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When working with numbers, the absolute value is a key concept to understand. It represents the distance of a number from zero on a number line, without considering its direction.
For example, the absolute value of both 7 and -7 is 7, as they are each 7 units away from zero. To denote this, we use the symbol "| |".

So, the absolute value of 7 is written as \(|7| = 7\), and the absolute value of \(-9\) is \(|-9| = 9\). This concept helps simplify calculations, especially when dealing with multiplication or division involving negative numbers. Instead of worrying about their signs initially, we focus on the absolute values.

When multiplying numbers, certain rules help determine the sign of the result. These rules don’t change with larger or smaller numbers. They remain constant no matter what. Here’s what you need to remember:

• A positive number multiplied by a positive number gives a positive result.
• A negative number multiplied by a negative number also gives a positive result.
• A positive number multiplied by a negative number gives a negative result. This is what we see in the exercise: \((7) \times (-9)\).

Understanding these rules makes it easier to figure out the sign of the answer before even calculating the actual product. By doing so, you can avoid simple mistakes and work through problems more efficiently.

The concept of getting a negative result when multiplying is straightforward once you understand the rules. Whenever you multiply a positive and a negative number, you end up with a negative product. In the given exercise, the numbers are 7 and -9.
The product of the absolute values is 63. But since one of the numbers (in this case, -9) is negative, the whole product becomes negative. Thus, the finalized result is \(-63\).

This might look a bit counterintuitive at first. Think about adding compliments and criticisms: a compliment (+) and a criticism (-), combined together, lean mostly towards a negative feeling overall. This simple analogy helps in remembering why a positive and a negative yield a negative.