Final answer:
Britain and France aided the Ottomans against Russia to prevent Russian control over the Mediterranean trade. The Ottoman Empire's geopolitical significance and control over trade routes made it valuable to European powers.
Step-by-step explanation:
The Ottomans, during their struggle against Russia in the seventeenth and eighteenth centuries, called upon Western European powers such as Britain and France to aid them. These European powers intervened because they feared Russian dominance over the Mediterranean trade network that could result if the Ottoman Empire were to collapse. The Ottoman Empire was so valuable because it served as a buffer state against Russian expansion and because it was a key player in European geopolitics after officially being included in the European international system of states post-Crimean War. Additionally, the empire was historically important for controlling trade routes and had been an expansive and multicultural power since its founding, attracting and integrating a diverse range of people and cultures.