Question

If we add 1 to the numerator and subtract 1 from the denominator of a fraction, it reduces to 1/2. If we only add to the denominator, what is the fraction?

A) 2/3
B) 3/4
C) 4/5
D) 5/6

Answer 1

The original fraction is determined by setting up an equation where adding 1 to the numerator and subtracting 1 from the denominator equals 1/2. Solving this equation, we find the fraction is 2/3 originally, which simplifies to 1/2 when only 1 is added to the denominator instead of both altering the numerator and denominator.

Step-by-step explanation:

The student's question involves finding the original fraction when altering its numerator and denominator leads to a specific result. To solve this, we need to set up an equation based on the information given: adding 1 to the numerator and subtracting 1 from the denominator of a fraction reduces it to 1/2.

Let's let the original fraction be x/(x+1). According to the problem, adding 1 to the numerator and subtracting 1 from the denominator gives us (x+1)/(x+1-1), which simplifies to (x+1)/x. This must equal 1/2, so we set up the equation (x+1)/x = 1/2. Solving for x, we get x = 2.

Now, if we only add 1 to the denominator of the original fraction as suggested by the latter part of the question, we'll have the fraction x/(x+1+1) which turns into 2/4 when x = 2. Simplifying 2/4, we get 1/2, which matches option B, 3/4, after considering that 3 is added to the initial 1 in the numerator and 4 is what we get when adding 1 more to the incremented denominator.