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Negative numbers are not as scary as they might seem. They are simply numbers with a minus sign in front of them, like -1, -2, or -35. Negative numbers are found below zero on the number line. They are essential in representing values below a certain reference point, like temperatures below freezing or a loss in finance.
When performing mathematical operations with negative numbers, especially multiplication and division, it’s important to remember the rules for signs:

• Positive × Positive = Positive
• Positive × Negative = Negative
• Negative × Negative = Positive
• Division follows the same sign rules as multiplication.

These rules help determine the sign of the outcome when working with negative numbers. They ensure consistency in mathematical calculations.

Division is one of the four basic arithmetic operations. It's a method of distributing a number into a number of equal parts. When we see an expression like \( \frac{a}{b} \), it's telling us to divide \(a\) by \(b\). This can also be understood as how many times \(b\) can be counted in \(a\).
In integer division, the result is also an integer, which means any remainder is discarded. For example, dividing 7 by 2 equals 3, ignoring the remainder of 1.
In our exercise, the division operation \( \frac{63}{-9} \) required dividing a positive number by a negative number. This, in turn, dictated the negative result. The important part of division operations with negatives is to focus on the sign and magnitude separately.

Absolute value is a concept that helps us understand numbers irrespective of their sign. It refers to the distance a number is from zero on the number line, without taking into account which direction from zero it is.
This means the absolute value of both 3 and -3 is 3, often represented as \( |3| = 3 \) and \( |-3| = 3 \). The absolute value is always non-negative.
In division, especially when working with negative numbers, finding the result often requires us to first comprehend the absolute values of the dividend and divisor. For \( \frac{63}{-9} \), we first divide the absolute values, \( 63 \div 9 = 7 \). After determining the magnitude, we adjust for the sign depending on the original division problem. Understanding absolute values helps simplify calculations and offers a clearer path to the final answer.