What Is The Quotient Of $36 \div (-9)$?A. -27 B. 4 C. -4 D. 27

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Introduction

When it comes to division, we often think of it as the inverse operation of multiplication. In other words, if we have a multiplication problem, we can use division to find the missing factor. However, when dealing with negative numbers, things can get a bit more complicated. In this article, we will explore the concept of division with negative numbers and find the quotient of $36 \div (-9)$.

Understanding Division with Negative Numbers

Division is a mathematical operation that involves finding the result of one number being divided by another. When we divide two numbers, we are essentially asking how many times the divisor fits into the dividend. For example, if we have the division problem $12 \div 3$, we can ask how many times 3 fits into 12. The answer, of course, is 4.

However, when we deal with negative numbers, things can get a bit more complicated. A negative number is a number that is less than zero. When we divide two negative numbers, we need to consider the signs of both numbers. If both numbers have the same sign (either both positive or both negative), the result will be positive. If the numbers have different signs, the result will be negative.

The Quotient of $36 \div (-9)$

Now that we have a basic understanding of division with negative numbers, let's apply this concept to the problem at hand: $36 \div (-9)$. To find the quotient, we need to consider the signs of both numbers. In this case, we have a positive number (36) being divided by a negative number (-9).

Since the numbers have different signs, the result will be negative. To find the absolute value of the quotient, we can simply divide the absolute value of the dividend (36) by the absolute value of the divisor (-9). The absolute value of 36 is 36, and the absolute value of -9 is 9.

Calculating the Quotient

Now that we have the absolute values of both numbers, we can calculate the quotient. To do this, we simply divide the absolute value of the dividend (36) by the absolute value of the divisor (9).

369=4\frac{36}{9} = 4

However, since the numbers have different signs, the result will be negative. Therefore, the quotient of $36 \div (-9)$ is -4.

Conclusion

In conclusion, when dealing with division with negative numbers, we need to consider the signs of both numbers. If both numbers have the same sign, the result will be positive. If the numbers have different signs, the result will be negative. In the case of $36 \div (-9)$, the quotient is -4.

Frequently Asked Questions

  • What is the quotient of $36 \div (-9)$?
  • Why is the result negative?
  • How do we calculate the quotient of a division problem with negative numbers?

Answer Key

  • The quotient of $36 \div (-9)$ is -4.
  • The result is negative because the numbers have different signs.
  • To calculate the quotient of a division problem with negative numbers, we need to consider the signs of both numbers and follow the rules of division.

Final Thoughts

Division with negative numbers can be a bit tricky, but with practice and patience, you can become proficient in solving these types of problems. Remember to always consider the signs of both numbers and follow the rules of division. With this knowledge, you will be well on your way to becoming a math whiz!

Introduction

Division with negative numbers can be a bit tricky, but with practice and patience, you can become proficient in solving these types of problems. In this article, we will answer some of the most frequently asked questions about division with negative numbers.

Q&A

Q: What is the quotient of $36 \div (-9)$?

A: The quotient of $36 \div (-9)$ is -4.

Q: Why is the result negative?

A: The result is negative because the numbers have different signs. When we divide a positive number by a negative number, the result will always be negative.

Q: How do we calculate the quotient of a division problem with negative numbers?

A: To calculate the quotient of a division problem with negative numbers, we need to consider the signs of both numbers and follow the rules of division. If both numbers have the same sign, the result will be positive. If the numbers have different signs, the result will be negative.

Q: What is the difference between dividing a positive number by a positive number and dividing a positive number by a negative number?

A: When we divide a positive number by a positive number, the result will always be positive. However, when we divide a positive number by a negative number, the result will always be negative.

Q: Can we divide a negative number by a negative number?

A: Yes, we can divide a negative number by a negative number. In this case, the result will always be positive.

Q: How do we handle zero in division with negative numbers?

A: When we divide a number by zero, the result will always be undefined. This is true regardless of whether the numbers are positive or negative.

Q: Can we divide a negative number by a positive number?

A: Yes, we can divide a negative number by a positive number. In this case, the result will always be negative.

Q: What is the quotient of $(-9) \div (-3)$?

A: The quotient of $(-9) \div (-3)$ is 3.

Q: Why is the result positive?

A: The result is positive because both numbers have the same sign. When we divide two negative numbers, the result will always be positive.

Q: Can we divide a positive number by a negative number and get a positive result?

A: No, we cannot divide a positive number by a negative number and get a positive result. The result will always be negative.

Q: How do we handle decimal numbers in division with negative numbers?

A: When we divide decimal numbers, we can use the same rules as we do with whole numbers. If both numbers have the same sign, the result will be positive. If the numbers have different signs, the result will be negative.

Conclusion

Division with negative numbers can be a bit tricky, but with practice and patience, you can become proficient in solving these types of problems. Remember to always consider the signs of both numbers and follow the rules of division. With this knowledge, you will be well on your way to becoming a math whiz!

Final Thoughts

Division with negative numbers is an important concept in mathematics, and it's essential to understand the rules and procedures involved. By practicing and mastering these concepts, you can become more confident and proficient in solving division problems with negative numbers.

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