Question

the numerator of a rational number is 2 less than the denominator if 16 is added to the numerator the fraction become 5/3.find the fraction​

Answer 1

Let the denominator be 'x'

then numerator = x - 2

According to the question,

$\implies(x-2)+\dfrac{16}{x}=\dfrac{5}{3}\\\\\\\implies\dfrac{x-2+16}{x}=\dfrac{5}{3}\\\\\\\implies\dfrac{x+14}{x}=\dfrac{5}{3}\\\\\\\implies3\:(x+14)=5\:x\:(by\:cross\:multiplication)\\\\\\\implies3x+42=5\:x\\\\\\\implies42=5x-3x\\\\\\\implies42=2x\\\\\\\implies x=\dfrac{42}{2}\\\\\\\implies x=21\:(denominator)\\\\\\\ Numerator=x-2\\\\=21-2\\\\=19\\\\\\the\:fraction=\dfrac{19}{21}$

Answer 2

Answer: 19/21

Step-by-step explanation:

Let the denominator of the fraction be x.

It is given that numerator is 2 less than denominator. So,

Numerator will be (x - 2)

Now,

According to second condition,

If 16 is added to the numerator then the fraction becomes 5/3

It means,

$\frac{(x-2)+16}{x}=\frac{5}{3}\\\;\\\frac{x-2+16}{x}=\frac{5}{3}\\\;\\\frac{x+14}{x}=\frac{5}{3}\\\;\\\textbf{Cross Multiplying;}\\\;\\3(x+14)=5x\\\;\\3x+42=5x\\\;\\42=5x-3x\\\;\\42=2x\\\;\\x=\frac{42}{2}\\\;\\\textbf{x\;=\;21}$

Hence,

Denominator = 21

Numerator = 21 - 2 = 19

Fraction = 19/21