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Multiplying fractions might seem tricky at first, but it follows a simple rule. You have to multiply the numerators (top numbers) together and the denominators (bottom numbers) together to get the new numerator and denominator for the product. For example, if you have two fractions
\( \frac{a}{b} \) and \( \frac{c}{d} \)
, their product would be \( \frac{a \times c}{b \times d} \) . It's essential to perform the multiplication before simplifying because this gives you the exact numerator and denominator for the resulting fraction. Sometimes, you can simplify the fractions before multiplying if they have common factors, but this step isn't always necessary and can be done after multiplication as well.

A fraction is said to be in its lowest terms when it cannot be reduced any further, meaning that the numerator and the denominator do not share any common factors other than 1. Simplifying fractions to their lowest terms makes them easier to understand and work with, especially when comparing fractions or converting them to decimals. To simplify a fraction, divide both the numerator and denominator by their greatest common factor (GCF), which is the largest number that divides both without a remainder. If the GCF is 1, the fraction is already in its lowest terms.

The Greatest Common Factor (GCF), also known as the greatest common divisor, is pivotal in simplifying fractions. It's the highest number that can divide both the numerator and the denominator without leaving a remainder. Finding it might seem daunting, but there are various methods to do so, such as listing out the factors of both numbers and choosing the largest one they have in common, or using the Euclidean algorithm. Once the GCF is determined, you divide both the numerator and the denominator by this number to simplify the fraction to its lowest terms. Always remember that the GCF is never larger than the smallest of the two numbers you're comparing.

Multiplication involving negative numbers follows specific rules. When multiplying two numbers with different signs (one positive and one negative), the result is always negative. Conversely, when multiplying two numbers with the same sign (both positive or both negative), the result is always positive. For example, \( (-4) \times 5 = -20 \) because the signs are different, and \( (-3) \times (-6) = 18 \) because the signs are the same. In our exercise, both numerators were negative, which will result in a positive product after multiplication, since a negative times a negative equals a positive.