Find The Quotient, Or, If Applicable, State That The Expression Is Undefined.\[$(-169) \div 13\$\]

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Introduction

In mathematics, division is a fundamental operation that involves finding the quotient of two numbers. When it comes to negative numbers, the rules of division can be a bit more complex. In this article, we will explore how to find the quotient of a negative number divided by a positive number, and discuss the implications of this operation.

The Rules of Division

When dividing two numbers, the quotient is the result of the division operation. However, when one of the numbers is negative, the quotient can be either positive or negative, depending on the sign of the other number. In general, the rules of division state that:

  • If both numbers have the same sign (both positive or both negative), the quotient is positive.
  • If the numbers have different signs (one positive and one negative), the quotient is negative.

Applying the Rules to the Given Expression

Now that we have reviewed the rules of division, let's apply them to the given expression: (−169)÷13(-169) \div 13. In this expression, the dividend is a negative number (-169), and the divisor is a positive number (13).

Step 1: Determine the Sign of the Quotient

Since the dividend is negative and the divisor is positive, the quotient will be negative. This is because the rules of division state that if the numbers have different signs, the quotient is negative.

Step 2: Find the Absolute Value of the Quotient

To find the absolute value of the quotient, we need to divide the absolute value of the dividend by the divisor. The absolute value of -169 is 169, and the divisor is 13.

Step 3: Calculate the Quotient

Now that we have the absolute value of the dividend and the divisor, we can calculate the quotient by dividing the absolute value of the dividend by the divisor.

169÷13=13169 \div 13 = 13

Step 4: Determine the Final Answer

Since the quotient is negative, we need to add a negative sign to the result. Therefore, the final answer is:

−13-13

Conclusion

In conclusion, when dividing a negative number by a positive number, the quotient is negative. By applying the rules of division and calculating the absolute value of the quotient, we can find the final answer. In this case, the final answer is −13-13.

Frequently Asked Questions

  • What is the quotient of (−169)÷13(-169) \div 13?
    • The quotient is −13-13.
  • Why is the quotient negative?
    • Because the dividend is negative and the divisor is positive.
  • How do I find the absolute value of the quotient?
    • By dividing the absolute value of the dividend by the divisor.

Final Answer

The final answer is −13-13.

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Introduction

In our previous article, we explored how to find the quotient of a negative number divided by a positive number. In this article, we will delve deeper into the world of negative numbers and division, and provide a comprehensive Q&A guide to help you understand this complex topic.

Q&A: Quotient of Negative Numbers

Q1: What is the quotient of (−169)÷13(-169) \div 13?

A1: The quotient is −13-13.

Q2: Why is the quotient negative?

A2: Because the dividend is negative and the divisor is positive.

Q3: How do I find the absolute value of the quotient?

A3: By dividing the absolute value of the dividend by the divisor.

Q4: What is the rule for dividing negative numbers?

A4: If both numbers have the same sign (both positive or both negative), the quotient is positive. If the numbers have different signs (one positive and one negative), the quotient is negative.

Q5: Can you provide an example of a negative number divided by a negative number?

A5: Yes, let's consider the expression (−25)÷(−13)(-25) \div (-13). In this case, both the dividend and the divisor are negative, so the quotient will be positive.

Q6: How do I calculate the quotient of (−25)÷(−13)(-25) \div (-13)?

A6: To find the quotient, we need to divide the absolute value of the dividend by the absolute value of the divisor. The absolute value of -25 is 25, and the absolute value of -13 is 13.

Q7: Calculate the quotient of (−25)÷(−13)(-25) \div (-13).

A7: 25÷13=1.9225 \div 13 = 1.92 (approximately)

Q8: What is the final answer for (−25)÷(−13)(-25) \div (-13)?

A8: The final answer is 1.921.92 (approximately).

Q9: Can you provide an example of a negative number divided by a positive number with a remainder?

A9: Yes, let's consider the expression (−17)÷3(-17) \div 3. In this case, the dividend is negative and the divisor is positive, so the quotient will be negative.

Q10: How do I calculate the quotient and remainder of (−17)÷3(-17) \div 3?

A10: To find the quotient and remainder, we need to divide the dividend by the divisor and find the remainder.

Q11: Calculate the quotient and remainder of (−17)÷3(-17) \div 3.

A11: −17÷3=−5-17 \div 3 = -5 with a remainder of 22.

Q12: What is the final answer for (−17)÷3(-17) \div 3?

A12: The final answer is −5-5 with a remainder of 22.

Conclusion

In conclusion, the quotient of negative numbers can be a complex topic, but with the right rules and examples, it can be understood. We hope this Q&A guide has provided you with a comprehensive understanding of the quotient of negative numbers and division.

Frequently Asked Questions

  • What is the quotient of (−169)÷13(-169) \div 13?
    • The quotient is −13-13.
  • Why is the quotient negative?
    • Because the dividend is negative and the divisor is positive.
  • How do I find the absolute value of the quotient?
    • By dividing the absolute value of the dividend by the divisor.

Final Answer

The final answer is −13-13.