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When you add or subtract fractions, the fractions must have the same denominator. The denominator is the bottom number of a fraction. For instance, in the fraction \(\frac{3}{5}\), 5 is the denominator. In our problem, we start with \(\frac{9}{8}\) and we need to subtract 2, which is an integer and doesn't have a denominator initially. To solve this, we convert the integer 2 into a fraction with the same denominator as \(\frac{9}{8}\). Since the denominator in \(\frac{9}{8}\) is 8, we convert 2 into \(\frac{16}{8}\). This way, both fractions have the same denominator.

Remember, only fractions with the same denominators can be directly subtracted or added. This makes the subtraction process simpler because you only need to focus on the numerators once the denominators are the same.

Simplifying a fraction means reducing it to its lowest terms so it is easier to understand and work with. You simplify a fraction by dividing the numerator and the denominator by their greatest common divisor (GCD).
In our problem, after subtracting \(\frac{16}{8}\) from \(\frac{9}{8}\), you get \(\frac{-7}{8}\). To check if \(\frac{-7}{8}\) can be simplified, find the GCD of -7 and 8. Here, the GCD is 1, so it's already in its simplest form. This means we cannot simplify \(\frac{-7}{8}\) any further.

Simplifying is useful because it produces the fraction in its most reduced form, making it simpler to use in future calculations.

Every fraction consists of a numerator and a denominator. The numerator is the top number of a fraction, representing how many parts we have. The denominator is the bottom number, indicating into how many parts the whole is divided.
For example, in \(\frac{9}{8}\), 9 is the numerator, and 8 is the denominator. When we convert the integer 2 into a fraction, it becomes \(\frac{16}{8}\), where 16 is the numerator, and 8 is the denominator.

To subtract or add fractions, you align the denominators and then perform the addition or subtraction within the numerators. In our problem, after converting 2 into \(\frac{16}{8}\), the actual subtraction step is performed on the numerators: 9 from \(\frac{9}{8}\) and 16 from \(\frac{16}{8}\). We get \(9 - 16 = -7\), making the resulting fraction \(\frac{-7}{8}\).
Understanding the roles of the numerator and denominator is crucial for working with and simplifying fractions effectively.