SOLUTION: If 1/8 + 1/3 = 1/N, what is the value of N? I have worked on this problem and so far I have gotten to the point where 1/8 +1/3 =11/24 and I am stuck on where to go from here. I

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Question 1208605: If 1/8 + 1/3 = 1/N, what is the value of N?
I have worked on this problem and so far I have gotten to the point where 1/8 +1/3 =11/24 and I am stuck on where to go from here. I also need to write a formal solution for this so any insight regarding how to write a formal solution would also be greatly appreciated.
Found 3 solutions by ikleyn, math_tutor2020, timofer:
Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
.

So, now you have

     = .


and you want to get N, based on it.  



        Nothing is easier than that !



Multiply both sides of this equality by  24N.  You will get

    11N = 24.


Divide both sides of this equality by 11.  You will get

    N = ,  or  N = 2,

which is the same.


So,  N =  = 2  is your answer,


and you just know  WHAT TO DO  in order for to get it.

Happy learning (!)


~~~~~~~~~~~~~~~~~~~~~~~~ 

In more simple terms, you have  

     = .

and you want to get N, based on it.    



Then you simply turn both fractions upside down, and you get

     =  = N,

which is exactly what you want.



Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

There are at least two methods to solve this.

Method 1
1/8 + 1/3 = 1/N
3/24 + 8/24 = 1/N
(3+8)/24 = 1/N
11/24 = 1/N ........... this is what you have so far
11N = 24 ........... cross multiply
N = 24/11

Method 2
1/8 + 1/3 = 1/N
24N*(1/8 + 1/3) = 24N(1/N) ........... multiply both sides by LCD to clear out fractions
24N*(1/8) + 24N*(1/3) = 24N(1/N)
3N + 8N = 24
11N = 24
N = 24/11

Side note:
24/11 = 2.181818...
the "18" repeats forever.
Answer by timofer(104)   (Show Source): You can put this solution on YOUR website!


LCD is 24 on the left side.



Their reciprocals are also equal. or
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