Final answer:
The expression |−7| − 7 equals 0, as the absolute value of −7 is 7, and subtracting 7 from 7 results in 0. The correct multiple-choice answer is A) 0. Additionally, understanding operations with negatives, such as addition, subtraction, and multiplication, is crucial for correctly simplifying expressions.
Step-by-step explanation:
The question given by the student involves the absolute value and basic arithmetic operations. Let's clarify the example provided: |-7| - 7. The absolute value of -7 is 7 because absolute value measures the distance a number is from zero on the number line, regardless of direction. So |-7| equals 7. After finding the absolute value, we then subtract 7, so the expression becomes: 7 - 7, which equals 0. Therefore, the correct answer is A) 0.
Examples to Understand Operations
For understanding addition and subtraction with negative numbers, consider this example: 5 - (+3) = 5 - 3 = 2. Here, the +3 becomes -3 when subtracted from 5. Similarly, for 2 - (-6) = 2 + 6 = 8, the subtraction of a negative number turns into addition.
When multiplying numbers, the sign of the result depends on the signs of the numbers involved: Two positive numbers give a positive result (2 x 3 = 6), two negative numbers give a positive result ((-4) x (-3) = 12), and numbers with opposite signs give a negative result ((-3) x 2 = -6, 4 x (-4) = -16).