Question

the numerator of a fraction is 4 less then its denomenator. if the numerator is decreased by 1, the fraction is equal to 2/3 , find the fraction​

Answer 1

Answer:

11/15

Step-by-step explanation:

Let the denominator = x

Numerator = x-4

If the numerator is decreased by 1

then the fraction will be

(x-4-1)/x = 2/3

(x-5)/x = 2/3

3(x-5) = 2x

3x-15 = 2x

3x-2x = 15

x = 15

Therefore the fraction is 11/15

Answer 2

Step-by-step explanation:

$\bf{\underline{\underline\red{Given:-}}}$

• The numerator of a fraction is 4 less then its denomenator.

• If the numerator is decreased by 1, the fraction is equal to ⅔.

$\bf{\underline{\underline\blue{To\:Find:-}}}$

• The fraction.

$\bf{\underline{\underline\green{Solution:-}}}$

According to the 1st condition:-

The numerator of a fraction is 4 less then its denomenator.

Let the denominator be x

The numerator = x - 4

According to the 2nd condition :-

If the numerator is decreased by 1, the fraction is equal to ⅔.

If the numerator is decreased by 1

The numerator = x - 4 - 1 = x - 5

The denominator = x

The fraction becomes ⅔

$\rm \implies \dfrac{x-5}{x } = \dfrac{2}{3}$

By cross multiplication

$\rm \implies{3(x-5)} = {2(x )}$

$\rm \implies{3x-15} = {2x}$

$\rm \implies{3x - 2x} = 15$

$\rm \implies{x} = 15$

The denominator = x = 15

The numerator

= x - 4

= 15 - 4

= 11

$\large\underline{ \boxed{ \purple{\rm \therefore The \: fraction = \frac{11}{15}} }}$