Final answer:
One tenth of the entire group at the picnic was seriously ill, as determined by multiplying one half by one fifth.
Step-by-step explanation:
The question asks us to determine what fraction of the whole group was seriously ill if one half of the people at the picnic went home sick and only one fifth of those were seriously ill. To calculate this, we multiply the two fractions together.
First, we take one half of the people, which is represented by the fraction 1/2. Then, we find out that one fifth of this half were seriously ill, represented by 1/5.
Multiplying these two fractions gives us:
(1/2) × (1/5) = 1/10
So, one tenth of the entire group was seriously ill.