Does not the taste of toothpaste break the fast?

The teeth can be brushed by both miswak and tooth brush. Brushing the teeth is the same as washing the hands because mouth is considered as an external organ of the body in the matter of fasting but you have to be careful while washing your mouth because it is very close to the throat. Having the taste  of toothpaste in the throat is like having scents in the nose. However, fasting is broken when a piece of toothpaste is swallowed.

It may be difficult to rinse off the toothpaste from the mouth completely, and the possibility of swallowing it with saliva is very high. Therefore, it is more convenient to use a miswak or to brush your teeth without toothpaste while fasting?