Math Question for Food Geeks

[Fat Guy]

We were talking elsewhere about mixing heavy cream and skim milk to make whole milk. Can somebody who does this stuff easily with spreadsheets tell us how much of each type of cream per how much of each type of milk one would have to use to do this? Assume the following fat percentages, which are inexact:

Heavy Cream = 36% (typical)

Whipping Cream = 30% (can be more)

Light Cream = 18% (can be more)

Half And Half = 11% (can be more)

Whole Milk = 4% (usually a little less)

2% Milk = 2% (duh)

Low Fat Milk = 1%

Skim Milk = 0% (it's really more like .5%)

[jordyn]

1 unit heavy cream plus 8 units skim milk yields 4% fat in the mixture.

Fat Guy: Do you want to know much of the other types of cream to add to skim milk to acheive 4% as well--I can't quite tell by your question...

[Orik]

We were talking elsewhere about mixing heavy cream and skim milk to make whole milk. Can somebody who does this stuff easily with spreadsheets tell us how much of each type of cream per how much of each type of milk one would have to use to do this? Assume the following fat percentages, which are inexact:

Heavy Cream = 36% (typical)

Whipping Cream = 30% (can be more)

Light Cream = 18% (can be more)

Half And Half = 11% (can be more)

Whole Milk = 4% (usually a little less)

2% Milk = 2% (duh)

Low Fat Milk = 1%

Skim Milk = 0% (it's really more like .5%)

Are these %s by volume or by weight?

[Fat Guy]

Jordyn: How the heck did you figure that out?

[jordyn]

I used a spreadsheet, just like you suggested.

But, the general formula is:

Fm = ((Fc*Vc) + (Fs+Vs))/(Vc+Vs)

Where:

Fm, Fc and Fs are percentage fat in the mixture, cream and skim milk

and

Vc and Vs are the volume of cream and skim milk

[Fat Guy]

Orik: I don't know; I'm looking on the USDA site and it only speaks in terms of percentage without specifying weight or volume. Most likely they'd measure this in volume, though, right?

[Fat Guy]

Fm = ((Fc*Vc) + (Fs+Vs))/(Vc+Vs)

Of course!

[jordyn]

Fat Guy: The idea behind figuring out the percentage is to see what proportion of fat there is to the total volume. So, this is a two step process.

First, you figure out the amount of fat. You take the volume of the various substances you are adding and multiply by their fat percentage. So, if you have 100 units of 36% fat cream, 36 of those units are fat, right? The skim milk has no fat, so it's easy. To simplify our example, we'll say we also have 100 units of skim milk, yielding zero units of fat for that part, and 36 total units of fat in the mixture.

Then we divide this by the total volume of both parts of the mixture. In this case it's 200. 36/200 = .18, so in this hypothetical example our mix would be 18% fat.

When one of your elements is skim milk, figuring out how much more skim milk you need than ccream is pretty easy. Take your starting percentage (36%), divide by your finishing percentage (4%), and subtract one. 36/4 = 9. Subtract one to get eight and you've got the number of units of skim milk you need to add to the cream.

[Edited for slightly better flow. Now we know why I don't write math books...]

[cabrales]

Excel has significant macro capabilities that could be tapped in the event more complex lines of analysis were required. As jordyn noted, the above is predicated on the formula he provided.

[Fat Guy]

Excel has significant macro capabilities that could be tapped in the event more complex lines of analysis were required.

I love it when you talk dirty, Cabrales.

Jordyn, explain it 35 more times and I might be able to pretend I get it.

[plunk]

In Canada, % milk is determined by weight, and I would assume this is true for the US as well. So 4% milk would contain 4 grams of milkfat in every 100 grams of milk.

Here's a snippet from a Canadian dairy (www.islandfarms.com):

How much fat does milk contain?

In the dairy industry, milk is named according to its milkfat (mf) content. Therefore, 2% milk contains 2% mf by weight; i.e., there are 2 grams of milkfat in every 100 grams of 2% milk. 1% contains 1%, homogenized contains 3.25%, and skim milk has less than 0.1%. And buttermilk? Well, Island Farms buttermilk is actually only about 2%mf, but culture is added to make it thick and creamy.

[Fat Guy]

Okay. Just to be clear, a gram can be a weight measure or a volume measure, right? But in this context it's a weight measure?

[cabrales]

Excel has significant macro capabilities that could be tapped in the event more complex lines of analysis were required.

I love it when you talk dirty, Cabrales.

Steven -- I would settle for just being able to speak, in Q&A forums just like every other forum.

[Fat Guy]

Stop behaving like a spoiled child, Cabrales.

[g.johnson]

Okay. Just to be clear, a gram can be a weight measure or a volume measure, right? But in this context it's a weight measure?

We now know that the decline in standards preceded FG’s education. Or, no, to answer your question more directly.

[=Mark]

Excel has significant macro capabilities that could be tapped in the event more complex lines of analysis were required. As jordyn noted, the above is predicated on the formula he provided. 

I can never get the Excel macros to do what I want, the cells I want relational become static and vice versa...

[Fat Guy]

G: They happened at about the same time, but in this case I was pre-metric. I guess it's ounces that can be either.

[plunk]

Are you really sure you want to know? :)

A gram is a measure of mass, or the amount of "stuff" a thing is composed of. Weight is determined by (mass * gravity). So 1kg of stuff on Earth weighs 2.2lbs while the same 1kg of stuff would weigh 0.8lbs on Mars.

Almost everyone (except for geeks) use weight and mass interchangably in everyday language since people almost always talk about earth-bound objects. So yes, a gram is usually thought of as a weight measure.

What you should not do is use weight and volume interchangably. Volume is a just a 3D spatial measure, 100mL on Earth is the same as 100mL on Mars.

Density is a measure of mass per volume. Milk fat and milk liquid (mostly water) have different densities, illustrated by the fact that butter floats on water. Since milk liquid is mostly water, 100g of milk would take up about 100mL of volume. 100g of butter, which has a lower density, would take up -more- than 100mL of volume.

[jordyn]

Being an American, I know precious little about the metric system, but I'm fairly certain that grams are only a measure of weight, not volume.

Ounces, on the other hand...

[g.johnson]

G: They happened at about the same time, but in this case I was pre-metric. I guess it's ounces that can be either.

Strictly speaking, one should still qualify the volume measure as "fluid ounce", the volume of water that weighs one ounce.

[plunk]

I'm a Canadian, I have to convert everything imperial to metric. Thank god I have a food scale which measures in ounces and grams. What irks me are "sticks of butter" measurements.

[g.johnson]

Anyone want to know the difference between imperial and US pints?

[Fat Guy]

Sure.

[plunk]

Yes, water is the "standard" for both ounces and grams.

1 liquid ounce of water weighs 1 ounce

1 Litre of water weighs 1 kg

[g.johnson]

US and imperial fluid ounces are approximately the same but an American pint is 16 fluid ounces and an imperial pint is 20 fluid ounces. Because we can take our drink.