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Understanding the division of negative numbers can initially be confusing, but it's based on a fundamental rule in mathematics. When we divide a negative number by another negative number, the two negatives 'cancel out', and the result is a positive number.

Consider the example \( \frac{-100}{-10} \). Here both the numerator (top number) and the denominator (bottom number) are negative. According to the rules of division with negatives, we can turn the division into \( \frac{100}{10} \), removing the negative signs from both numbers. This is because any number divided by itself equals 1, and -1 divided by -1 also equals 1, so multiplying or dividing negative numbers results in a positive product or quotient.

Always remember, a negative number divided by a negative number yields a positive result; it's like two wrongs making a right in the world of mathematics.

Steps to Simplifying

The process of simplifying algebraic expressions involves a series of steps designed to reduce the expression to its most basic form. It's like breaking down a large, complex puzzle into small, easy-to-handle pieces. Simplifying can make expressions easier to work with, especially when solving for variables or working with equations.

For numerical fractions such as \( \frac{100}{10} \), simplifying involves dividing the numerator by the denominator to find the simplest form. The simplest form is achieved when both numbers cannot be divided any further by the same number, except for 1. In our example, 100 divided by 10 simplifies cleanly to 10.

This principle extends to algebraic expressions as well. Variables and coefficients are treated similarly: divide them where possible, and reduce to the lowest possible terms to simplify the expression.

When working with negative numbers, it can seem counterintuitive that multiplying or dividing two negatives can result in a positive. However, this is a consistent rule in mathematics and has practical applications.

Think of it as a scenario in everyday life: If you were to take a negative, such as 'going back' (like reversing) and apply it to another negative, like 'losing something' (also a reversal of having), you would actually end up 'going back to having it', which is a positive outcome.

In mathematics, this is expressed through the rule that states multiplying or dividing an even number of negative numbers results in a positive number. It's essential to grasp this concept because it lays the foundation for understanding more complex mathematical operations involving negative numbers.