Answer:

To find out what fraction of the rope Neil has left, we can subtract the length of rope he used from the total length he started with.

Neil started with 5 ⅕ meters of rope, which can be written as an improper fraction:

5 ⅕ = 5 + 1/5 = 25/5 + 1/5 = 26/5 meters

So, Neil had 26/5 meters of rope to begin with.

He used 2 ⅔ meters of it, which can also be written as an improper fraction:

2 ⅔ = 2 + 2/3 = 6/3 + 2/3 = 8/3 meters

Now, we need to subtract the length of rope he used (8/3 meters) from the total length he had (26/5 meters):

Remaining rope = Total rope - Used rope

Remaining rope = (26/5) - (8/3)

To subtract these fractions, we need a common denominator, which in this case is 15:

Remaining rope = (26/5) - (8/3)

To find a common denominator of 15, we can multiply the first fraction by 3/3 and the second fraction by 5/5:

Remaining rope = (26/5) * (3/3) - (8/3) * (5/5)

Remaining rope = (78/15) - (40/15)

Now, subtract the fractions:

Remaining rope = (78/15) - (40/15)

Remaining rope = (78 - 40)/15

Remaining rope = 38/15 meters

So, Neil has 38/15 meters of rope left.