Solve: -4(-3) Calculation Explained | Math Problem

Hey everyone! Let's dive into this math problem together and break it down step-by-step. We're going to tackle the expression -4(-3) and figure out which of the given options (A)-12, B)-7, C) 1, or D) 12) is the correct answer. Math can sometimes seem intimidating, but with a clear explanation, it becomes much easier to understand. So, grab your pencils, and let's get started!

Understanding the Basics

Before we jump right into solving -4(-3), let's quickly review some fundamental concepts that will help us. When you see two numbers next to each other with parentheses, like -4(-3), it means we need to multiply them. It's super important to remember the rules for multiplying negative numbers because they're crucial for getting the correct answer. A negative number multiplied by a negative number always gives a positive number. Think of it like this: the two negatives cancel each other out, resulting in a positive. On the other hand, a negative number multiplied by a positive number (or vice versa) always results in a negative number. These rules are the building blocks for more complex math, so it's worth making sure you're comfortable with them.

Also, understanding the concept of integers is essential here. Integers are whole numbers (not fractions) that can be positive, negative, or zero. When we're working with expressions like -4(-3), we're dealing with integer multiplication. Knowing how integers behave under different operations helps in solving various mathematical problems. For example, adding a negative number is the same as subtracting a positive number, and subtracting a negative number is the same as adding a positive number. Remembering these rules will make solving math problems much smoother and more intuitive.

Step-by-Step Solution of -4(-3)

Now, let’s solve the expression -4(-3) step-by-step. Remember, the expression means we need to multiply -4 by -3. Both numbers are negative, so we know the result will be positive, according to the rules we discussed earlier. So, we simply multiply the absolute values of the numbers: 4 multiplied by 3. 4 times 3 equals 12. Because both original numbers were negative, the final result is positive 12. Therefore, -4 multiplied by -3 equals 12. So, the correct answer is D) 12.

To recap, here’s what we did:

1. Recognized that -4(-3) means -4 multiplied by -3.
2. Remembered the rule that a negative number multiplied by a negative number results in a positive number.
3. Multiplied the absolute values: 4 * 3 = 12.
4. Concluded that -4(-3) = 12.

By following these steps, you can confidently solve similar problems. Always remember to pay close attention to the signs and apply the multiplication rules correctly.

Why the Other Options Are Incorrect

It's also helpful to understand why the other options are incorrect. This can prevent similar mistakes in the future. Let’s take a look at why A)-12, B)-7, and C) 1 are not the correct answers.

• A) -12: This answer is incorrect because it assumes that multiplying two negative numbers results in a negative number, which is not true. As we discussed, a negative number multiplied by a negative number always gives a positive number.
• B) -7: This answer might come from mistakenly adding the numbers instead of multiplying them, or from incorrectly applying the negative signs. Remember, we're dealing with multiplication here, not addition or subtraction.
• C) 1: This answer doesn't seem to have a clear logical basis based on the given expression. It's important to always double-check your work and make sure you're following the correct mathematical operations.

Understanding why these options are wrong reinforces the correct method and helps you avoid common errors. Always take the time to review your steps and ensure that each operation is done accurately.

Real-World Applications

Understanding how to multiply negative numbers isn't just useful for solving textbook problems; it has real-world applications too! For example, consider temperature changes. If the temperature is dropping by 4 degrees Celsius each hour for 3 hours, you can represent this as -4 degrees/hour * 3 hours = -12 degrees. This tells you that the total temperature drop is 12 degrees. Similarly, in finance, if you're calculating losses, negative numbers are often used. If a business loses $4 per item sold and sells 3 items, the total loss can be calculated as -4 * 3 = -$12.

These examples show how important it is to understand negative number multiplication in practical situations. Whether you're tracking changes in weather, managing finances, or analyzing scientific data, the ability to work with negative numbers is a valuable skill.

Tips for Mastering Integer Multiplication

To become truly comfortable with multiplying integers, here are a few tips:

• Practice Regularly: The more you practice, the more natural these operations will become. Try solving a variety of problems with different combinations of positive and negative numbers.
• Use Visual Aids: Sometimes, visualizing the numbers can help. Think of a number line and how moving in the negative direction twice results in a positive direction.
• Create Flashcards: Make flashcards with multiplication problems involving negative numbers. This can be a fun way to quiz yourself and reinforce the rules.
• Review the Rules: Keep the multiplication rules handy until they become second nature. A quick reminder can prevent simple mistakes.

Conclusion

In summary, the correct answer to the problem -4(-3) is D) 12. We arrived at this answer by understanding that multiplying two negative numbers results in a positive number and then performing the multiplication. By following these steps and understanding the underlying concepts, you can confidently solve similar math problems. Remember to practice regularly and review the rules to master integer multiplication. Keep up the great work, and you'll become a math whiz in no time! Keep practicing, and you'll nail it!