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.

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) (Show Source): You can put this solution on YOUR website!
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:
+ =
common denominator
+ =
we can say
8a + 7b = 51
8a = -7b + 51
a = b +
only one integer solution to this equation, b=5, find a
a = (5) +
a = +
a =
a = 2
:
Our fractions: & , which is the greatest

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