Question

If 1 is added to the denominator of a fraction, the fraction becomes 1/2. If 1 is added to the numerator, the fraction becomes 1. The fraction is:

a. 4/7
b. 5/9
c. 2/3
d. 10/11
​​

Answer 1

C)

$\frac{2}{3}$

Hope it helps...!

Answer 2

Answer:-

$\large\sf \frac{2}{3}$

Step by step explanation:-

❐ Given:-

2 conditions have been given here:-

• If 1 is added to the denominator of a fraction the fraction becomes ½
• If 1 is added to the numerator the fraction becomes 1

❐ To Find:-

• The fraction

❐ Solution:-

Let the fraction be $\sf {\dfrac{x}{y}}$

★᭄According to the first condition:-

$\large \looparrowright \sf \frac{x}{y + 1} = \frac{1}{2}$

$\small \looparrowright \sf {2x = y + 1}$

$\small \looparrowright \sf{2x - 1 = y \: \: \: \: \: \: \: \: \: \: \: \mapsto\blue{(1)}}$

★᭄According to the second condition:-

$\large \looparrowright \sf \frac{x + 1}{y} = 1$

$\small \looparrowright \sf{x + 1 = y}$

$\small \looparrowright \sf{x + 1 = 2x - 1} \: \: \: \: \: \: \: \: \: \: \: \mapsto{\blue {(from \: 1)}}$

$\small \looparrowright \sf{1 + 1 = 2x - x}$

$\small \looparrowright \sf{2 = x} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \mapsto {\blue{putting \: 1}}$

$\small \looparrowright \sf{2(2) - 1 = y}$

$\small \looparrowright \sf{4 - 1 = y}$

$\small \looparrowright \sf{3 = y}$

$\therefore \sf \red{The \: fraction \: is \: \large\frac{2}{3}}$