- #1
Greychu
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Homework Statement
For positive integers m, k, and n , let mkn be defined as mkn = kmn , where [itex] k\frac {m}{n} [/itex] is a mixed fraction. What is the value of 643 + 364 ?
Homework Equations
I attempt the other few similar questions where the solution are as follow
832 + 382 = [itex] \frac {169}{24} [/itex]
641 + 164 = [itex] \frac {85}{6} [/itex]
The answer for this question.
643 + 364 = [itex] \frac {21}{2} [/itex]
But the problem is I have no idea how to get the answer.
The Attempt at a Solution
Based on the problem, I can see that
643 + 364 = 463 + 634
= 463 + 364
= 643 + 634
or more simply
643 = 463 and 364 = 634
Notice that 463 and 364 are in reverse position with each other.
Since it mention that [itex] m\frac {k}{n} [/itex] is a mixed fraction, I suspect that
643 + 364 = 643 + 634
I try to relate 643 = [itex] 6 \frac {4}{3} [/itex] and 364 = [itex] 3 \frac {6}{4} [/itex]
but they are not the same for 463 and 634 if expressed in term of mixed fraction
Even attempt the way:
643 = 463 → (24)3 and 364 = 634 → (18)4 by multiply the first 2 numbers and
643 = 463 = (10)3 and 364 = 634 → (9)4 by adding the first 2 numbers.
Not sure if mkn = kmn = [itex] k\frac {m}{n} [/itex]
Please try to give some hints about how to see this problem.