Question

If 1 is added to the denominator of a fraction, it becomes
and it 1/2 and if 2 is added to the numerator, the
fraction becomes 1. What is the fraction?​

Answer 1

A number in form of A/B i.e, A is numerator and B is danomenator

Answer 2

Step-by-step explanation:

Correct Question:-

If 1 is added to the denominator of a fraction, it becomes and it ½ and if 1 is added to the numerator, the fraction becomes 1. What is the fraction?

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

• If 1 is added to the denominator of a fraction, it becomes ½.

• If 2 is added to the numerator, the
• fraction becomes 1.

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

• The fraction.

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

$\sf Let \:the\: numerator\: be\: x$

$\sf And\: denominator \:be\: y$

According to the 1st condition:-

$\sf If \:1 \:is\: added \:to\: denominator$

$\sf The \:denominator = y + 1$

$\sf The\: numerator = x$

$\sf The\: fraction \:becomes \: \dfrac{1}{2}$

$\sf \implies\dfrac{x}{y + 1} = \dfrac{1}{2}$

$\sf \implies{2(x)} = {1(y + 1)}$

$\sf \implies{2x} = {y + 1}$

$\sf \implies{2x - y} = { 1} .....(i)$

According to the 2nd condition:-

$\sf If \:1 \:is\: added \:to\: numerator$

$\sf The \: numerator = x + 1$

$\sf The\: denominator = y$

$\sf \implies \dfrac{x + 1}{y} = 1$

$\sf \implies{x + 1} = y$

$\sf \implies{x - y} = - 1 ....(ii)$

$\sf Subtracting\: equation\:(ii)\: from\:(i)$

$\sf \implies2x - y - (x - y) = 1 - ( - 1)$

$\sf \implies2x - y - x + y = 1 +1$

$\sf \implies x= 2$

$\sf Substituting \:x = 2 \:in \:equation \:(ii)$

$\sf \implies x - y= - 1$

$\sf \implies 2 - y= - 1$

$\sf \implies - y= - 1 - 2$

$\sf \implies - y= - 3$

$\sf \implies y= 3$

$\sf The\: numerator = x = 2$

$\sf The \:denominator = y = 3$

$\underline{ \boxed{ \purple{\sf \therefore The \: fraction= \frac{2}{3}}}}$