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Negative numbers are numbers that are less than zero. They are denoted with a minus sign (-) in front. These numbers represent quantities that are below zero, such as temperatures below freezing or debts. Negative numbers are located to the left of the zero on a number line. They are essential in various real-life scenarios such as banking, where they might represent owed money, or in thermometers representing temperatures below zero.

When dealing with negative numbers in operations, remember:

• Adding a negative number is like subtracting its positive counterpart.
• Subtracting a negative number is like adding its positive counterpart.
• Multiplying or dividing two negative numbers results in a positive number.
• Multiplying or dividing a positive and a negative number results in a negative number.

The absolute value of a number is the distance that number is from zero on a number line, regardless of direction. It is always a non-negative number. For example, both -3 and 3 have an absolute value of 3 because they are three units away from zero.

Absolute value is shown using vertical bars on either side of the number, such as \(|-4.9| = 4.9\). This shows that the magnitude or "size" of the number is 4.9 regardless of whether it's negative or positive.

Knowing how to calculate the absolute value is essential because it helps simplify and understand equations and inequalities. It especially comes into play when figuring out opposites of negative and positive numbers, as the opposite of a number is the same distance away from zero but in the other direction.

Positive numbers are greater than zero and do not have a minus sign in front of them, though it's common to leave out the positive sign (+) as it is usually understood. They are used to represent values or quantities greater than zero, like a bank credit, temperatures above zero, or the total of counted items.

On a number line, positive numbers are found to the right of zero. They have particular properties when used in different operations:

• Adding two positive numbers results in a positive number.
• Subtracting a smaller positive number from a larger one keeps the result positive.
• Multiplying two positive numbers also results in a positive number.
• Dividing one positive number by another results in a positive number as long as the divisor isn't zero.

Understanding positive numbers helps in finding the opposite of negative numbers, as discussed in the original exercise where a negative number's opposite was found by changing its sign to positive.