Como Calcular Números Negativos
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Negative numbers are essential in mathematics and real-world applications. This guide explains how to perform basic operations with negative numbers, understand the rules that govern them, and see practical examples of their use.
Basic Operations with Negative Numbers
Negative numbers represent values that are less than zero. They are used in various mathematical operations and real-world scenarios. Here's how to perform basic operations with negative numbers:
Addition and Subtraction
When adding or subtracting negative numbers, follow these rules:
- Adding a negative number is the same as subtracting its positive counterpart.
- Subtracting a negative number is the same as adding its positive counterpart.
- Subtracting a positive number is the same as adding its negative counterpart.
Addition: a + (-b) = a - b
Subtraction: a - (-b) = a + b
Multiplication and Division
When multiplying or dividing negative numbers, follow these rules:
- A negative times a negative equals a positive.
- A negative times a positive equals a negative.
- A positive times a negative equals a negative.
- A positive times a positive equals a positive.
Multiplication: (-a) × (-b) = a × b
Division: (-a) ÷ (-b) = a ÷ b
Absolute Value
The absolute value of a number is its distance from zero on the number line, regardless of direction. The absolute value of a negative number is its positive counterpart.
Absolute Value: |-a| = a
Rules for Negative Numbers
Understanding the rules for negative numbers is crucial for performing accurate calculations. Here are the key rules:
Addition and Subtraction Rules
- Adding two negative numbers results in a negative number.
- Subtracting a negative number from a positive number results in a positive number.
- Subtracting a positive number from a negative number results in a negative number.
Addition: (-a) + (-b) = -(a + b)
Subtraction: (-a) - (-b) = -a + b
Multiplication and Division Rules
- Multiplying two negative numbers results in a positive number.
- Multiplying a negative number by a positive number results in a negative number.
- Dividing two negative numbers results in a positive number.
- Dividing a negative number by a positive number results in a negative number.
Multiplication: (-a) × (-b) = a × b
Division: (-a) ÷ (-b) = a ÷ b
Order of Operations
When performing calculations with negative numbers, follow the order of operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
Worked Examples
Let's look at some worked examples to see how negative numbers are used in calculations.
Example 1: Addition and Subtraction
Calculate the following expressions:
- 5 + (-3) = 2
- -4 - (-2) = -2
- -7 + 3 = -4
Example 2: Multiplication and Division
Calculate the following expressions:
- -6 × (-4) = 24
- -8 ÷ (-2) = 4
- 5 × (-3) = -15
Example 3: Absolute Value
Calculate the absolute values of the following numbers:
- |-9| = 9
- |5| = 5
- |-2.5| = 2.5
| Expression | Calculation | Result |
|---|---|---|
| 5 + (-3) | 5 - 3 | 2 |
| -4 - (-2) | -4 + 2 | -2 |
| -7 + 3 | -7 - 3 | -10 |
| -6 × (-4) | 6 × 4 | 24 |
| -8 ÷ (-2) | 8 ÷ 2 | 4 |
| 5 × (-3) | 5 × -3 | -15 |
Real-World Applications
Negative numbers are used in various real-world applications, including finance, science, and engineering. Here are some examples:
Finance
In finance, negative numbers represent debts, losses, or decreases in value. For example, a bank account balance of -$50 indicates a debt of $50.
Science
In science, negative numbers represent values below a reference point, such as below sea level or below freezing. For example, a temperature of -5°C indicates 5 degrees below freezing.
Engineering
In engineering, negative numbers represent values in the opposite direction, such as left or downward. For example, a displacement of -3 meters indicates a movement of 3 meters to the left.
Negative numbers are essential in various fields and help represent values that are less than zero. Understanding how to work with negative numbers is crucial for accurate calculations and problem-solving.
FAQ
What is a negative number?
A negative number is a number that is less than zero. It represents a value that is opposite in direction or sense to a positive number.
How do you add and subtract negative numbers?
To add or subtract negative numbers, follow the rules for addition and subtraction of negative numbers. Adding a negative number is the same as subtracting its positive counterpart, and subtracting a negative number is the same as adding its positive counterpart.
How do you multiply and divide negative numbers?
To multiply or divide negative numbers, follow the rules for multiplication and division of negative numbers. A negative times a negative equals a positive, and a negative times a positive equals a negative. Similarly, a negative divided by a negative equals a positive, and a negative divided by a positive equals a negative.
What is the absolute value of a negative number?
The absolute value of a negative number is its positive counterpart. For example, the absolute value of -5 is 5.
Where are negative numbers used in real life?
Negative numbers are used in various real-world applications, including finance, science, and engineering. In finance, negative numbers represent debts or losses. In science, negative numbers represent values below a reference point. In engineering, negative numbers represent values in the opposite direction.