Put your elementary school math knowledge to good use—with alcohol.
Cocktails are built on ratios. So much so that bartenders often begin to think and certainly speak in ratios. You’ll hear bartenders rattle off numbers—"Oh, it’s 1 1/2, 1, 3/4, 1/4, and a dash"—as though they mean something. And they do—that is, if you know what each number applies to.
Some ratios are particularly useful—priceless, even—because you can keep them in the back of your mind to guide you through making a variety of seemingly different cocktails all based on the same ratio.
My very favorite ratio is 2 : 3/4 : 3/4—that is 2 parts of base spirit to 3/4 part sweet and 3/4 sour. (I usually make the math easy and use 2 ounces + 3/4 ounce + 3/4 ounce; in this case, 1 ounce = 1 part. But, one part could also be a different measurement. If it's 50 milliliters, for example, that would make the 3/4 part 37 1/2 milliliters, and so on.)
This opens up a whole family of cocktails that are cousins of the sour (though a real sour usually also includes egg white to soften all the flavors). 2 : 3/4 : 3/4 is a bit boozier than the traditional sour ratio, which is 2 : 1 : 1, but unless you’re using a poor-quality base spirit that you’re trying to cover up with sweet and sour, you’ll find that 2 : 3/4 : 3/4 yields a more nicely balanced cocktail that's less overpoweringly sweet-tart and more sophisticated tasting.
At our bar, I’d say that at least half (if not more) of the cocktails we serve wind up being based on this ratio. One of my favorite classic cocktails that we serve, called the Bee’s Knees, features gin, lemon juice, and honey syrup in this ratio.
I also like to make variations on a gimlet/daiquiri, mixing up the base spirit—sometimes gin, sometimes aquavit, sometimes vodka, sometimes rum—and augmenting them with 3/4 ounces each of lime juice and simple syrup.
You can also split your sweet and your sour into multiple components. You can use lemon or lime, but you can also combine the two, or even use a mix of unsweetened cranberry juice with lemon or lime and grapefruit juice. Instead of plain simple syrup you can use flavored syrups or liqueurs. Subtle tweaks in flavors can lead to an almost infinite menu of drinks.
Perhaps you remember learning about proportions in fourth grade. Now, finally, you have a decent use for them!