Final answer:
The expression representing the distance between -1/4 and 3/4 is option 3) which is |-1/4 - 3/4|, equaling 1. This is the correct option because distance is always a positive quantity and taking the absolute value ensures this.
Step-by-step explanation:
The question concerns the distance between two numbers on a number line. To calculate the distance between two points, you can subtract the smaller number from the larger number and take the absolute value to ensure the distance is positive. Therefore, options 1) and 4) would give you the net displacement, which is zero in this case, because adding a negative number is the same as subtracting its positive counterpart.
Option 2) correctly calculates the displacement by adding the opposite of -1/4 to 3/4, resulting in a positive distance. However, the best representation of the distance, which must always be positive, is option 3) which takes the absolute value of the difference between the two numbers. Thus, the expression representing the distance between -1/4 and 3/4 is |-1/4 - 3/4|, which equals 1. To summarize, the distance is the absolute difference, generally written as |a - b| where 'a' and 'b' are the two points in question.