Part A (a) Is $64 \div (-8)$ Positive Or Negative? (A) Positive (B) Negative Part B What Is The Value Of The Expression $-48 \div (-4)$? Answer: $\square$
Introduction
Division is a fundamental operation in mathematics that involves sharing a certain quantity into equal parts or groups. When it comes to negative numbers, division can be a bit more complex. In this article, we will explore the concept of dividing negative numbers and understand how to determine the sign of the result.
The Basics of Negative Numbers
Before we dive into the world of division, let's quickly review the basics of negative numbers. A negative number is a number that is less than zero. It is denoted by a minus sign (-) and is the opposite of a positive number. For example, -3 is a negative number, and it is the opposite of 3.
Division with Positive Numbers
When we divide two positive numbers, the result is always positive. For example, 12 ÷ 4 = 3, and 24 ÷ 6 = 4. The sign of the dividend (the number being divided) and the divisor (the number by which we are dividing) are both positive, so the result is also positive.
Division with Negative Numbers
Now, let's consider division with negative numbers. When we divide a negative number by a positive number, the result is always negative. For example, -12 ÷ 4 = -3, and -24 ÷ 6 = -4. The sign of the dividend is negative, and the divisor is positive, so the result is also negative.
Division with Two Negative Numbers
When we divide two negative numbers, the result is always positive. For example, -12 ÷ -4 = 3, and -24 ÷ -6 = 4. The sign of both the dividend and the divisor are negative, so the result is also positive.
The Sign of the Result
To determine the sign of the result when dividing two numbers, we can use the following rule:
- If the dividend and the divisor have the same sign (both positive or both negative), the result is positive.
- If the dividend and the divisor have different signs (one positive and one negative), the result is negative.
Applying the Rule to the Given Problem
Now, let's apply this rule to the given problem: $64 \div (-8)$. In this case, the dividend is 64, which is positive, and the divisor is -8, which is negative. Since the dividend and the divisor have different signs, the result is negative.
Conclusion
In conclusion, when dividing two numbers, the sign of the result depends on the signs of the dividend and the divisor. If they have the same sign, the result is positive, and if they have different signs, the result is negative.
Solving the Second Part of the Problem
Now, let's solve the second part of the problem: $-48 \div (-4)$. Using the rule we learned earlier, we can determine that the result is positive, since both the dividend and the divisor are negative.
The Final Answer
The final answer to the second part of the problem is:
Conclusion
In this article, we explored the concept of dividing negative numbers and understood how to determine the sign of the result. We learned that if the dividend and the divisor have the same sign, the result is positive, and if they have different signs, the result is negative. We also applied this rule to the given problem and solved the second part of the problem.
Introduction
In our previous article, we explored the concept of dividing negative numbers and understood how to determine the sign of the result. However, we know that there are many more questions that our readers might have. In this article, we will answer some of the most frequently asked questions about dividing negative numbers.
Q: What is the rule for dividing negative numbers?
A: The rule for dividing negative numbers is as follows:
- If the dividend and the divisor have the same sign (both positive or both negative), the result is positive.
- If the dividend and the divisor have different signs (one positive and one negative), the result is negative.
Q: What is the sign of the result when dividing a negative number by a positive number?
A: The sign of the result when dividing a negative number by a positive number is always negative.
Q: What is the sign of the result when dividing a positive number by a negative number?
A: The sign of the result when dividing a positive number by a negative number is always negative.
Q: What is the sign of the result when dividing two negative numbers?
A: The sign of the result when dividing two negative numbers is always positive.
Q: Can you give an example of each of these cases?
A: Here are some examples:
- Dividing a negative number by a positive number: -12 ÷ 4 = -3
- Dividing a positive number by a negative number: 12 ÷ -4 = -3
- Dividing two negative numbers: -12 ÷ -4 = 3
Q: How do I remember the rule for dividing negative numbers?
A: One way to remember the rule is to use the following acronym:
- Same sign, same sign (positive result)
- Different signs, different signs (negative result)
Q: Can you give me some practice problems to try?
A: Here are some practice problems:
- -24 ÷ 6 = ?
- 36 ÷ -9 = ?
- -48 ÷ -8 = ?
- 72 ÷ 12 = ?
Q: What if I get a negative result when I expect a positive result?
A: If you get a negative result when you expect a positive result, it's likely because you made a mistake in your calculation. Double-check your work and make sure you're using the correct rule for dividing negative numbers.
Conclusion
In this article, we answered some of the most frequently asked questions about dividing negative numbers. We hope that this article has been helpful in clarifying any confusion you may have had about this topic. Remember, the key to dividing negative numbers is to understand the rule for same signs and different signs.
Additional Resources
If you're still having trouble understanding dividing negative numbers, here are some additional resources that may be helpful:
- Khan Academy: Dividing Negative Numbers
- Mathway: Dividing Negative Numbers
- IXL: Dividing Negative Numbers
Conclusion
We hope that this article has been helpful in answering your questions about dividing negative numbers. Remember to practice, practice, practice to become more confident in your ability to divide negative numbers.