Simplifying Fractions: Multiplying -5 * 2/3 * -7/4

Hey guys! Today, we're diving into the fascinating world of multiplying fractions, specifically tackling a problem that might seem a little intimidating at first glance. We've got a series of multiplications involving negative numbers and fractions, and our ultimate goal is to simplify the answer to its simplest form. Don't worry, though! We'll break it down step by step, making sure everyone understands the process. So, grab your pencils and let's get started!

Understanding the Basics of Fraction Multiplication

Before we jump into the main problem, let's quickly recap the fundamental principles of multiplying fractions. Multiplying fractions is actually quite straightforward: you simply multiply the numerators (the top numbers) together and the denominators (the bottom numbers) together. That’s the core concept, but the magic truly begins when you are faced with negative numbers, like in our problem! Remember the rules of multiplying integers: a negative times a negative equals a positive, and a negative times a positive equals a negative. Keeping these rules fresh in your mind will make multiplying fractions a breeze. Once we've multiplied, our journey isn't over. We often need to simplify the resulting fraction to its simplest form. This means finding the greatest common factor (GCF) of the numerator and the denominator and dividing both by it. This process ensures we've expressed the fraction in its most reduced form, making it easier to understand and work with in future calculations. This is crucial because a simplified fraction represents the same value as the original but in a more concise way. Imagine it like this: 4/8 and 1/2 both represent the same amount, but 1/2 is much easier to visualize and use in further calculations. So, always aim for the simplest form!

Tackling Negative Signs: The Golden Rules

Now, let's talk about the negative signs. These can sometimes trip us up, but don't worry, we've got some golden rules to guide us. When multiplying numbers with the same sign (either both positive or both negative), the result is always positive. This is because a negative times a negative cancels each other out, resulting in a positive product. Think of it like this: if you're consistently doing the opposite of a negative action, you're effectively doing something positive. Conversely, when multiplying numbers with different signs (one positive and one negative), the result is always negative. This is because the negative sign essentially