Question

the denominator of a rational number is greater than its numerator by 5. if the numerator is increased by 7 and denominator decrease by 4, the number obtained is 5/3. find the rational number​

Answer 1

Answer:

The rational number is $\frac{8}{13}$

Step-by-step explanation:

Let x be the numerator and x + 5 be the denominator.

⇒ $\frac{(x)+7}{(x+5)-4} = \frac{5}{3}$

⇒ x + 7 = $\frac{5}{3}$ ×$\frac{(x+5)- 4}{1}$

⇒ x + 7 = $\frac{5x + 25 - 20 }{3}$

⇒ x + 7 = $\frac{5x + 5}{3}$

⇒ 3(x + 7) = 5x + 5

⇒ 3x + 21 = 5x + 5

⇒ 5x - 3x = 21 - 5

⇒ 2x = 16

⇒ x = 8

Thus, the numerator is 8 and the denominator is 13. The rational number is $\frac{8}{13}$

I hope this helps!!

Regards,

Lilac584

Answer 2

The rational number is $\dfrac{8}{13}$

Step-by-step explanation:

Let,

• Numerator = x
• Denominator = x + 5

If the numerator is increased by 7

• Numerator = x + 7

And denominator decrease by 4

• Denominator = x + 5 - 4 = x + 1

The number obtained is 5/3

★ According to the Question :

⇒ $\dfrac{x \: + \: 7}{x \: + \: 1} \: = \: \dfrac{5}{3}$

⇒ 3 (x + 7) = 5 (x + 1)

⇒ 3x + 21 = 5x + 5

⇒ 21 - 5 = 5x - 3x

⇒ 16 = 2x

⇒ x = 16/2

⇒ x = 8

Numerator = 8

• Denominator = x + 5

⇒ x + 5

⇒ 8 + 5

⇒ 13

Denominator = 13

The rational number = $\dfrac{8}{13}$

Therefore, the rational number is

$\dfrac{8}{13}$