Fractional reserve banking (FRB) as is taught in most econ textbooks and courses is a myth. There's a very nice paper by the bank of england debunking this (Money creation in the modern economy). The idea behind QE and bailing out the banks was to create lending and liquidity in the market largely via the FRB mechanism however that failed to materialise for reasons the bank of england paper goes into but basically banks don’t lend out their reserves as the theory expects but it’s the process of lending that creates deposits not the other way around. The money given to banks didn't result in increased lending but instead went into financial markets buying up assets. There was some wealth effect going on so people with some assets got richer and then spent more but overall it was a really trickled down effect.