Clara Multiplies \[$(-6)(-7)(-1)\$\] And Gets 42. Is Her Answer Reasonable?A. No, Because The Solution Should Have A Negative Answer.B. No, Because The Solution Should Have A Positive Answer.C. Yes, Because The Solution Should Have A Negative
Is Clara's Answer Reasonable? A Mathematical Analysis
In mathematics, multiplication is a fundamental operation that involves the combination of two or more numbers to produce a product. When multiplying negative numbers, it's essential to understand the rules governing the signs of the numbers involved. In this article, we will delve into the world of negative numbers and explore whether Clara's answer to the multiplication problem {(-6)(-7)(-1)$}$ is reasonable.
Before we proceed, let's briefly review the concept of negative numbers. A negative number is a number that is less than zero. In the context of multiplication, when two or more negative numbers are multiplied together, the result is a positive number. This is because the negative signs cancel each other out, resulting in a positive product.
Clara is faced with the multiplication problem {(-6)(-7)(-1)$}$. To determine whether her answer is reasonable, we need to follow the rules of multiplication involving negative numbers. When multiplying three negative numbers, we can use the following steps:
- Multiply the first two numbers: {(-6)(-7)$ = 42}$
- Multiply the result by the third number: ${42(-1)\$ = -42}
Now that we have the correct solution to the multiplication problem, let's examine whether Clara's answer is reasonable. According to the rules of multiplication involving negative numbers, the product of three negative numbers should be a positive number. However, Clara's answer is 42, which is a positive number. Therefore, her answer is reasonable.
In conclusion, Clara's answer to the multiplication problem {(-6)(-7)(-1)$}$ is reasonable. The rules of multiplication involving negative numbers dictate that the product of three negative numbers should be a positive number. By following these rules, we can determine that Clara's answer is correct. This analysis demonstrates the importance of understanding the rules of multiplication involving negative numbers in mathematics.
To further reinforce the concept of negative numbers and multiplication, let's consider a few additional examples:
- {(-3)(-4)$ = 12}$
- {(-5)(-6)$ = 30}$
- {(-2)(-3)(-4)$ = -24}$
In each of these examples, the product of two or more negative numbers results in a positive number. This is a fundamental property of multiplication involving negative numbers.
In conclusion, Clara's answer to the multiplication problem {(-6)(-7)(-1)$}$ is reasonable. By understanding the rules of multiplication involving negative numbers, we can determine that the product of three negative numbers should be a positive number. This analysis demonstrates the importance of mathematical reasoning and problem-solving skills in mathematics.
For those interested in further exploring the concept of negative numbers and multiplication, we recommend the following resources:
- Khan Academy: Multiplication of Negative Numbers
- Mathway: Multiplication of Negative Numbers
- Wolfram Alpha: Multiplication of Negative Numbers
These resources provide a comprehensive overview of the rules of multiplication involving negative numbers and offer additional examples and exercises to reinforce understanding.
- "Multiplication of Negative Numbers" by Khan Academy
- "Multiplication of Negative Numbers" by Mathway
- "Multiplication of Negative Numbers" by Wolfram Alpha
Note: The references provided are online resources that offer a comprehensive overview of the rules of multiplication involving negative numbers. They are not academic papers or research articles.
Clara's Answer: A Q&A on Multiplication of Negative Numbers
In our previous article, we explored whether Clara's answer to the multiplication problem {(-6)(-7)(-1)$}$ was reasonable. We determined that her answer was correct, and the product of three negative numbers is indeed a positive number. In this article, we will delve into a Q&A session to further clarify the rules of multiplication involving negative numbers.
Q: What is the rule for multiplying negative numbers?
A: When multiplying two or more negative numbers, the result is a positive number. This is because the negative signs cancel each other out, resulting in a positive product.
Q: Can you provide an example of multiplying two negative numbers?
A: Yes, let's consider the example {(-3)(-4)$ = 12}$. In this case, the two negative numbers are multiplied together, resulting in a positive product.
Q: What happens when we multiply three negative numbers?
A: When we multiply three negative numbers, the result is a positive number. This is because the negative signs cancel each other out, resulting in a positive product. For example, {(-6)(-7)(-1)$ = 42}$.
Q: Can you explain why the product of three negative numbers is positive?
A: When we multiply three negative numbers, we can think of it as multiplying three negative signs together. Since the negative signs cancel each other out, the result is a positive number. This is a fundamental property of multiplication involving negative numbers.
Q: What about the product of two positive numbers and a negative number?
A: When we multiply two positive numbers and a negative number, the result is a negative number. This is because the negative sign "cancels out" one of the positive signs, resulting in a negative product. For example, {(3)(4)(-1)$ = -12}$.
Q: Can you provide an example of multiplying a positive number and a negative number?
A: Yes, let's consider the example {(5)(-2)$ = -10}$. In this case, the positive number and the negative number are multiplied together, resulting in a negative product.
Q: What about the product of three positive numbers and a negative number?
A: When we multiply three positive numbers and a negative number, the result is a negative number. This is because the negative sign "cancels out" one of the positive signs, resulting in a negative product. For example, {(6)(7)(8)(-1)$ = -336}$.
Q: Can you explain why the product of three positive numbers and a negative number is negative?
A: When we multiply three positive numbers and a negative number, we can think of it as multiplying three positive signs together and then multiplying by a negative sign. Since the negative sign "cancels out" one of the positive signs, the result is a negative number.
In conclusion, the rules of multiplication involving negative numbers are straightforward: the product of two or more negative numbers is a positive number, and the product of a positive number and a negative number is a negative number. By understanding these rules, we can determine the product of any combination of positive and negative numbers.
To further reinforce the concept of negative numbers and multiplication, let's consider a few additional examples:
- {(-2)(-3)(-4)$ = 24}$
- {(2)(3)(-4)$ = -24}$
- {(-5)(-6)(-7)$ = 210}$
In each of these examples, the product of two or more negative numbers results in a positive number, and the product of a positive number and a negative number results in a negative number.
In conclusion, the rules of multiplication involving negative numbers are essential to understanding the concept of negative numbers and multiplication. By following these rules, we can determine the product of any combination of positive and negative numbers.
For those interested in further exploring the concept of negative numbers and multiplication, we recommend the following resources:
- Khan Academy: Multiplication of Negative Numbers
- Mathway: Multiplication of Negative Numbers
- Wolfram Alpha: Multiplication of Negative Numbers
These resources provide a comprehensive overview of the rules of multiplication involving negative numbers and offer additional examples and exercises to reinforce understanding.
- "Multiplication of Negative Numbers" by Khan Academy
- "Multiplication of Negative Numbers" by Mathway
- "Multiplication of Negative Numbers" by Wolfram Alpha
Note: The references provided are online resources that offer a comprehensive overview of the rules of multiplication involving negative numbers. They are not academic papers or research articles.