What Is The Quotient? ( − 7 ) 2 ( − 7 ) − 1 \frac{(-7)^2}{(-7)^{-1}} ( − 7 ) − 1 ( − 7 ) 2 ​ A. -343 B. -7 C. 7 D. 343

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Introduction

In mathematics, a quotient is the result of a division operation. It is a fundamental concept in arithmetic and algebra, and it plays a crucial role in various mathematical operations. In this article, we will explore the concept of quotient, its properties, and how to calculate it. We will also examine a specific example, (−7)2(−7)−1\frac{(-7)^2}{(-7)^{-1}}, and determine the correct answer among the given options.

What is a Quotient?

A quotient is the result of dividing one number by another. It is a measure of how many times one number contains another. For example, if we divide 12 by 3, the quotient is 4, because 3 contains 4 times in 12. The quotient can be a whole number, a fraction, or a decimal.

Properties of Quotient

The quotient has several properties that are essential to understand:

  • Division is Commutative: The order of the dividend and divisor does not change the quotient. For example, 123=312\frac{12}{3} = \frac{3}{12}.
  • Division is Associative: When we divide a number by a product of two numbers, the order in which we divide does not change the result. For example, 123×4=124×3\frac{12}{3 \times 4} = \frac{12}{4 \times 3}.
  • Division is Distributive: When we divide a number by a sum of two numbers, we can divide it by each number separately and then add the results. For example, 123+4=123+124\frac{12}{3 + 4} = \frac{12}{3} + \frac{12}{4}.

Calculating the Quotient

To calculate the quotient, we need to divide the dividend by the divisor. The dividend is the number being divided, and the divisor is the number by which we are dividing. For example, to calculate 123\frac{12}{3}, we need to divide 12 by 3.

Example: (−7)2(−7)−1\frac{(-7)^2}{(-7)^{-1}}

Now, let's examine the specific example, (−7)2(−7)−1\frac{(-7)^2}{(-7)^{-1}}. To calculate this quotient, we need to follow the order of operations (PEMDAS):

  1. Exponentiation: Calculate the exponentiation of -7. (−7)2=49(-7)^2 = 49 and (−7)−1=−17(-7)^{-1} = -\frac{1}{7}.
  2. Division: Divide the result of the exponentiation of the dividend by the result of the exponentiation of the divisor. 49−17=−343\frac{49}{-\frac{1}{7}} = -343.

Conclusion

In conclusion, the quotient is the result of a division operation. It is a fundamental concept in mathematics, and it plays a crucial role in various mathematical operations. The quotient has several properties, including commutativity, associativity, and distributivity. To calculate the quotient, we need to follow the order of operations (PEMDAS). In the example, (−7)2(−7)−1\frac{(-7)^2}{(-7)^{-1}}, we calculated the quotient to be -343.

Frequently Asked Questions

  • What is the quotient of 12 and 3?
    • The quotient of 12 and 3 is 4.
  • What is the quotient of -7 and -7?
    • The quotient of -7 and -7 is 1.
  • What is the quotient of 0 and 5?
    • The quotient of 0 and 5 is 0.

Final Answer

The final answer is −343\boxed{-343}.

Introduction

In our previous article, we explored the concept of quotient in mathematics, its properties, and how to calculate it. In this article, we will provide a comprehensive Q&A section to help you better understand the concept of quotient and its applications.

Quotient Q&A

Q1: What is the quotient of 12 and 3?

A1: The quotient of 12 and 3 is 4.

Q2: What is the quotient of -7 and -7?

A2: The quotient of -7 and -7 is 1.

Q3: What is the quotient of 0 and 5?

A3: The quotient of 0 and 5 is 0.

Q4: What is the quotient of 24 and 4?

A4: The quotient of 24 and 4 is 6.

Q5: What is the quotient of -9 and 3?

A5: The quotient of -9 and 3 is -3.

Q6: What is the quotient of 15 and 5?

A6: The quotient of 15 and 5 is 3.

Q7: What is the quotient of 0 and 0?

A7: The quotient of 0 and 0 is undefined.

Q8: What is the quotient of -12 and 4?

A8: The quotient of -12 and 4 is -3.

Q9: What is the quotient of 18 and 6?

A9: The quotient of 18 and 6 is 3.

Q10: What is the quotient of -20 and 5?

A10: The quotient of -20 and 5 is -4.

Quotient Properties Q&A

Q1: Is division commutative?

A1: Yes, division is commutative. The order of the dividend and divisor does not change the quotient.

Q2: Is division associative?

A2: Yes, division is associative. When we divide a number by a product of two numbers, the order in which we divide does not change the result.

Q3: Is division distributive?

A3: Yes, division is distributive. When we divide a number by a sum of two numbers, we can divide it by each number separately and then add the results.

Quotient Calculations Q&A

Q1: How do I calculate the quotient of two numbers?

A1: To calculate the quotient, you need to divide the dividend by the divisor. The dividend is the number being divided, and the divisor is the number by which we are dividing.

Q2: What is the order of operations for calculating the quotient?

A2: The order of operations for calculating the quotient is PEMDAS: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Conclusion

In conclusion, the quotient is a fundamental concept in mathematics that plays a crucial role in various mathematical operations. We hope that this Q&A section has helped you better understand the concept of quotient and its applications.

Frequently Asked Questions

  • What is the quotient of 12 and 3?
    • The quotient of 12 and 3 is 4.
  • What is the quotient of -7 and -7?
    • The quotient of -7 and -7 is 1.
  • What is the quotient of 0 and 5?
    • The quotient of 0 and 5 is 0.

Final Answer

The final answer is −343\boxed{-343}.