What is the ruling on tartar accumulated on teeth that contains remnants of toothpaste, and does it affect the validity of prayer and fasting?

Tartar does not affect the validity of prayer or fasting. However, one should pay attention to using a miswak (tooth-stick) and removing tartar and dirt from the teeth, especially during ablution and prayer, as the Prophet (peace be upon him) said: "Were it not that I would overburden my Ummah, I would have commanded them to use the miswak with every ablution." And in another narration: "Were it not that I would overburden my Ummah, I would have commanded them to use the miswak with every prayer." One must beware of obsessive thoughts and turn away from them.