## Posts tagged ‘recipe’

### The Life and Times (and Fractions) of Eliza Acton

You may know Eliza Acton as an English poet or Victorian cookbook author, but I prefer to think of her as the **Queen of MP.6**.

CCSS.Math.Practice.MP6:

Attend to precision.

Her bestselling *Modern Cookery for Private Families* — which was first published in 1845, ran through 13 editions by 1853, remained in print until 1918, was reissued in 1968 and 1974, and then resurrected again in 1996 by Southover Press, with two more editions since — might very well be the greatest cookbook ever produced.

The prose within the volume is magnificent. She included recipes for “Poor Author’s Pudding,” “Printer’s Pudding,” and “Publisher’s Pudding,” the last of which “can’t be made *too* rich.” The directions for the “Publisher’s Pudding” explain that it should be covered with a “sheet of buttered writing paper,” which no doubt gives recipe readers some idea about the thickness of paper to be used, but also implies something about the publishing industry. (The complete text is available from Google Books, if you’d like to check it out for yourself.)

But what makes this work mathematically interesting is that it is **the first cookbook that used precise measurements** in its recipes. Without *Modern Cookery*, a middle school word problem might look like this:

The recipe for a loaf of bread calls for some flour, a dash of salt, and enough water to make the dough pliable. How much salt would you need to make two loaves?

I suppose the answer is “two dashes,” though printers would likely call that an *em dash*. (Cue cheeky, all-knowing editor’s laugh here.)

It was the recipes of Ms. Acton — like the one for a disgusting drink known as Milk Lemonade, which calls for 6 oz. sugar, ¼ pint lemon juice, ¼ pint sherry, and ¾ pint cold milk — that paved the way for the wonderful word problems that students enjoy today:

My recipe calls for ⅔ cups of white flour and 2⅕ cups of wheat flour. How much flour do I need in total for my recipe?

Oh, wait… did I say *wonderful*? I meant *awful*.

Who the hell measures flour in fifths of a cup? And why would anyone need to know the total amount of flour? Just dump it in a bowl and mix!

The word problem above without specific measurements is purely speculative; it’s almost certain that someone else would have thought to include exact measurements had Eliza Acton not come along, and students would have still been subjected to unrealistic fraction-containing word problems. But the purported imprecision within recipes is spot on, as shown by this recipe taken from an early 18th century English text:

Fill yr pott halph full of wien & [a] good share of sugar. Milke in as much cream & stirr itt once about very softly. Let itt stand two houres before you eate itt.

[from MS Codex 753, compliments of rarecooking.com]

Admittedly, that recipe is for an Ordinary Sillibub, which is basically a red wine float, and hence the recipe is very nearly useless. But it is typical of the imprecision that was commonplace before Ms. Acton’s arrival.

All hail Eliza Acton, **Queen of MP.6**!

### Fractional Eggs

I search for new recipes at **allrecipes.com** all the time. This morning, a search yielded a delicious recipe for pumpkin pancakes, which sounded like the perfect breakfast for a crisp fall morning.

One of the things I love about allrecipes is the ability to customize the number of servings. The default number of servings for the pumpkin pancake recipe was six, but I could adjust it to four, a more appropriate number for our two-adult, two-child family:

So I did. And as you’d expect, each item in the ingredient list was reduced to ⅔ its previous amount. Sort of. Two cups of flour was reduced to 1⅓ cups. One cup of pumpkin puree was reduced to ⅔ cup. But 2 teaspoons of baking powder was reduced to 1¼ teaspoons, and 1 teaspoon of cinnamon was reduced to ¾ teaspoon.

The reduction in the number of servings was 33⅓%, yet the range of reductions in the ingredients varied from 25% for salt (from 1 teaspoon to ¾ teaspoon) to 50% for ground ginger (from ½ teaspoon to ¼ teaspoon).

But I get it. It’s not typical for most kitchens to contain a spoon that measures ⅙ teaspoon. So there’s clearly some part of the algorithm that completes the conversion but then finds a “nice” fraction that’s in the right neighborhood. Fair enough.

But what the hell’s going on here?

Is it really better to display ⅝ egg instead of ⅔ egg? Couldn’t the algorithm recognize that fractional eggs just aren’t all that common and leave it as a whole number?

My guess is that the programmer is one of the folks to which this statement alludes:

5 out of 4 people aren’t very good with fractions.

That joke represents one-fifth of my favorite fraction jokes. Here are the other four:

Why won’t fractions marry decimals?

They don’t want to convert.I’m right 4/5 of the time. Who cares about the other 10%?

There’s a fine line between a numerator and a denominator.

Sex is like fractions. It’s improper for the larger one to be on top.

If you find a store that sells ⅝ egg, please let us know about it in the comments.