Question

denominator of a fraction is 4 more than twice its numerator. Denomina
nes 12 times the numerator, if both the numerator and the denominator
ed by 6. Find the fraction.​

Answer 1

Answer:

Step-by-step explanation:

Correct Question :-

The denominator of a fraction is 4 more than twice its numerator. Denominator becomes 12 times the numerator ,if both the numerator and denominator are reduced by 6.find the fraction.

Given :-

The denominator of a fraction is 4 more than twice its numerator.

Denominator becomes 12 times the numerator ,if both the numerator and denominator are reduced by 6.

To Find :-

The Fraction.

Solution :-

Let the numerator be x.

And the denominator be (2x + 4)

Fraction = x/(2x + 4)

⇒ 12(x - 6) = (2x + 4 - 6)

⇒ 12x - 72 = 2x - 2

⇒ 12x - 2x = -2 + 72

⇒ 10x = 70

⇒ x = 70/10

⇒ x = 7

Numerator = x = 7

Denominator = 2x + 4 = 2 × 7 + 4) = (14 + 4) = 18

Hence, The Fraction is 7/18.

Answer 2

Answer:

$\large{\underline{\boxed{\mathfrak\green{Fraction = \dfrac{7}{18} }}}}$

Given:-

• Denominator = (2 × numerator) + 4
• (Denominator - 6) = 12 × (numerator - 6)

To find:-

• Fraction = ?

Let numerator be x

$\therefore$ Denominator = 2x + 4

$\therefore$ Fraction = x/2x+4

A/Q,

$\dashrightarrow\sf (2x + 4 - 6) = 12(x - 6) \\\\\dashrightarrow\sf 2x - 2 = 12x - 72 \\\\\dashrightarrow\sf 2x - 12x = - 72 + 2 \\\\\dashrightarrow\sf -10x = -70 \\\\\dashrightarrow\sf x = -70/-10 \\\\\dashrightarrow\large{\underline{\boxed{\sf\green{x = 7 }}}}$

$\therefore{\underline{\sf{Numerator(x) = 7 }}}$

$\rule{100}{2}$

$\dashrightarrow\sf Denominator = 2x + 4 \\\\\dashrightarrow\sf Denominator = 2(7) + 4 \\\\\dashrightarrow\sf Denominator = 14 + 4 \\\\\dashrightarrow\large{\underline{\boxed{\sf\blue{Denominator = 18 }}}}$

$\rule{200}{1}$

$\dashrightarrow\sf Fraction = \dfrac{Numerator(x)}{Denominator(2x + 4)} \\\\\dashrightarrow\large{\underline{\boxed{\sf\purple{ Fraction = \dfrac{7}{18} }}}}$