Question

The numerator of a fraction is one less than the denominator. If one is subtracted from the numerator, the fraction becomes 5/6.Find the fraction.​

Answer 1

Answer:

The fraction is $\dfrac{11}{12}$

Step-by-step explanation:

Let,

• The numerator of a fraction = x
• The denominator of a fraction = x + 1

If 1 is subtracted from the numerator

• The numerator of a fraction = x - 1

If 1 is subtracted from the numerator, the fraction becomes 5/6.

★ According to the Question :

⇒ $\dfrac{(x \: - \: 1)}{(x \: + \: 1)} \: = \: \dfrac{5}{6}$

⇒ 6 (x - 1) = 5 (x + 1)

⇒ 6x - 6 = 5x + 5

⇒ 6x - 5x = 5 + 6

⇒ x = 11

The numerator of a fraction = 11

• The denominator of a fraction = x + 1

⇒ x + 1

⇒ 11 + 1

⇒ 12

The denominator of a fraction = 12

The fraction = $\dfrac{11}{12}$

Therefore, the fraction is $\dfrac{11}{12}$

Answer 2

⇝ Given :-

• The numerator of a fraction is 1 less than the denominator.

• If 1 is subtracted from the numerator, the fraction becomes 5/6

⇝ To Find :-

• The Original Fraction.

⇝ Solution :-

For the Original Fraction Let,

• Numerator = $\large \rm x$

As The numerator of a fraction is 1 less than the denominator.

Therefore,

• Denominator = $\large \rm (x+1)$

So ,

$\text{Original Fraction = } \frac{\text x}{\text x + 1}$

❒ When 1 is subtracted from the numerator :

$\text{Fraction Becomes : } \frac{\text x-1}{\text x + 1}$

⏩ According To Question :

$\bf \large\red{ \frac{ x - 1}{x + 1}  =  \frac{5}{6}}$

✧ On Cross Multiplying ;

$:\longmapsto \rm 6(x - 1) = 5(x + 1)$

$:\longmapsto \rm 6x - 6 = 5x + 5$

$:\longmapsto \rm 6x - 5x = 6 + 5$

$\purple{ \large :\longmapsto  \underline {\boxed{{\bf x =11} }}}$

∴ Numerator of Fraction is 11 .

❒ As The numerator of a fraction is 1 less than the denominator.

$\therefore \rm Denominator = Numerator + 1$

$:\longmapsto \rm Denominator = 11 + 1$

∴ Denominator of Fraction is 12 .

Therefore,

$\large\underline{\pink{\underline{\frak{\pmb{Original \: Fraction = \frac{11}{12} }}}}}$