Question

The numerator of a fraction is 2 less than the demoninator is one is added to its denominator, it becomes 1/2 find the fraction​

Answer 1

Given:-

• Numerator of a fraction is 2less than the denominator.
• If one added to denominator it becomes 1/2

To find:-

The fraction

Solution:-

• Let the denominator=x
• Numerator=x-2

The fraction

$\\ \sf\hookrightarrow \dfrac{x-2}{x}$

ATQ

$\\ \sf\hookrightarrow \dfrac{x-2}{x+1}=\dfrac{1}{2}$

• use Cross multiplication

$\\ \sf\hookrightarrow 2(x-2)=1(x+1)$

$\\ \sf\hookrightarrow 2x-4=x+1$

$\\ \sf\hookrightarrow 2x-x=1+4$

$\\ \sf\hookrightarrow x=5$

$\\ \sf\hookrightarrow x-2=5-2=3$

$\\ \underline{\boxed{\bf{\therefore The\:fraction\:is\:\dfrac{3}{5}}}}$

Answer 2

• Answer:

Let the numerator be x Denominator = x+2 When 1 is added to Denominator:- Denominator = x+2+1=x+3 A.T.Q. (x)/(x+3)=1/2 Cross multiplying x+3=2x 2x-x=3 x=3 Original Numerator = x = 3 Original Denominator = x+2 = 3+2 = 5 Original fraction = 3 /5 Verification:- Fraction = 3/5 1 is added to the Denominator:- 3/(5+1) = 1/2 3/6 = 1/2 %3D 1/2 = 1/2 Hence verified