Welcome to Eid-ul-Fitr
In fact, the Qur'an says more about fasting. Here are some examples:
"O you who believe! Fasting is prescribed for you, as it was prescribed for those before you, so that you may guard [against evil]." (Sura 2.183)
"...accomplish the pilgrimage and the visit for Allah, but, if you are prevented, [send] whatever offering is easy to obtain, and do not shave your heads until the offering reaches its destination; but whoever among you is sick or has an ailment of the head, he [should effect] a compensation by fasting or alms or sacrificing, then when you are secure, whoever profits by combining the visit with the pilgrimage [should take] what offering is easy to obtain; but he who cannot find [any offering] should fast for three days during the pilgrimage and for seven days when you return; these [make] ten [days] complete; this is for him whose family is not present in the Sacred Mosque, and be careful [of your duty] to Allah, and know that Allah is severe in requiting [evil]." (Sura 2.196)