In a given fraction, if 1 is subtracted from the numerator and 2 is added to the denominator, it becomes $\frac{1}{2}$. If 7 is subtracted from the numerator and 2 is subtracted from the denominator, it becomes $\frac{1}{3}$. The fraction is ______.

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In a given fraction, if 1 is subtracted from the numerator and 2 is added to the denominator, it becomes $\frac{1}{2}$. If 7 is subtracted from the numerator and 2 is subtracted from the denominator, it becomes $\frac{1}{3}$. The fraction is underlinebb($\frac{15}{26}$). Explanation: Let the fraction be x/y. From the first condition: (x - 1)/(y + 2) = $\frac{1}{2}$ $\Rightarrow$ 2(x – 1) = y + 2 $\Rightarrow$ y = 2x – 4 From the second condition: (x - 7)/(y - 2) = $\frac{1}{3}$ $\Rightarrow$ 3(x – 7) = y – 2 $\Rightarrow$ y = 3x – 19 Equate the two expressions for y: 2x – 4 = 3x – 19 $\Rightarrow$ x = 15 Then y = 2(15) – 4 = 26 So, the fraction is $\frac{15}{26}$.

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