The numerator of a fraction is $6$ less then the denomiator. If $3$ is added to the numerator, the fraction becomes equal to $\frac{2}{3}$ . Find the original fraction.

Open in App

Solution

Let the denominator be $x$ ,

Hence, numerator $= x - 6$

According to question,

$\frac{x - 6 + 3}{x} = \frac{2}{3}$

$⟹ 3 x - 9 = 2 x$

$⟹ x = 9$

So, original fraction, $\frac{3}{9}$

Suggest Corrections

Similar questions

Q. The numerator of a fraction is

6

less than the denominator. If

3

is added to the numerator, the fraction is equal to

\frac{2}{3}

, find the original fraction

The numerator of a fraction is 5 less than its denominator. If 3 is added to the numerator, and denominator both, the fraction becomes $\frac{2}{3}$ . Find the original fraction.

The numerator of a fraction is 6 less than the denominator. If 3 is added to the numerator, the fraction is equal to $\frac{2}{3}$ . What is the original fraction equal to ?

Q. The numerator of a fraction is 6 less than the denominator. If 3 is added to the numerator, the fraction is equal to

\frac{2}{3}

. What is the original fraction equal to?

Q. The numerator of a fraction is

5

less than its denominator. If

3

is added to the numerator and denominator both, the fraction becomes

\frac{4}{5}

. Find the original fraction.

Join BYJU'S Learning Program

The numerator of a fraction is 6 less then the denomiator. If 3 is added to the numerator, the fraction becomes equal to 23. Find the original fraction.

Let the denominator be x,Hence, numerator =x−6According to question,x−6+3x=23⟹3x−9=2x⟹x=9So, original fraction, 39

The numerator of a fraction is $6$ less then the denomiator. If $3$ is added to the numerator, the fraction becomes equal to $\frac{2}{3}$ . Find the original fraction.

Let the denominator be $x$ ,

Hence, numerator $= x - 6$

According to question,

$\frac{x - 6 + 3}{x} = \frac{2}{3}$

$⟹ 3 x - 9 = 2 x$

$⟹ x = 9$

So, original fraction, $\frac{3}{9}$