What Is The Quotient Of 6 And $-\frac{1}{2}$?A. $-12$ B. $-\frac{1}{12}$ C. $ 1 12 \frac{1}{12} 12 1 ​ [/tex] D. 12

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When dealing with mathematical operations, it's essential to understand the concept of quotient, which is the result of dividing one number by another. In this article, we will explore the quotient of 6 and $-\frac{1}{2}$, and examine the different options provided.

What is a Quotient?

A quotient is the result of dividing one number by another. It's a fundamental concept in mathematics that helps us understand the relationship between numbers. When we divide one number by another, we are essentially finding the number of times the divisor fits into the dividend.

The Quotient of 6 and $-\frac{1}{2}$

To find the quotient of 6 and $-\frac{1}{2}$, we need to divide 6 by $-\frac{1}{2}$. This can be done using the following steps:

  1. Change the sign of the divisor: Since the divisor is negative, we need to change the sign of the dividend as well. This means that we will multiply the dividend by -1.
  2. Multiply the dividend by the reciprocal of the divisor: The reciprocal of $-\frac{1}{2}$ is $-\frac{2}{1}$, which is equal to -2. We will multiply the dividend (6) by -2.
  3. Simplify the expression: After multiplying the dividend by the reciprocal of the divisor, we get -12.

Evaluating the Options

Now that we have found the quotient of 6 and $-\frac{1}{2}$, let's evaluate the options provided:

  • A. $-12$: This option is correct, as we have found that the quotient of 6 and $-\frac{1}{2}$ is indeed -12.
  • B. $-\frac1}{12}$ This option is incorrect, as we have found that the quotient of 6 and $-\frac{1{2}$ is not $-\frac{1}{12}$.
  • C. $\frac1}{12}$ This option is also incorrect, as we have found that the quotient of 6 and $-\frac{1{2}$ is not $\frac{1}{12}$.
  • D. 12: This option is incorrect, as we have found that the quotient of 6 and $-\frac{1}{2}$ is not 12.

Conclusion

In conclusion, the quotient of 6 and $-\frac{1}{2}$ is -12. This can be found by changing the sign of the divisor, multiplying the dividend by the reciprocal of the divisor, and simplifying the expression. We have evaluated the options provided and found that only option A is correct.

Understanding the Concept of Division

Division is a fundamental concept in mathematics that helps us understand the relationship between numbers. When we divide one number by another, we are essentially finding the number of times the divisor fits into the dividend. In this article, we have explored the quotient of 6 and $-\frac{1}{2}$ and found that it is -12.

Real-World Applications of Division

Division has many real-world applications, including:

  • Cooking: When we are cooking, we often need to divide ingredients into equal parts. For example, if we are making a recipe that calls for 2 cups of flour, and we want to make half the recipe, we would need to divide 2 cups by 2.
  • Shopping: When we are shopping, we often need to divide the cost of an item by the number of people who will be using it. For example, if we are buying a pack of 12 donuts that costs $5, and we want to know how much each donut costs, we would need to divide $5 by 12.
  • Science: When we are conducting scientific experiments, we often need to divide materials into equal parts. For example, if we are conducting an experiment that requires 3 grams of a certain substance, and we want to make 2 samples, we would need to divide 3 grams by 2.

Conclusion

Frequently Asked Questions

In this article, we will answer some of the most frequently asked questions about the quotient of 6 and $-\frac{1}{2}$.

Q: What is the quotient of 6 and $-\frac{1}{2}$?

A: The quotient of 6 and $-\frac{1}{2}$ is -12.

Q: How do I find the quotient of 6 and $-\frac{1}{2}$?

A: To find the quotient of 6 and $-\frac{1}{2}$, you need to divide 6 by $-\frac{1}{2}$. This can be done using the following steps:

  1. Change the sign of the divisor.
  2. Multiply the dividend by the reciprocal of the divisor.
  3. Simplify the expression.

Q: Why do I need to change the sign of the divisor?

A: You need to change the sign of the divisor because the divisor is negative. When you divide a number by a negative number, the result is also negative.

Q: What is the reciprocal of $-\frac{1}{2}$?

A: The reciprocal of $-\frac{1}{2}$ is $-\frac{2}{1}$, which is equal to -2.

Q: How do I multiply the dividend by the reciprocal of the divisor?

A: To multiply the dividend by the reciprocal of the divisor, you need to multiply 6 by -2.

Q: What is the result of multiplying 6 by -2?

A: The result of multiplying 6 by -2 is -12.

Q: Why is the quotient of 6 and $-\frac{1}{2}$ not $-\frac{1}{12}$?

A: The quotient of 6 and $-\frac{1}{2}$ is not $-\frac{1}{12}$ because the result of dividing 6 by $-\frac{1}{2}$ is -12, not $-\frac{1}{12}$.

Q: Why is the quotient of 6 and $-\frac{1}{2}$ not $\frac{1}{12}$?

A: The quotient of 6 and $-\frac{1}{2}$ is not $\frac{1}{12}$ because the result of dividing 6 by $-\frac{1}{2}$ is -12, not $\frac{1}{12}$.

Q: Why is the quotient of 6 and $-\frac{1}{2}$ not 12?

A: The quotient of 6 and $-\frac{1}{2}$ is not 12 because the result of dividing 6 by $-\frac{1}{2}$ is -12, not 12.

Conclusion

In conclusion, the quotient of 6 and $-\frac{1}{2}$ is -12. We have answered some of the most frequently asked questions about the quotient of 6 and $-\frac{1}{2}$ and provided step-by-step instructions on how to find the quotient.

Real-World Applications of Quotient

The quotient of 6 and $-\frac{1}{2}$ has many real-world applications, including:

  • Cooking: When we are cooking, we often need to divide ingredients into equal parts. For example, if we are making a recipe that calls for 2 cups of flour, and we want to make half the recipe, we would need to divide 2 cups by 2.
  • Shopping: When we are shopping, we often need to divide the cost of an item by the number of people who will be using it. For example, if we are buying a pack of 12 donuts that costs $5, and we want to know how much each donut costs, we would need to divide $5 by 12.
  • Science: When we are conducting scientific experiments, we often need to divide materials into equal parts. For example, if we are conducting an experiment that requires 3 grams of a certain substance, and we want to make 2 samples, we would need to divide 3 grams by 2.

Conclusion

In conclusion, the quotient of 6 and $-\frac{1}{2}$ is -12. We have answered some of the most frequently asked questions about the quotient of 6 and $-\frac{1}{2}$ and provided step-by-step instructions on how to find the quotient. The quotient of 6 and $-\frac{1}{2}$ has many real-world applications, including cooking, shopping, and science.