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Multiplying fractions might seem tricky at first, but it's quite straightforward once you understand the steps. When you multiply fractions, follow these easy steps:

* **Multiply the Numerators:** This means you take the top numbers of your fractions and multiply them. In our exercise, we multiplied 9 and -7 to get -63.
* **Multiply the Denominators:** For this step, you take the bottom numbers of your fractions and multiply them. In the exercise, we multiplied 20 and 15 to get 300.

So, the operation \(\frac{9}{20} \times -\frac{7}{15}\) results in \(\frac{-63}{300}\). It's just that simple! Remember, you don't need to find a common denominator before you multiply.

Fractions often look neater and are easier to understand when they are simplified. To simplify a fraction, you divide both the numerator and the denominator by their greatest common divisor (GCD).

Here's a step-by-step method to simplify fractions:

* **Find the GCD of the numerator and denominator:** The GCD is the largest number that can exactly divide both numbers. In the solution, the GCD of 63 and 300 is 3.

* **Divide both the numerator and the denominator by the GCD:** This step reduces your fraction to its simplest form. For our example, dividing -63 by 3 and 300 by 3 gives us \(\frac{-21}{100}\).

And there you have it—a simplified fraction! When you encounter a fraction, ask yourself if the numbers share any common factors and simplify them accordingly.

Understanding the Greatest Common Divisor (GCD) can help simplify your work with fractions. The GCD is the largest number that can evenly divide two or more numbers.

Here's a straightforward method to find the GCD:

* **List the factors of each number:** Factors are numbers you can multiply together to get the original number.
* **Identify the common factors:** Look for numbers that appear in the factor lists of both the numerator and the denominator.
* **Choose the largest common factor:** This number is the GCD.

Let's apply this to our exercise:

*Factors of 63:* 1, 3, 7, 9, 21, 63
*Factors of 300:* 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
The common factors of 63 and 300 are 1 and 3, with 3 being the largest. Therefore, the GCD is 3.