What is −63 divided by 7?
The Correct Answer and Explanation is :
The result of dividing (-63) by (7) is (-9). This can be calculated as follows:
[
-63 \div 7 = -9
]
To understand this calculation more thoroughly, let’s break down the process and the concepts involved.
Understanding Division
Division is the operation of determining how many times one number is contained within another. When we divide a negative number by a positive number, the result is negative. In this case, we are dividing (-63) by (7).
Step-by-Step Calculation
- Identify the Numbers: We have a numerator of (-63) and a denominator of (7).
- Divide the Absolute Values: First, we consider the absolute values of the numbers involved. The absolute value of (-63) is (63), and the absolute value of (7) is (7). Now we perform the division: [
63 \div 7 = 9
] - Determine the Sign: Since we are dividing a negative number by a positive number, the result must be negative. Therefore, we attach a negative sign to the result: [
-63 \div 7 = -9
]
Real-World Application
Division is commonly used in real-world scenarios. For example, if you had a debt of (-63) dollars and needed to pay it off in equal installments of (7) dollars, you would find that it takes (9) installments to pay off the debt, but since you owe money, this remains a negative context.
Conclusion
The operation (-63 \div 7) illustrates a fundamental rule in mathematics regarding the division of negative and positive numbers. The result, (-9), reflects how many times the divisor (7) fits into the negative quantity (-63), reinforcing the concept of negative values in mathematics.