Once children are old enough to understand the mitzvot of Yom Kippur, we instruct them not to wash, apply cream, or wear shoes on Yom Kippur. Generally, children reach this stage at age five or six.
However, we wait until the age of nine to encourage healthy children to fast part of the day. For example, if they generally eat breakfast at eight in the morning, they should wait until the afternoon to eat. Weaker children should begin fasting at age ten rather than nine. From the age of eleven, children should be encouraged to fast the whole day. If they are weak, they should fast only half the day.
As we said above (13:10), when children reach halakhic maturity, they are considered adults. Girls from the age of twelve have a biblical obligation to fast, while boys have a rabbinic obligation. If a twelve-year-old boy is weak, he should still make an effort to fast the whole day. If he is sick (even if not dangerously ill), he is not obligated to fast, since he is not yet thirteen. Nevertheless, he should try to fast until the afternoon. From the age of thirteen, boys too have a biblical obligation to fast.