Question

the numerator of rational number is 2 less than the dinominator if the denominator is increased by 5 and the numerator by 2, we get the rational number 1/2 find the rational number

Answer 1

Let the numerator be x and the denominator be y
=> rational number = x/y
given that the numerator is 2 less than the denominator,
=> x = y-2
therefore, numerator = y-2
                denominator = y
if we increase denominator by 5 and numerator by 2, 
new numerator  = y-2+2 = y
new denominator = y+5
=> new rational number will be y/(y+5)
but new rational number = 1/2
=> y/(y+5) = 1/2
cross multiplying, we get
2y = y + 5
=> 2y - y =5
=> y=5
therefore,
numerator = y-2 = 3
denominator = y = 5
rational number = 3/5