Directed numbers, also known as signed numbers, are a mathematical concept that extends the set of natural numbers to include both positive and negative integers. Directed numbers are essential in various areas of mathematics, including algebra, calculus, and geometry. In this article, we will explore the concept of directed numbers, their representation, operations, and applications.

## REPRESENTATION OF DIRECTED NUMBERS

Directed numbers are represented using a sign** (+ or -)** in front of the number. The positive sign **(+)** is used to indicate a number greater than zero, while the negative sign **(-)** is used to indicate a number less than zero. For example, **+5** represents a positive number, and **-3** represents a negative number.

## OPERATIONS WITH DIRECTED NUMBERS

### ADDITION AND SUBTRACTION

When adding or subtracting directed numbers, we consider the signs of the numbers involved:

If the signs are the same (both positive or both negative), when adding, we add their absolute values and keep the common sign.

For example: (+3) + (+2) = +5 and (-4) + (-2) = -6.

If the signs are different, we subtract the smaller absolute value from the larger absolute value and use the sign of the number with the larger absolute value.

For example: (+4) + (-2) = +2 and (-5) + (+3) = -8.

### MULTIPLICATION AND DIVISION

When multiplying or dividing directed numbers, we consider the signs of the numbers involved:

If the signs are the same, the result is positive.

For example, (+3) \times (+2) = +6 and \frac{(-4)}{(-2)} = +2.

If the signs are different, the result is negative.

For example: (-4) \times (+2) = -8 and \frac{(+5)}{(-2)} = -2.5.

**See also: PERCENTAGES AND ITS RELATIONSHIP WITH FRACTIONS AND DECIMALS WITH VIDEO**

## APPLICATIONS OF DIRECTED NUMBERS

### TEMPERATURE

Directed numbers are commonly used to represent temperatures. Positive numbers represent temperatures above the reference point (such as 0 degrees Celsius), while negative numbers represent temperatures below the reference point. For example, +10°C represents a temperature of 10 degrees above 0°C, while -5°C represents a temperature of 5 degrees below 0°C.

### ELEVATION

Directed numbers are used to represent elevation or altitude. Positive numbers represent points above a reference level, such as sea level, while negative numbers represent points below the reference level. For instance, +100 meters represents an elevation of 100 meters above sea level, while -50 meters represents a depth of 50 meters below sea level.

### FINANCIAL TRANSACTION

Directed numbers find applications in finance and accounting, where they are used to represent gains and losses. Positive numbers represent gains or profits, while negative numbers represent losses or expenses. For example, +$100 indicates a gain of $100, while -$50 represents a loss of $50.

### VECTOR OPERATIONS

Directed numbers play a crucial role in vector operations in physics and geometry. Vectors have both magnitude and direction, which can be represented using directed numbers. Positive and negative signs indicate the direction of vectors, such as upward or downward, right or left, etc.

## CONCLUSION

Directed numbers, or signed numbers, expand the concept of numbers beyond natural numbers to include positive and negative integers. They are represented using a sign (+ or -) in front of the number, with the positive sign indicating numbers greater than zero and the negative sign indicating numbers less than zero.

Directed numbers are involved in various mathematical operations, including addition, subtraction, multiplication, and division. They find applications in temperature measurement, elevation, financial transactions, vector operations, and many other areas of mathematics and real-world scenarios.

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