X (a) 12 × (-50) + 12 × (45) = -60
Introduction
In the world of mathematics, negative numbers can be a source of confusion and frustration for many students. However, with a clear understanding of the rules and concepts, solving equations involving negative numbers becomes a breeze. In this article, we will delve into the world of negative numbers and explore how to solve equations like x (a) 12 × (-50) + 12 × (45) = -60.
Understanding Negative Numbers
Before we dive into the solution, let's take a moment to understand what negative numbers are. A negative number is a number that is less than zero. It is denoted by a minus sign (-) and is used to represent a quantity that is opposite in direction or magnitude to a positive quantity. For example, -5 is a negative number that is opposite in direction to the positive number 5.
The Rules of Negative Numbers
When working with negative numbers, there are a few key rules to keep in mind:
- The product of two negative numbers is a positive number: When you multiply two negative numbers together, the result is a positive number. For example, (-2) × (-3) = 6.
- The product of a negative number and a positive number is a negative number: When you multiply a negative number and a positive number together, the result is a negative number. For example, (-2) × 3 = -6.
- The sum of two negative numbers is a negative number: When you add two negative numbers together, the result is a negative number. For example, (-2) + (-3) = -5.
- The sum of a negative number and a positive number is a negative number: When you add a negative number and a positive number together, the result is a negative number. For example, (-2) + 3 = 1.
Solving the Equation
Now that we have a solid understanding of negative numbers, let's tackle the equation x (a) 12 × (-50) + 12 × (45) = -60.
Step 1: Multiply 12 by -50
To start solving the equation, we need to multiply 12 by -50. Using the rule that the product of a negative number and a positive number is a negative number, we can calculate the result as follows:
12 × (-50) = -600
Step 2: Multiply 12 by 45
Next, we need to multiply 12 by 45. Using the rule that the product of two positive numbers is a positive number, we can calculate the result as follows:
12 × 45 = 540
Step 3: Add the Results
Now that we have the results of the two multiplications, we can add them together to get the final result:
-600 + 540 = -60
Step 4: Solve for x
The equation x (a) 12 × (-50) + 12 × (45) = -60 is now solved. However, we still need to solve for x. To do this, we can set up an equation using the result we obtained in step 3:
x (a) -600 + 540 = -60
Simplifying the equation, we get:
x (a) -60 = -60
Dividing both sides of the equation by -60, we get:
x (a) = 1
Step 5: Interpret the Result
The final result of x (a) = 1 means that the value of x is 1. This makes sense, as the original equation x (a) 12 × (-50) + 12 × (45) = -60 is a true statement when x is equal to 1.
Conclusion
In conclusion, solving the equation x (a) 12 × (-50) + 12 × (45) = -60 requires a clear understanding of negative numbers and the rules that govern their behavior. By following the steps outlined in this article, we can solve the equation and obtain the final result of x (a) = 1. Whether you're a student struggling with negative numbers or a seasoned mathematician looking to brush up on your skills, this article provides a comprehensive guide to solving equations involving negative numbers.
Frequently Asked Questions
Q: What is the product of two negative numbers?
A: The product of two negative numbers is a positive number.
Q: What is the product of a negative number and a positive number?
A: The product of a negative number and a positive number is a negative number.
Q: What is the sum of two negative numbers?
A: The sum of two negative numbers is a negative number.
Q: What is the sum of a negative number and a positive number?
A: The sum of a negative number and a positive number is a negative number.
Additional Resources
For more information on negative numbers and how to solve equations involving them, check out the following resources:
- Khan Academy: Negative Numbers
- Mathway: Solving Equations with Negative Numbers
- Wolfram Alpha: Negative Numbers and Equations
Final Thoughts
Q: What is the definition of a negative number?
A: A negative number is a number that is less than zero. It is denoted by a minus sign (-) and is used to represent a quantity that is opposite in direction or magnitude to a positive quantity.
Q: What is the product of two negative numbers?
A: The product of two negative numbers is a positive number. For example, (-2) × (-3) = 6.
Q: What is the product of a negative number and a positive number?
A: The product of a negative number and a positive number is a negative number. For example, (-2) × 3 = -6.
Q: What is the sum of two negative numbers?
A: The sum of two negative numbers is a negative number. For example, (-2) + (-3) = -5.
Q: What is the sum of a negative number and a positive number?
A: The sum of a negative number and a positive number is a negative number. For example, (-2) + 3 = 1.
Q: How do I solve an equation with a negative number?
A: To solve an equation with a negative number, follow these steps:
- Simplify the equation by combining like terms.
- Use the rules of negative numbers to evaluate the expression.
- Solve for the variable.
Q: What is the difference between a negative number and a positive number?
A: A negative number is a number that is less than zero, while a positive number is a number that is greater than zero.
Q: Can I add a negative number and a positive number together?
A: Yes, you can add a negative number and a positive number together. The result will be a negative number.
Q: Can I multiply a negative number and a positive number together?
A: Yes, you can multiply a negative number and a positive number together. The result will be a negative number.
Q: What is the order of operations for negative numbers?
A: The order of operations for negative numbers is the same as for positive numbers:
- Parentheses
- Exponents
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)
Q: How do I evaluate an expression with multiple negative numbers?
A: To evaluate an expression with multiple negative numbers, follow these steps:
- Simplify the expression by combining like terms.
- Use the rules of negative numbers to evaluate the expression.
- Follow the order of operations to evaluate the expression.
Q: What is the difference between a negative number and a zero?
A: A negative number is a number that is less than zero, while a zero is a number that is equal to zero.
Q: Can I divide a negative number by a positive number?
A: Yes, you can divide a negative number by a positive number. The result will be a negative number.
Q: Can I divide a positive number by a negative number?
A: Yes, you can divide a positive number by a negative number. The result will be a negative number.
Q: What is the result of dividing a negative number by a negative number?
A: The result of dividing a negative number by a negative number is a positive number.
Q: What is the result of dividing a positive number by a positive number?
A: The result of dividing a positive number by a positive number is a positive number.
Q: How do I round a negative number?
A: To round a negative number, follow these steps:
- Determine the digit to the right of the rounding digit.
- If the digit is 5 or greater, round up.
- If the digit is less than 5, round down.
Q: Can I use a calculator to evaluate an expression with negative numbers?
A: Yes, you can use a calculator to evaluate an expression with negative numbers. However, make sure to follow the order of operations and use the correct signs.
Q: What is the difference between a negative number and a decimal number?
A: A negative number is a number that is less than zero, while a decimal number is a number that has a decimal point.
Q: Can I add a negative number and a decimal number together?
A: Yes, you can add a negative number and a decimal number together. The result will be a negative number.
Q: Can I multiply a negative number and a decimal number together?
A: Yes, you can multiply a negative number and a decimal number together. The result will be a negative number.
Q: What is the result of dividing a negative number by a decimal number?
A: The result of dividing a negative number by a decimal number is a negative number.
Q: What is the result of dividing a decimal number by a negative number?
A: The result of dividing a decimal number by a negative number is a negative number.
Conclusion
In conclusion, negative numbers are an important concept in mathematics, and understanding how to work with them is crucial for solving equations and evaluating expressions. By following the rules of negative numbers and using the correct signs, you can evaluate expressions and solve equations with ease. Whether you're a student struggling with negative numbers or a seasoned mathematician looking to brush up on your skills, this article provides a comprehensive guide to negative numbers and equations.