Question

the numerator of a rational number is smaller than it's denominator by 4.if the numerator is increased by 3 and denominator is decreased by 5, the number becomes 2.find the rational number

Answer 1

Let the number is a/b.

We are given that The numerator of a rational number is smaller than it's denominator by 4.

So a=b-4...................(1)

if the numerator is increased by 3 and denominator is decreased by 5, the number becomes 2.

$\frac{a+3}{b-5} =2$........................(2)

Substituting value of a from equation (1) in (2)

$\frac{b-4+3}{b-5} =2$

[tex] \frac{b-1}{b-5} =2

cross multiplying

b-1=2(b-5)

b-1=2b-10

2b-b=-1+10

b=9

from equation 1,

a=b-4=9-4=5

Answer: So the rational number is 5/9