Final answer:
Expression 1) 2/3 - 1/3 + 5, expression 3) 2/3 + 5 - 1/3, and expression 4) 5 + 2/3 - 1/3 can be easily simplified using the commutative property, as the like fractions can be combined.
Step-by-step explanation:
The student is asking which expression would be easier to simplify using the commutative property to change the order of the numbers 2/3, -1/3, and 5. By utilizing the commutative property A+B=B+A, which indicates that the order of addition does not affect the sum, we can rearrange the terms to simplify the calculation.
Option 1) 2/3 - 1/3 + 5 is already arranged in such a way that the first two terms can easily be combined because they are like fractions. By changing the subtraction to addition and respecting the rules that subtraction of a negative is like addition, option 2) 5 - 1/3 + 2/3 can be simplified by first adding 2/3 and -1/3. We'll get the same result for option 3) 2/3 + 5 - 1/3 and option 4) 5 + 2/3 - 1/3 following the same principle - the latter two terms are like fractions and can easily be combined regardless of their order.
Therefore, any expression where the like fractions (2/3 and -1/3) are positioned next to each other would be easier to simplify, so options 1, 3, and 4 are equally suitable.