Certainly! Let's walk through a detailed, step-by-step solution to fully understand the fraction [tex]\(\frac{121}{256}\)[/tex].
1. Understanding the Fraction:
- The fraction [tex]\(\frac{121}{256}\)[/tex] consists of a numerator, which is 121, and a denominator, which is 256.
2. Simplifying the Fraction:
- First, we want to see if the fraction can be simplified. To simplify a fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator.
- Here, the numerator is 121 and the denominator is 256. We need to check if there are any common factors other than 1.
- By inspecting 121 and 256, we see that 121 is a perfect square (11^2), and 256 is a power of 2 (2^8). Since they have no common factors, the GCD is 1.
- This means the fraction [tex]\(\frac{121}{256}\)[/tex] is already in its simplest form.
3. Interpretation:
- The fraction [tex]\(\frac{121}{256}\)[/tex] represents a part of a whole where the whole is divided into 256 equal parts, and we are considering 121 of those parts.
4. Converting to Decimal (Optional):
- If we convert the fraction to a decimal, we divide the numerator by the denominator.
- [tex]\(\frac{121}{256} \approx 0.47265625\)[/tex] (This step is optional and often helpful for a clear, conceptual understanding).
5. Conclusion:
- In summary, the fraction [tex]\(\frac{121}{256}\)[/tex] cannot be simplified further. It represents a precise division of a whole and is accurately expressed in its given form.
By understanding and following these steps, we can confidently deal with the fraction [tex]\(\frac{121}{256}\)[/tex].
