Final answer:
The fraction of the Christian empire conquered by Muslims is not specified in historical records and is not easily quantified. The Muslims did establish a significant empire that encompassed parts of the formerly Christian Byzantine Empire and Visigothic Spain by 750 CE under the Umay_yad Dynasty.
Step-by-step explanation:
The student is inquiring about the extent of the territories conquered by the Muslims during the expansion of their empire. Given the historical context, it is challenging to quantify the exact fraction of Christian empire conquered by early Muslim expansion without a clear reference to the time and specific empire in question. However, taking into consideration the vast conquests of the Umay_yad Dynasty by 750 CE and how they included significant portions of the formerly Christian Byzantine Empire and Visigothic Spain, we can surmise they dominated a significant portion of the Christian lands at their peak.
The Islamic conquests began after the death of the Prophet Muhammad and continued into the early eighth century. By the time of the Umay_yad Caliphate, Muslims had conquered territories spanning from the Iberian Peninsula in the west to the Indus River valley in the east. This vast empire included significant Christian territories, particularly following their entrance into Spain in 711 CE.
References to specific fractions such as one half or two thirds are therefore not straightforward without additional details regarding what is meant by the 'Christian empire.' The Islamic state under the Caliphate, at its height, was considered the largest empire the world had yet seen, surpassing the realm of Alexander the Great, the Romans, or the Han Chinese. However, it's important to note that the boundaries and control over territories fluctuated over time.