Evaluate the expression. 56 Divided by (-8)
The Correct Answer and Explanation is :
The correct answer is: (-7)
To evaluate the expression (56 \div (-8)), we follow the standard procedure for division involving a positive and a negative number.
Step 1: Understand the Division Operation
Division is essentially the process of determining how many times one number can be subtracted from another. In this case, we are trying to find out how many times (-8) can fit into (56).
Step 2: Ignore the Sign
When dividing a positive number by a negative number, the division can first be computed without considering the sign. We take the absolute values of the numbers involved. Here, the absolute value of (56) is (56) and that of (-8) is (8).
Step 3: Perform the Division
Now we perform the division of the absolute values:
[
56 \div 8 = 7
]
This result indicates that (-8) fits into (56) exactly (7) times.
Step 4: Apply the Sign Rules
The rules of multiplication and division dictate that when you divide a positive number by a negative number, the result is negative. Thus, since we are dividing a positive number ((56)) by a negative number ((-8)), we append a negative sign to our previous result:
[
56 \div (-8) = -7
]
Conclusion
The final answer to the expression (56 \div (-8)) is (-7).
Key Points to Remember
- Division of Signs: The sign of the result depends on the signs of the numbers involved. A positive divided by a negative yields a negative result.
- Absolute Values: Always consider absolute values to simplify the division process before applying the final sign.
- Practical Implications: Understanding division with negatives is crucial in various mathematical applications, such as solving equations or evaluating expressions in real-world scenarios, where direction (such as debt or loss) is indicated by negative values.
Thus, (56 \div (-8) = -7).