Which Set Of Numbers Gives The Correct Possible Values Of / / / For N = 3 N=3 N = 3 ?A. 0 , 1 , 2 0, 1, 2 0 , 1 , 2 B. 0 , 1 , 2 , 3 0, 1, 2, 3 0 , 1 , 2 , 3 C. − 2 , − 1 , 0 , 1 , 2 -2, -1, 0, 1, 2 − 2 , − 1 , 0 , 1 , 2 D. − 3 , − 2 , − 1 , 0 , 1 , 2 , 3 -3, -2, -1, 0, 1, 2, 3 − 3 , − 2 , − 1 , 0 , 1 , 2 , 3

Which Set of Numbers Gives the Correct Possible Values of $/$ for $n=3$?

Understanding the Problem

The problem requires us to determine the correct set of numbers that gives the possible values of $/$ for $n=3$. To solve this problem, we need to understand the concept of division and the properties of integers.

Division and Integers

Division is a mathematical operation that involves splitting a number into equal parts. When we divide a number by another number, we are essentially finding the quotient and the remainder. In the case of integers, division can be a bit more complex.

Properties of Integers

Integers are whole numbers that can be positive, negative, or zero. They do not have any fractional parts. When we divide an integer by another integer, the result can be an integer or a fraction.

Possible Values of $/$ for $n=3$

To determine the possible values of $/$ for $n=3$, we need to consider the properties of integers and the concept of division. Let's analyze each option:

Option A: $0, 1, 2$

This option suggests that the possible values of $/$ for $n=3$ are $0, 1,$ and $2$. However, this is not possible because when we divide $3$ by $1$, the result is $3$, not $0, 1,$ or $2$.

Option B: $0, 1, 2, 3$

This option suggests that the possible values of $/$ for $n=3$ are $0, 1, 2,$ and $3$. However, this is not possible because when we divide $3$ by $1$, the result is $3$, not $0, 1, 2,$ or $3$.

Option C: $-2, -1, 0, 1, 2$

This option suggests that the possible values of $/$ for $n=3$ are $-2, -1, 0, 1,$ and $2$. This option is more plausible because when we divide $3$ by $1$, the result is $3$, which is not in the list. However, when we divide $3$ by $-1$, the result is $-3$, which is not in the list. But when we divide $3$ by $-2$, the result is $1.5$, which is not an integer. However, when we divide $3$ by $-3$, the result is $-1$, which is in the list.

Option D: $-3, -2, -1, 0, 1, 2, 3$

This option suggests that the possible values of $/$ for $n=3$ are $-3, -2, -1, 0, 1, 2,$ and $3$. This option is the most plausible because when we divide $3$ by $1$, the result is $3$, which is in the list. When we divide $3$ by $-1$, the result is $-3$, which is in the list. When we divide $3$ by $-2$, the result is $1.5$, which is not an integer. However, when we divide $3$ by $-3$, the result is $-1$, which is in the list.

Conclusion

Based on our analysis, the correct set of numbers that gives the possible values of $/$ for $n=3$ is Option D: $-3, -2, -1, 0, 1, 2, 3$. This option includes all the possible values of $/$ for $n=3$, including positive, negative, and zero values.

Understanding the Concept of Division

The concept of division is essential in mathematics, and it is used to solve a wide range of problems. When we divide a number by another number, we are essentially finding the quotient and the remainder. In the case of integers, division can be a bit more complex.

Properties of Integers

Integers are whole numbers that can be positive, negative, or zero. They do not have any fractional parts. When we divide an integer by another integer, the result can be an integer or a fraction.

Possible Values of $/$ for $n=3$

To determine the possible values of $/$ for $n=3$, we need to consider the properties of integers and the concept of division. Let's analyze each option:

Option A: $0, 1, 2$

This option suggests that the possible values of $/$ for $n=3$ are $0, 1,$ and $2$. However, this is not possible because when we divide $3$ by $1$, the result is $3$, not $0, 1,$ or $2$.

Option B: $0, 1, 2, 3$

This option suggests that the possible values of $/$ for $n=3$ are $0, 1, 2,$ and $3$. However, this is not possible because when we divide $3$ by $1$, the result is $3$, not $0, 1, 2,$ or $3$.

Option C: $-2, -1, 0, 1, 2$

This option suggests that the possible values of $/$ for $n=3$ are $-2, -1, 0, 1,$ and $2$. This option is more plausible because when we divide $3$ by $1$, the result is $3$, which is not in the list. However, when we divide $3$ by $-1$, the result is $-3$, which is not in the list. But when we divide $3$ by $-2$, the result is $1.5$, which is not an integer. However, when we divide $3$ by $-3$, the result is $-1$, which is in the list.

Option D: $-3, -2, -1, 0, 1, 2, 3$

This option suggests that the possible values of $/$ for $n=3$ are $-3, -2, -1, 0, 1, 2,$ and $3$. This option is the most plausible because when we divide $3$ by $1$, the result is $3$, which is in the list. When we divide $3$ by $-1$, the result is $-3$, which is in the list. When we divide $3$ by $-2$, the result is $1.5$, which is not an integer. However, when we divide $3$ by $-3$, the result is $-1$, which is in the list.

Conclusion

Based on our analysis, the correct set of numbers that gives the possible values of $/$ for $n=3$ is Option D: $-3, -2, -1, 0, 1, 2, 3$. This option includes all the possible values of $/$ for $n=3$, including positive, negative, and zero values.

Real-World Applications

The concept of division is essential in many real-world applications, including finance, science, and engineering. For example, when we divide a budget by the number of people, we are essentially finding the amount each person should receive. When we divide a distance by the speed, we are essentially finding the time it takes to cover that distance.

Conclusion

In conclusion, the correct set of numbers that gives the possible values of $/$ for $n=3$ is Option D: $-3, -2, -1, 0, 1, 2, 3$. This option includes all the possible values of $/$ for $n=3$, including positive, negative, and zero values. The concept of division is essential in mathematics and has many real-world applications.
Q&A: Understanding the Concept of Division

Frequently Asked Questions

In this article, we will answer some of the most frequently asked questions about the concept of division.

Q: What is division?

A: Division is a mathematical operation that involves splitting a number into equal parts. It is the inverse operation of multiplication.

Q: How do I divide a number by another number?

A: To divide a number by another number, you need to find the quotient and the remainder. The quotient is the result of the division, and the remainder is the amount left over.

Q: What is the difference between division and multiplication?

A: Division and multiplication are inverse operations. Division involves splitting a number into equal parts, while multiplication involves combining numbers to get a product.

Q: Can I divide a number by zero?

A: No, you cannot divide a number by zero. Division by zero is undefined in mathematics.

Q: What is the result of dividing a number by a negative number?

A: When you divide a number by a negative number, the result is also negative. For example, dividing 6 by -2 gives you -3.

Q: Can I divide a fraction by a fraction?

A: Yes, you can divide a fraction by a fraction. To do this, you need to invert the second fraction and multiply it by the first fraction.

Q: What is the result of dividing a decimal by a decimal?

A: When you divide a decimal by a decimal, the result is also a decimal. For example, dividing 0.5 by 0.2 gives you 2.5.

Q: Can I divide a number by a decimal?

A: Yes, you can divide a number by a decimal. To do this, you need to convert the decimal to a fraction and then divide the number by the fraction.

Q: What is the result of dividing a negative number by a negative number?

A: When you divide a negative number by a negative number, the result is positive. For example, dividing -6 by -2 gives you 3.

Q: Can I divide a number by a fraction?

A: Yes, you can divide a number by a fraction. To do this, you need to invert the fraction and multiply it by the number.

Q: What is the result of dividing a decimal by a fraction?

A: When you divide a decimal by a fraction, the result is also a decimal. For example, dividing 0.5 by 1/2 gives you 1.

Conclusion

In conclusion, division is a fundamental concept in mathematics that involves splitting a number into equal parts. It is the inverse operation of multiplication and has many real-world applications. We hope that this Q&A article has helped you understand the concept of division better.

Real-World Applications of Division

Division has many real-world applications, including:

• Finance: Division is used to calculate interest rates, investment returns, and other financial metrics.
• Science: Division is used to calculate the concentration of a solution, the density of a substance, and other scientific metrics.
• Engineering: Division is used to calculate the stress on a material, the strain on a structure, and other engineering metrics.
• Cooking: Division is used to calculate the amount of ingredients needed for a recipe, the cooking time, and other culinary metrics.

Conclusion

In conclusion, division is a fundamental concept in mathematics that has many real-world applications. We hope that this Q&A article has helped you understand the concept of division better.

Additional Resources

If you want to learn more about division, we recommend the following resources:

• Khan Academy: Division
• Mathway: Division
• Wolfram Alpha: Division

Conclusion

In conclusion, division is a fundamental concept in mathematics that has many real-world applications. We hope that this Q&A article has helped you understand the concept of division better.