A fraction greater than 1/8 and less than 1/4 is in simplest form and denominator is 4 more than its numerator...what is the fraction?

Answer 1

first, write inequality equations using the given statements/description:
let x = numerator
let x+4 = denominator
1/8 < x/(x+4) *fraction is greater than 1/8
x + 4 < 8x
7x > 4
x > 4/7

x/(x+4) < 1/4 *fraction is less than 1/4
4x < x + 4
3x < 4
x < 4/3

now, x is between 4/7 and 4/3 ,, we then find value of x which is a whole number (since numerator and denominator of a fraction are integers or whole numbers),, values between these two are:
4/6 , 4/5, 4/4
therefore the only whole number here in simplest form is 4/4 = 1 = x
the fraction is thus 1/5

so there,, :)