# 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

You need another equation...
M and n can be any values
m could be 14 and n could be 2 or
ecc.
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bobby commented
Can you give me the explanation?
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.

See en.m.wikipedia.org/wiki?search=Egyptian+fraction
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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 answered
N=4, M=7.
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Mark Mottian commented
That's incorrect! 1/7 + 1/4 is not equal to 4/7!
Well 4 divided by 7 = .57 so...ok leave me alone I'm only in fifth grade! Lol
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I am the best in maths :-see the solution
1/m+1/n=4/7
n+m/mn=4/7
n+m/mn=4/7
then cross multiply.
7n+7m=4mn
7(n+m)/4mn.final ans
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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
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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 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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