Answer:
3/5
Step-by-step explanation:
We want to find the fraction of the original branch that remains, so we will assume a length of the branch in order to make our calculation easier.
Since Kim marks it off in thirds and fifths, let's find the least common multiple of 3 & 5.
Least common multiple of 3 & 5 is 15.
Thus,let's make the length of the branch to be 15-meter long.
Now, if the branch is 15 m long, considering the markings of thirds and fifths, the branch would be cut at:
3, 5, 6, 9, 10, 12 meters.
We are told that She then breaks the branch along all the markings and removes one piece of every distinct length. Thus;
Distinct lengths are;
3 metres
5 - 3 = 2 metres
10 - 9 = 1 meter
Total she removes = 3 + 2 + 1 = 6 meters.
Total remaining is;
15 - 6 = 9 meters
Expressing this as a fraction of the original branch gives:
9/15
Divide both numerator and denominator by 3 to get; 3/5
r^2h/3