Question

If adding 1 to the denominator of a fraction becomes 1/2, and subtracting 2 in the numerator becomes 1/3, find the fraction.

Answer 1

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Answer 2

Answer:

The answer to your question is 5/9.

Explanation:

Step 1: Lets suppose "x" is the numerator and "y" is the denominator. So our fraction becomes x/y.

Step 2: As per the question if 1 is added to the denominator then the fraction would become 1/2. So, adding "1" to the denominator of our supposed fraction  

x/(y+1)=1/2

This implies:

2x = y+1

x = (y+1)/2   [eq. 1]

Step 3: As per the question if "2" is subtracted from the numerator then the fraction would become 1/3. So subtracting "2" from the numerator of our supposed fraction

(x-2)/y = 1/3

This implies

3(x-2) = y   [eq. 2]

Now putting value of y in eq. 1

So eq. 1 would become

x = [3(x-2) +1]/2

x = (3x-6+1)/2

x = (3x-5)/2

2x = 3x -5

This implies

5 = 3x-2x

Solving for x

x = 5

Now placing the value of "x" in eq. 2

eq. 2 would become

3(5-2) = y

3(3) = y

Rearranging the equation

y = 9

So the Answer (i.e. fraction) is:   5/9