I mean, the way I read this, I think the source of the problem is your confusion about \( \frac{3\pi}{8} \) versus \( \frac{1.5\pi}{4} \).

Remember, **they are the same number**. If you typed \( \frac{1.5}{4} \) and \( \frac{3}{8}\) into your calculator, you'll get the same number. This is because we can go from \( \frac{1.5}{4}\) to \( \frac{3}{8}\) by multiplying both the numerator and denominator by 2. Which is equivalent to multiplying the entire expression by 1, and hence does not change the number.

Similarly, we can go from \( \frac{3}{8}\) to \( \frac{1.5}{4} \) by dividing by 2.

However as a convention, we always like to keep a fraction as a **simplified fraction** where possible. This is when the fraction is written as \( \frac{a}{b} \), where \(a\) and \(b\) are both integers (whole numbers), but also have no common factors. So for example, rather than \( \frac{1.5}{4}\), we prefer to write it as \( \frac{3}{8}\) to avoid the decimal. As another example, rather than \( \frac{6}{24}\), we prefer to cancel it back down to \( \frac14\).