In the kitchen this morning …
Mix # 1 for waffles required 3/2 cups of mix, 3/4 cup of water, 3 tablespoons of water, and 1 egg.
But, I have only 3/4 cups of the mix, so the egg is going to be a problem.
Mix # 2 from a second box required 2 cups of mix, 3/4 cup of water, and 1/3 cup of oil, but no eggs.
I don’t want to try and come up with half an egg, and it’s clear from the first recipe that it’s substituting an egg for some oil. But how much?
A quick trip to the internet shows that 1/4 cup of oil can be substituted for 1 egg.
So, I measure out a half batch of Mix # 1: 3/4 cup of mix, 3/8 cup of water, 3/2 tablespoons of oil, and 1 egg.
Knowing there’s 1/2 egg extra in there, I substitute the extra 1/2 egg for 1/8 cup of oil in the second recipe. I’m making a half-batch of that too, so I use: 1 cup of mix, 3/8 cup of water, and 1/6 cup of oil minus the 1/8 cup of oil I’m getting from the egg.
To simplify, you note that the denominators 6 and 8 are common factors of 24. Then 1/6 cup is the same as 4/24 cup, and 1/8 cup is the same as 3/24 cup. So what I needed was 4/24 minus 3/24 equals 1/24 cup of oil.
A cup has 8 ounces. There’s two tablespoons in an ounce, so that’s 16 tablespoons in a cup. There’s 3 teaspoons in a tablespoon, so that’s 48 teaspoons in a cup. And 1/24 of a cup is then 48/24, or exactly 2 teaspoons. That’s how much extra oil I needed to add.*
I added that oil, whisked both half-batches together, started pouring onto the new waffle iron I got for Christmas, and the kids were happy with the waffles.
Tim Worstall is probably going to comment back that he just would’ve gone out for breakfast, but he’s not as geeky as me.
* The beauty of the customary system of weights and measures is that it is based on multiples of 2’s and 3’s, making the sort of arithmetic I used much more straightforward for someone with a basic grasp of fractions than using a calculator.