Question

The numerator of a fraction is less than denominator by 2 if 3is added to both numerator and denominator the value of fraction becomes 8/9 find the fraction

Answer 1

Answer:

x=15/13

Step-by-step explanation:

Let the fraction be x/y.

x=y-2--------♡

y-x=2

(x+3)/(y+3)=8/9

9(x+3)=8(y+3)

9x+27=8y+24

8y-9x=27-24

8y-9x=3

8y-9(y-2)=3[From ♡]

8y-9y+18=3

-y+18=3

18-3=y

15=y

y=15

x=y- 2

x=15-2

x=13

HOPE THIS BRING A SMILE IN YOUR FACE

Answer 2

Question :

The numerator of a fraction is less than denominator by 2 if 3is added to both numerator and denominator the value of fraction becomes 8/9 find the fraction?

Solution :

Let the denominator be x

⇒Numerator = x-2

$\sf fraction = \dfrac{x - 2}{x}$

Now according to the question:

If 3is added to both numerator and denominator the value of fraction becomes 8/9.

$\sf \implies \dfrac{x - 2 + 3}{x + 3} = \dfrac{8}{9}$

$\sf \implies \dfrac{x + 1}{x + 3} = \dfrac{8}{9}$

$\sf \implies9x + 9 = 8(x + 3)$

$\sf \implies9x + 9 = 8x + 24$

$\sf \implies \: x = 15$

Therefore ,

$\sf \: fraction = \dfrac{x - 2}{x} = \dfrac{15 - 2}{15} = \dfrac{13}{15}$

________________________

Verification:

If 3 is added to both numerator and denominator the value of fraction becomes 8/9 .

Fraction=$\dfrac{13 + 3}{15 + 3} = \cancel{\dfrac{16}{18} } = \dfrac{8}{9}$

Hence verified