Finding the Required Fraction

Video Explanation

Question

The numerator of a fraction is 4 less than the denominator. If the numerator is decreased by 2 and the denominator is increased by 1, then the denominator becomes eight times the numerator. Find the fraction.

Solution

Step 1: Let the Variables

Let the denominator = \(x\)

Then the numerator = \(x – 4\)

Step 2: Apply the Second Condition

After modification:

New numerator = \(x – 4 – 2 = x – 6\)

New denominator = \(x + 1\)

According to the condition:

\[ x + 1 = 8(x – 6) \]

Step 3: Solve the Equation

\[ x + 1 = 8x – 48 \]

\[ x – 8x = -48 – 1 \]

\[ -7x = -49 \]

\[ x = 7 \]

Step 4: Find the Numerator

\[ \text{Numerator} = x – 4 = 7 – 4 = 3 \]

Conclusion

Required fraction:

\[ \boxed{\frac{3}{7}} \]

Final Answer (For Exam)

The required fraction is 3/7.