Are you a master in maths? Who can solve the following and explain to me how to do it? 1/m + 1/n = 4/7. What are the values of m and n?


6 Answers

Roderick Abdilla Profile
You need another equation...
M and n can be any values
m could be 14 and n could be 2 or
Oddman Profile
Oddman answered
1/2 + 1/14 = 4/7

The only integer solutions are {m=2, n=14} or {m=14, n=2}. Counting both permutations, there are 2 solutions.

thanked the writer.
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Oddman commented
The link regarding Egyptian Fractions tells ways to work these problems, with several formulas that will apply to 4/7. I did it by trail and error. Trying 1/2 as one fraction gave a solution. The reference shows there are no more 2 term solutions.
Oddman commented
Logic, too, shows there are no other 2-term solutions. The largest fraction cannot be smaller than 2/7, so must be 1/3 or 1/2. Only 1/2 gives a solution. 1/3+5/21 = 4/7, so more terms are needed if you want all numerators to be 1.
Oddman commented
Only you know how you worked it. Only you can provide that explanation.
Rylee Hilton Profile
Rylee Hilton answered
N=4, M=7.
Aimee Brooksbank Profile
Well 4 divided by 7 = .57 so...ok leave me alone I'm only in fifth grade! Lol
Duane Bryant Profile
Duane Bryant answered
1/m + 1/n = 4/7  SO: Invert the whole problem and: M/1 + n/1 = 7/4 or    m + n = 7/4
thanked the writer.
Oddman commented
You can legitimately invert both sides of an equation. However, 1/(1/m+1/n) is not equal to m/1+ n/1. Rather it is equal to (m*n)/(m+n).
Duane Bryant
Duane Bryant commented
You're right again! Answer is 2, 14 or 14, 2. Now I need to go home and figure out HOW.

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