Final answer:
The two expressions representing the positive distance between −4/3 and 1/3 are 1/3 - (−4/3) from option a) and −1/3 - (−4/3) from option d), both simplifying to positive fractions.
Step-by-step explanation:
The distance between two points on a number line is the absolute value of the difference between the coordinates of these points. To calculate the distance between −4/3 and 1/3, we need to find the positive difference between the two.
Option a) 1/3 - (−4/3) calculates this difference and simplifies to 1/3 + 4/3, which equals 5/3. This is the positive distance, as required.
Option d) −1/3 - (−4/3) also calculates the difference between the two numbers and simplifies to −1/3 + 4/3, which equals 3/3 or 1, another positive distance.
Options b) and c) both result in negative and lesser values respectively, which do not represent the actual distance between the points when considering distance as a positive value.