SOLUTION: The denominators of two fractions are consecutive natural numbers. Both fractions are in their lowest terms. Their sum is 51/56. Find the greater of these two fractions.

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Question 873614: The denominators of two fractions are consecutive natural numbers. Both fractions are in their lowest terms. Their sum is 51/56. Find the greater of these two fractions.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The denominators of two fractions are consecutive natural numbers. Both fractions are in their lowest terms. Their sum is 51/56. Find the greater of these two fractions.
:
Let a = numerator of the 1st fraction
let b = numerator of the 2nd fraction
:
Regarding the denominator, only two consecutive numbers are factors of 56
So we have:
a%2F7 + b%2F8 = 51%2F56
common denominator
%288a%29%2F56 + %287b%29%2F56 = 51%2F56
we can say
8a + 7b = 51
8a = -7b + 51
a = -7%2F8b + 51%2F8
only one integer solution to this equation, b=5, find a
a = -7%2F8(5) + 51%2F8
a = -35%2F8 + 51%2F8
a = 16%2F8
a = 2
:
Our fractions: 2%2F7 & 5%2F8, which is the greatest