On my last exam there were a few people who mentioned they had trouble with the math conversions. While there are definitely days when I'm disgruntled with my seemingly unhelpful engineering degree, on occasion it does have its advantages. Here is how to do math conversions like a pro.
First off, for cooking there are only 6 basic SI (Système Internationale or International System - how very French) conversions that you HAVE to remember. In the mathematical world these conversions are called identity factors (more on this in a bit). The factors you should remember are as follows:
Remember, at three, tea is served on the table:
3 teaspoons
--------------
1 tablespoon
Both of these conversions are 16 ounces per a "p" unit:
16 ounces
------------
1 pound
and
16 ounces
------------
1 pint
Next, I use a stick of butter to remember that:
8 tablespoons 1 stick of butter
--------------- or ---------------
1/2 cup 4 ounces
But you can also just remember that there are:
16 tablespoons
-----------------
1 cup
These last three conversion factors are related. Just remember that 2+2=4 and start small:
2 cups 2 pints 4 quarts
-------- -------- ---------
1 pint 1 quart 1 gallon
Now, aside from metric units or unusual conversions (such as number of large eggs in a cup or something wonky like that) these should be all you would need to know off the top of your head.
The important thing to remember about all conversions is that you are working with different variations of the number 1. Many people will remember the identity property from high school math that basically says when you divide anything by itself, the answer is 1. It follows that anything multiplied by 1 is itself. In other words:
a * 1 = a
And
a
-- = 1
a
All of our conversions equal 1. Two cups is the same thing as one pint. When you divide something by itself, you get 1. Therefore:
2 cups 1 pint
------- = ------- = 1
1 pint 2 cups
Basically, all of the conversions given above are still true if you invert them and they are equal to one in every case. That said, the moment you don't write down the units, the statement is no longer true. Always write down the units.
The fun thing about math is that if it's true for numbers it's also true for random words meaning that units cancel just the same as numbers do. So if I want to cancel words on the diagonal of a multiplication problem, there is nothing to stop me. That said, just because I've cancelled the words doesn't mean I can cancel the numbers. Let us ask the question how many cups are in a gallon. You probably already know the answer but it's a good simple problem to start with.
1 gallon = ? cups
What happens when we multiply something by 1? It stays the same so let's multiply it by 1 a bunch of times do we can cancel the units. This is also called multiplying by an identity factor (a fancy word for the number 1 which includes units in the numerator and denominator). We want to choose our identity factors such that our ending unit does not cancel but our original unit does. We can use multiple identity factors such that we can cancel as many times as necessary to leave only the desired units:
2 cups 2 pints 4 quarts
1 gallon * ------- * --------- * ---------- = ? cups
1 pint 1 quart 1 gallon
Cancel on the multiplication diagonals and calculate!
2 cups 2
1
1
I don't want to get too terribly long and boring here but I have two more problems to show. Let's say we need to determine the number of gallons there are in something outlandish like 2048 ounces of fluid (2048 is a phenomenally addictive game by the way; I highly recommend it). Then we will take it a step further and ask how many whole large (2 oz) eggs we would need to make that number of gallons of fluid.
Always write out the question of course:
2048 ounces = ? gallons
Multiply by one or several identity factors:
1 pint 1 quart 1 gallon
2048 ounces x ----------- x --------- x -------- = ? gallons
16 ounces 2 pints 4 quarts
Then cancel what cancels and run the multiplication and division problem:
1
2048
16
2048 * 1 * 1 * 1 gallon 2048 gallon
------------------------------ = ------------------- = 8 gallons
16 * 2 * 4 256
TA DA!
Now for the egg-y bit. Yes, if your eggs are 2 ounces, then why not just do the math the easy way and divide the original 2048 ounces by 2 ounces? You get 1024 eggs." True, but say you don't happen to remember how many ounces an egg is but you do happen to know that there are 4 large eggs in a cup.
Ask the question:
2048 ounces = ? eggs
Multiply the given amount by the identity factors:
1 cup 4 eggs
2048 ounces * ----------- * ---------- = ? eggs
8 ounces 1 cup
Cancel appropriate units then multiply and divide. Do not forget to leave any units that were not cancelled (in our case we wanted to leave eggs for our final unit so we choose our identity factors such that everything but "eggs" cancel)!
1
2048
8
So yes, you were right! The point is that you can convert almost anything if you know the basic steps and the basic identity factors. Let's try this with sticks of butter, shall we? How many sticks of butter is in 2048 ounces of butter?
State the question:
2048 ounces = ? sticks
Multiply by an identity factor:
1 sticks
2048 ounces * ----------------- = ? sticks
4 ounces
Cancel, compute and voila; more butter more better!
1 stick 1 * 2048 sticks
2048
4
Alrighty, please feel free to comment if you have any questions. I think I covered everything but I am more than happy to add-on or explain further. :-)
Enjoy!
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