Question

the numerator of a fraction is 7 less than the denominator if the numerator is increased by 2 and the denominator by 9 we again get the same fraction find the fraction​

Answer 1

ANSWER:

• Original fraction = 2/9

GIVEN:

• The numerator of a fraction is 7 less than the denominator.
• if the numerator is increased by 2 and the denominator by 9 we again get the same fraction.

TO FIND:

• Original fraction.

SOLUTION:

Let the denominator of fraction be 'x'.

Then Numerator = (x-7)

Original fraction = (x-7)/x

According to Question;

$\implies \: \dfrac{(x - 7) + 2}{x + 9} = \dfrac{x - 7}{x} \\ \\ \implies \: \dfrac{x - 5}{x + 9} = \dfrac{x - 7}{x} \\ \\ \implies \: x(x - 5) = (x - 7)(x + 9) \\ \\ \implies \: x {}^{2} - 5x = x {}^{2} + 9x - 7x - 63 \\ \\ \implies \: x {}^{2} - 5x = x {}^{2} + 2x - 63 \\ \\ \implies \: x {}^{2} + 2x - 63 - x {}^{2} + 5x = 0 \\ \\ \implies \: 7x - 63 = 0 \\ \\ \implies \: 7x = 63 \\ \\ \implies \: x = \frac{63}{7} \\ \\ \implies \:x = 9$

Original fraction = (x-7)/x

= (9-7)/9

= 2/9