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# Math and the Holidays: Recipes, Ratio, and Proportion

Dec 23, 2015

What’s your favorite holiday dish? From fruitcake to latkes, whatever it is, it’s most likely made by following step-by-step instructions and fixed quantities of ingredients listed in a recipe!

The relationship between ingredients in a recipe can be expressed as a ratio. As an example, if a brownie recipe calls for one cup of sugar and two eggs, the ratio of sugar to eggs is 1 to 2. Because recipes list ingredients in proportion (or in balance, in order to create a specific outcome), if you increase or decrease the amount of one ingredient, you must increase or decrease the others by the same factor (read: maintain the original ratios) in order to produce the desired result. Cooking a big dinner for 16 but stuck with a recipe that only serves 8? To make sure no one goes hungry, double the quantity of all the ingredients to feed all 16 guests. Increasing or decreasing one ingredient without adjusting the others makes the recipe disproportionate—and the resulting dish not so tasty.

As using "a pinch of this and a touch of that" only takes you so far (and because recreating recipes from memory is a pain), it’s surprising that numerically standardizing quantities and cooking times only became common practice in the 19th century. Until then, recipes were heavily reliant on a cook’s intuitive knowledge of food and food preparation, and approximated quantities such as “a handful of,” or “cook until done.” The oldest surviving recipes are written in Akkadian (an ancient language used in Mesopotamia), and date as far back as 1600 BC (per Wikipedia), but these were merely step-by-step guides that served to standardize cooking procedures.

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