Question

The numerator of a fraction is 8 less than its denominator. If 2 is added to both numerator and denominator, fraction become 11/9. Find the fraction.​

Answer 1

Given : The numerator of a fraction is 8 less that the denominator. When, 2 is added to both numerator and denominator, fraction becomes 11/9.

To Find : The fraction.

⠀⠀⠀⠀⠀⠀_______________

⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀

Let

• Denominator = x
• Numerator = (x - 8)

⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀

When 2 is added

• 2 is added to denominator = (x + 2)
• 2 is added to numerator = x - 8 + 2 = (x - 6)

⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀

Now,

$\sf : \implies \: \dfrac{(x - 6)}{(x + 2)} = \dfrac{11}{19} \\ \\ \\ \sf : \implies \: 19(x - 6) = 11(x + 2) \\ \\ \\ \sf : \implies \: 19x - 114 = 11x + 22 \\ \\ \\ \sf : \implies \: 19x - 11x = 22 + 114 \\ \\ \\ \sf : \implies \: 8x = 136 \\ \\ \\ \sf : \implies \: x = \cancel\frac{136}{ 8} \\ \\ \\ \sf : \implies \: \underline{\boxed{\sf\purple{x = 17}}} \: \bigstar$

Now,

⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀

• Denominator = x = 17
• Numerator = x - 8 = 17 - 8 = 9

⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀

$\sf\therefore{\underline{Hence, \: the \: fraction \: is \: \dfrac{9}{17}. }}$

Answer 2

Answer :

• The fraction is 9/17.

Given :-

• The numerator of a fraction is 8 less that the denominator. When, 2 is added to both numerator and denominator, fraction becomes 11/9.

To Find :-

• The fraction ?

Solution :-

• Let the Denominator be x.
• And Numerator be (x - 8)

Where, 2 is added,

• 2 is added to denominator = (x + 2)
• 2 is added to numerator = x - 8 + 2 = (x - 6)

• Putting all values,

➻ (x - 6)/(x + 2) = 11/19

➻ 19(x - 6) = 11(x + 2)

➻ 19x - 144 = 11x + 22

➻ 19x - 11x = 22 + 114

➻ 8x = 136

➻ x = 136/8

➻ x = 17

Therefore,

➻ Denominator x = 17

➻ Numerator = x - 8 = 17 - 8 = 9

• Hence, the fraction is 9/17.

▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅