Final answer:
After calculating the fractions of nests lost to different events, we find that 9/20 of the bird nests are left in the forest.
Step-by-step explanation:
To determine what fraction of the bird nests are left in the forest after 1/4 of them are blown away by high winds and 2/5 are pulled apart.
Given that 2/5 of the remaining nests are pulled apart after the wind event, we can calculate the fraction of nests left as follows:
Start with the full amount: 1 (or whole)
Subtract the fraction lost to wind: 1 - 1/4 = 3/4
Calculate the fraction remaining after the wind event: 3/4
Subtract the fraction of the remaining nests taken by another event: (3/4) - (2/5)×(3/4)
First, multiply 2/5 by 3/4 to find the fraction of nests pulled apart after the wind: (2/5)×(3/4) = 3/10
Now, subtract that fraction from the nests that were left after the wind: (3/4) - (3/10)
To subtract the fractions, we must have a common denominator.
Converting both to the same denominator (in this case, 20, because it's a common multiple of 4 and 10), we get:
3/4 = 15/20
3/10 = 6/20
15/20 - 6/20 = 9/20
Therefore, 9/20 of the bird nests are left in the forest.