The Numerator is the top part of the fraction and the Denominator would obviously be the bottom part of it. Let's take an example with EUR/USD
EUR would be the Numerator (the first currency which is on top)
USD would be the Denominator (the currency that comes below or after the EUR)
The numerator is called the base currency and the denomiator is known as the counter currency.
Now whenever you place a "BUY" order in a Forex platform for example with the EUR/USD pair, what you are actually doing is buying the EUR and selling the USD. Buying in the Forex is known as going "LONG".
On the other hand if you were to sell the pair, you would be selling the EUR and buying the USD. This is known as going "SHORT" exactly like short selling in a stock market. (Short-selling is where you sell a stock/currency/commodity first and then try to buy it back at a lower price).
If you buy or sell a currency pair, you would be buying/selling the base currency (the one on top, NUMERATOR).
It would be the exact opposite of what you did to base currency if you were to sell a currency pair.
You are always buying one currency (the base) and selling another (the counter). If you sell the pair you are simply flipping which one you buy and which one you sell. The transaction is eventually the same.
The great thing about the Forex market unlike trading stocks is that you can always short sell with no restrictions. The good news here is that you can make money when the market drops as well as when it rises. Unlike the stock market where the market has to go up for you to make money, you can make money in both directions trading in the Forex.
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