Complex sentence: After the war, the UK received the League of Nations mandate over a number of former German and Ottoman colonies, and the British Empire had reached its greatest extent, covering a fifth of the world's land surface and a quarter of its population.
Split into simpler sentences: After the war, the UK received the League of Nations mandate over a number of former German and Ottoman colonies. The British Empire reached its greatest extent, covering a fifth of the world's land surface and a quarter of its population.