Examine The Expression Below. Do Not Solve. Use The Dropdowns To State If The Answer Should Be Positive, Negative, Or Zero, And Explain Why. − 8 × − 9 -8 \times -9 − 8 × − 9 Answer:The Answer Would Be ______ Because This Is A ______ Problem. Submit Answer

When dealing with multiplication involving negative numbers, it's essential to understand the rules and conventions that govern these operations. In this article, we'll examine the expression $-8 \times -9$ and determine whether the answer should be positive, negative, or zero, along with the reasoning behind our conclusion.

The Concept of Negative Numbers

Negative numbers are a fundamental concept in mathematics, representing quantities that are less than zero. They are often used to indicate debt, temperature below zero, or other values that are less than the reference point. In the context of multiplication, negative numbers can be thought of as a way to indicate the direction or magnitude of a quantity.

The Rules of Multiplication with Negative Numbers

When multiplying two negative numbers, we need to consider the rules that govern this operation. In general, the product of two negative numbers is a positive number. This is because the negative signs "cancel out" each other, resulting in a positive product.

Applying the Rules to the Expression $-8 \times -9$

Now that we've established the rules for multiplying negative numbers, let's apply them to the expression $-8 \times -9$. Since both numbers are negative, we can expect the product to be positive.

Why the Answer is Positive

The answer to the expression $-8 \times -9$ is positive because this is a multiplication problem involving two negative numbers. As we discussed earlier, the product of two negative numbers is always positive. Therefore, the answer to this expression is a positive number.

Conclusion

In conclusion, the answer to the expression $-8 \times -9$ is positive because it involves the multiplication of two negative numbers. This is a fundamental rule in mathematics, and understanding this concept is essential for solving problems involving negative numbers.

Common Misconceptions

One common misconception about negative numbers is that they are always negative. However, as we've seen, the product of two negative numbers is actually positive. This can be confusing, especially for students who are new to the concept of negative numbers.

Real-World Applications

Understanding the rules of multiplication with negative numbers has real-world applications in various fields, such as finance, physics, and engineering. For example, in finance, a negative return on investment can indicate a loss, while in physics, a negative velocity can indicate a direction opposite to the reference point.

Tips for Solving Problems with Negative Numbers

When solving problems involving negative numbers, it's essential to remember the following tips:

• Understand the rules of multiplication with negative numbers.
• Identify the signs of the numbers involved in the problem.
• Apply the rules to determine the product.
• Check your answer to ensure it makes sense in the context of the problem.

By following these tips, you'll be well on your way to mastering the concept of negative numbers and solving problems with confidence.

Conclusion

In conclusion, the answer to the expression $-8 \times -9$ is positive because it involves the multiplication of two negative numbers. Understanding the rules of multiplication with negative numbers is essential for solving problems in mathematics and real-world applications. By following the tips outlined in this article, you'll be able to tackle problems involving negative numbers with confidence.

Final Thoughts

In the previous article, we explored the concept of negative numbers and the rules of multiplication with negative numbers. However, we know that there are many more questions and concerns that students and educators may have about negative numbers. In this article, we'll address some of the most frequently asked questions about negative numbers.

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. For example, -5 is a negative number, while 5 is a positive number.

Q: Why do we need negative numbers?

A: Negative numbers are essential in mathematics and real-world applications. They allow us to represent quantities that are less than zero, such as debt, temperature below zero, or other values that are less than the reference point.

Q: How do I add and subtract negative numbers?

A: When adding or subtracting negative numbers, you need to follow the rules of addition and subtraction. For example, -3 + (-4) = -7, while -3 - (-4) = 1.

Q: What is the rule for multiplying negative numbers?

A: The rule for multiplying negative numbers is that the product of two negative numbers is a positive number. For example, -3 × -4 = 12.

Q: What is the rule for dividing negative numbers?

A: The rule for dividing negative numbers is that the quotient of two negative numbers is a positive number. For example, -12 ÷ -4 = 3.

Q: Can I have a negative number as a fraction?

A: Yes, you can have a negative number as a fraction. For example, -1/2 is a negative fraction.

Q: Can I have a negative number as a decimal?

A: Yes, you can have a negative number as a decimal. For example, -0.5 is a negative decimal.

Q: How do I compare negative numbers?

A: When comparing negative numbers, you need to follow the rules of comparison. For example, -3 is less than -2, while -2 is greater than -3.

Q: Can I have a negative number as an exponent?

A: Yes, you can have a negative number as an exponent. For example, 2^(-3) = 1/8.

Q: Can I have a negative number as a root?

A: Yes, you can have a negative number as a root. For example, the square root of -4 is 2i.

Q: How do I graph negative numbers on a number line?

A: When graphing negative numbers on a number line, you need to place the negative number to the left of the reference point. For example, -3 is graphed to the left of 0 on a number line.

Conclusion

In conclusion, negative numbers are an essential concept in mathematics and real-world applications. By understanding the rules of addition, subtraction, multiplication, and division with negative numbers, you'll be able to tackle problems with confidence. Remember to always follow the rules and conventions that govern these operations, and don't be afraid to ask for help when you need it.

Final Thoughts

The concept of negative numbers may seem complex at first, but with practice and patience, you'll become proficient in solving problems involving negative numbers. Remember to always understand the rules and conventions that govern these operations, and don't be afraid to ask for help when you need it. With persistence and dedication, you'll master the art of solving problems with negative numbers.