The key to understanding the fractional reserve system is that banks take title to your money when you deposit it, and you get in return an asset (the account) which is essentially a promise to pay you that money on demand.

A bank can't just "create" $900 million by making a $1 billion loan when it only has $100 million on hand. Rather, depending on the reserve ratios, $1 billion in notional assets can exist backed by only $100 million in central bank money. That's because those notional assets are not in fact money, but IOU's that people are willing to treat as functionally equivalent to money.

A better intro than the link you posted is this one: http://neweconomicperspectives.org/2011/09/mmp-blog-15-clear...

The crux is that there are really (at least) two types of money: Central bank money, and money used by "the public". They live in two different "monetary circuits", and while those circuits are not entirely unrelated, they are completely isolated from each other; money cannot go from one circuit to the other.

Ignoring cash for simplicity (and it is little volume anyway), central bank money is only the electronic currency on accounts at the central bank, and it only moves between banks and other financial institutions.

Money used by the public is cash in circulation as well as money on checking accounts and so on.

Banks cannot create central bank money, but they can and do create money in the other "monetary circuit". It is true that the amount of money in the public monetary circuit must be less than the amount of central bank money times a factor (the inverse of the reserve ratio).

However, in practice, this limit works the other way around: When the amount of money in public use grows "too large", central bank money is automatically created by the central bank (this has nothing to do with quantitative easing; it is part of the normal market operations that the central bank always performs to achieve its interest rate target). Because of this, the reserve ratio does not limit the creation of money by banks.

This is a straightforward conclusion of how monetary aggregates such as M1 are defined: Among other things, M1 includes money in checking and similar accounts. The creation of the loan involves, among other things, adding $1000 million to some checking account, without reducing the amount of money anywhere else.

Hence, $1000 million is created net.

This contradicts the story that most people are familiar with, but it is a more accurate description of reality than that other story.

But the bank still needs to have the $1.1 billion on hand first, so that it can have that $100 million after the billion-dollar check goes out.