The numerator of a fraction is 4 less than the denominator. If 1 is added to both its numerator and denominator , it becomes 1/2. Find the fraction.

Answer

To solve the problem step by step, we will follow the logic presented in the video transcript.

### Step 1: Define the Variables
Let the denominator of the fraction be \( x \). Since the numerator is 4 less than the denominator, we can express the numerator as:
\[ \text{Numerator} = x - 4 \]

### Step 2: Write the Fraction
Now, we can write the fraction as:
\[ \text{Fraction} = \frac{x - 4}{x} \]

### Step 3: Set Up the Equation
According to the problem, if 1 is added to both the numerator and the denominator, the fraction becomes \( \frac{1}{2} \). Therefore, we can set up the equation:
\[ \frac{(x - 4) + 1}{x + 1} = \frac{1}{2} \]
This simplifies to:
\[ \frac{x - 3}{x + 1} = \frac{1}{2} \]

### Step 4: Cross-Multiply
To eliminate the fraction, we cross-multiply:
\[ 2(x - 3) = 1(x + 1) \]
This expands to:
\[ 2x - 6 = x + 1 \]

### Step 5: Rearrange the Equation
Now, we will rearrange the equation to isolate \( x \):
\[ 2x - x = 1 + 6 \]
This simplifies to:
\[ x = 7 \]

### Step 6: Find the Numerator
Now that we have the value of \( x \), we can find the numerator:
\[ \text{Numerator} = x - 4 = 7 - 4 = 3 \]

### Step 7: Write the Final Fraction
Thus, the fraction is:
\[ \frac{\text{Numerator}}{\text{Denominator}} = \frac{3}{7} \]

### Conclusion
The required fraction is:
\[ \frac{3}{7} \]

---