Negative Rational Numbers

Negative rational numbers can be whole numbers, decimals, or fractions carrying a negative sign (-) in front of them. Examples include -1/2, -4, and -3/5.

A number line is an endless line that extends infinitely on both sides. It has 0 as its midpoint; numbers to the right of 0 are positive, and numbers to the left are negative. Like other numbers, even negative rational numbers can be represented on a number line. Let’s see how:

• Draw a horizontal line and mark a point in the center as 0 (zero).

• Mark equal intervals to the left and right of zero to represent numbers.

• Since we are dealing with negative rational numbers, we will focus on the left side of zero.

• Convert the negative rational number into its fraction or decimal form when conversion is needed.

• Divide the space between whole numbers into equal parts, depending on the denominator.

Example 1: Represent -3/4

• Find the space between 0 and -1 on the number line.
   
• Divide it into 4 equal parts (because the denominator is 4).
   
• From 0 toward -1, count 3 parts and mark it as −3/4.

Example 2: Represent −1.5

• Locate −1 and -2 on the number line.

• Since −1.5 is halfway between -1 and -2, place a point in the middle; that’s -1.5.

It is the fraction that represents the number with a negative sign in front of the fraction or in the numerator. For example, - a/b where: 
a and b are positive integers. You can see that the negative sign is placed in front of the fraction, which is in its lowest (simplest) form. It is important to note that the denominator is always positive.

Examples:

• −4/6 → simplify to - 2/3 → standard form 
   
• −6/8 → rewrite as −3/4 → standard form
   
• −10/20 → simplify to −1/2 → standard form
   
• −7 → can be written as −7/1 → standard form

Here, the numbers −4/6, −6/8, and −10/20 are simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD). 

There are many real-life applications of negative rational numbers that we use. Let's see some examples, which are mentioned below.

• Temperature: In cold climates, temperatures like –10°C or –5°F are common. Negative numbers are used to represent temperatures below the freezing point.

• Elevation Below Sea Level: The Dead Sea is about –430 meters below sea level. Negative values show depth or places below the reference level.

• Stock Market Losses: If a stock drops by (-2.5%), it means the value decreased. Negative percentages show losses or decreases in value.

• Weight Change or Calorie Deficit: If someone burns more calories than they eat, the result might be a 500-calorie-per-day deficit. Used in tracking weight loss or diet deficits.

• Gaming (Losing Points or Lives): A player loses a life or 50 points; the loss of 50 points is indicated using the negative sign (–50 points).