Difficulty: Easy
Correct Answer: 12
Explanation:
Introduction / Context:
This problem tests basic operations with negative numbers and the correct interpretation of subtraction of negative terms. It asks for the difference between two expressions, both involving subtraction of negative numbers, which is a typical area where sign errors can occur if you do not proceed carefully.
Given Data / Assumptions:
Concept / Approach:
The key idea is that subtracting a negative number is equivalent to adding its positive counterpart. So we need to simplify each expression separately, then subtract the second result from the first to see how much larger it is. This is a direct application of sign rules in addition and subtraction of integers.
Step-by-Step Solution:
Simplify Expression 1: −4 − (−10). Subtracting a negative is adding a positive, so −4 − (−10) = −4 + 10.Compute −4 + 10 = 6.Simplify Expression 2: −10 − (−4) = −10 + 4.Compute −10 + 4 = −6.Now find how much greater 6 is than −6: 6 − (−6) = 6 + 6 = 12.
Verification / Alternative check:
You can visualize the numbers on a number line: −6 is 6 units left of zero, and 6 is 6 units right of zero.The distance between −6 and 6 is 12 units, which matches the computed difference.
Why Other Options Are Wrong:
An answer of 10 or 6 usually arises from incorrectly treating only one of the subtractions of a negative as addition while leaving the other unchanged.An answer of 0 would imply that both expressions are equal, which they clearly are not, since one simplifies to 6 and the other to −6.
Common Pitfalls:
The most frequent mistake is to forget that "minus minus" becomes plus, leading to expressions like −4 − (−10) being incorrectly simplified as −4 − 10.Another pitfall is to compare 6 and −6 by simply subtracting in the wrong order, such as −6 − 6, which would give −12 instead of the required positive difference.
Final Answer:
The value of −4 − (−10) is 12 greater than the value of −10 − (−4), so the required difference is 12.
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