Great question! Here is how I think of two options for solving this problem:
Option A: Use the commutative property to move the numbers around so that "like" denominators are next door to each other. Then subtract each of the three other numbers one at a time until we get to the final answer of 1.
Option B: Start by using the commutative property to move the numbers around. Then use the associative property to subtract the first two numbers. Rather than subtracting each of the final numbers one at a time, we can add them together and then subtract all at once.
Using simpler numbers,
10 - 5 - 3 could be solved by doing 10 - (5+3). This is because subtracting 5 and THEN subtracting 3 is the same as simply subtracting 8.
I hope this helps!