
= 5/3 *1/10 (the reciprocal of 10 is 1/10 )
= 1/6
-28 5/36 + 16 7/30 (turn these into improper fractions as well)
= - 1013/36 + 487/30
Uh oh.. now we have a problem. Some big numbers here ; don't let it worry you. We need to find the LCM of both the denominators, 36 and 30. This is the lowest common multiple; it's just a fancy term to mean the smallest number that is a multiple of both 36 and 30. The LCM makes the denominator the same so that you can work the problem.
To find LCM, we need to do some prime factorization:
36 : 12 * 3 = 4 * 3 * 3 = 2 * 2 * 3 * 3
30 : 6 * 5 = 2 *3 * 5
Let's arrange the prime factors :
36 : 2 2 3 3
30 : 2 3 5
Note: Please put it into columns on your own scratch paper as it won't show up here very clearly. You should have '2's' in the 2 column and '3's' in the 3 column and '5' will be by itself. I will try to upload an illustration if anyone requests it.
To find the LCM, we use the number in each column; no matter how many times it is repeated, we only use it once. In this case, it would be
2 * 2 * 3 * 3 * 5 = 180
Now we can finish the problem:
- 1013 /36 + 487 / 30
= - 5065/180 + 2922/ 180
= - 2143/ 180
And that's your answer. 2143 is a prime number , so you can't really simplify any more than that.
RELATED QUESTIONS
I am having trouble with the order I am suppose to work problems. I am also having... (answered by longjonsilver)

I am stuck on the following problems and can not figure them out and I have been working... (answered by jim_thompson5910)

I am working on dividing a rational expression with another rational expression and I am... (answered by josgarithmetic,MathTherapy)

I do not seem to understand reciprocals. I have a couple of problems as examples that I... (answered by richard1234)

I actually have 2 questions and i am really having problems. i have tried the first one... (answered by jim_thompson5910)

Im having trouble with some word problems i have many for my homework i understand the... (answered by stanbon,lwsshak3)

i have 3 problems to figure out. the first one is: 14-10+x<-x-8. i started to do 4+x<-x-8 (answered by stanbon,mananth)

I am dividing Rational expression by another rational expression and am getting stuck.... (answered by Boreal,MathTherapy)

I am trying to help my son with some algebra. I am wanting to confirm the following... (answered by ankor@dixie-net.com)