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When multiplying fractions, it's helpful to think of it as simply multiplying two numbers together, but with one extra step. First, you need to multiply the numerators, which are the numbers on the top of each fraction.
For example, when multiplying \(-\frac{8}{12}\) and \(\frac{10}{20}\), you multiply \(-8\) (the numerator of the first fraction) by \(10\) (the numerator of the second fraction). This gives you \(-80\).

Next, multiply the denominators, which are the bottom numbers. For our example, multiply \(12\) by \(20\), resulting in \(240\).
So, after multiplying both the numerators and denominators, the product before simplification is \(-\frac{80}{240}\).

Multiplying fractions is straightforward as it only requires these two multiplication steps. However, keep in mind that a crucial step follows: simplification.

Simplifying fractions involves reducing them to their simplest form, where the numerator and the denominator no longer share any common factors other than 1.
For the fraction \(-\frac{80}{240}\), we look to simplify by dividing both the numerator and the denominator by their greatest common factor.
This simplification ensures the fraction is as easy to understand and use as possible.

To simplify \(-\frac{80}{240}\), after finding that \(80\) is the greatest common factor of both the numerator and the denominator, we divide each by \(80\).
This results in \(-\frac{1}{3}\), which is the fraction in its simplest form.
Simplification helps make fractions cleaner and easier to interpret in calculations and comparisons.

The greatest common divisor (GCD) is the largest number that divides both the numerator and the denominator without leaving a remainder.
It is a tool used for simplifying fractions to their lowest terms, ensuring that no further division of common factors is possible.

To find the GCD of two numbers, you can use methods like listing the factors of each number or using the Euclidean algorithm, which involves repeated division.

• By listing factors, consider the two numbers \(80\) and \(240\), whose common factors include \(1, 2, 4, 5, 8, 10, 20, 40,\) and \(80\).
• The largest of these is \(80\), making it their GCD.

Once the GCD is found, you then divide both the numerator and the denominator by it to simplify the fraction.
This method not only aids in simplification but also enhances overall calculation efficiency and comprehension.