Most Commonwealth member states were once part of what?
The British Empire.
The Commonwealth grew out of the old British Empire. As colonies became independent, many chose to stay linked as equal partners. That is why most members share a history with Britain. The door is not closed to others, though: a small number of countries with no imperial past have joined too.
Why it matters: A classic true/false item: the handbook says most, not all, members were once in the British Empire.
Memory hook: Empire ended, Commonwealth extended: most came from the Empire, a few came from elsewhere.
Official handbook: Chapter 5, section 5.7, page 90