Question

A fraction in its lowest terms can be expressed as 4/17 . if it's numerator and denominator differ by 91.find its numerator

Answer 1

As they are in the lowest terms so they must have a common factor. Let's say its k.
So, 4k/17k is the required fraction.
Now 17k-4k=91
Or, 13k=91
Or, k=7
Therefore, Numerator=4k=4*7=28.

Answer 2

let the numerator be x and denominator be y

x/y = 4/17
= 17x = 4y ... (1)

x - y = 91. ... (2)
= x = 91 + y
by substituting this value in (1),

17(91 + y) = 4y
= 1547 + 17y = 4y
= 1547 = -13y
= 1547/-13 = y
= -119 = y
by substituting this value in (2),
x = 91 + 119
x = 210