Math 110
Worksheet #4
Ratios
The math name for a fraction is ratio. A ratio is just a fancy way to say a fraction. In the
Culinary Arts, you use ratios all the time. The Working Factor is a ratio.
working factor = new yield
old yield
You can use ratios when you convert from one unit to another. Since 16 ounces = 1 pound,
the conversion ratios are
16 ounces
and
1 pound
1 pound
16 ounces
You can see that these ratios relate pounds and ounces.
Example 1: using a ratio
To convert from 2 pounds into an equivalent number of ounces, we use the first ratio.
2 pounds * 16 ounces = 2 pounds * 16 ounces = 32 ounces
1 pound
1 pound
so 2 pounds equals 32 ounces.
Example 2: using a ratio
To convert from 40 ounces into an equivalent number of pounds, we use the second ratio.
40 ounces * 1 pounds = 40 ounces * 1 pounds = 2.5 pounds
16 ounces
16 ounces
so 40 ounces equals 2.5 pounds.
Notice that in each case, you use the conversion ratio that forces the units to cancel (divide)
out. The units tell you which form of the conversion ratio you must use.
Proportions
A proportion is two ratios set equal to one another. That is, a proportion is a fraction equal to
a fraction. The above problems can be done using proportions. Note that one of the
conversion ratios is used. Surprisingly, it doesn’t matter which one you pick to use in the
proportion. The result will always be the same. Just make sure you put the units in the same
order as the conversion proportion. The units on the left side of the proportion must always
be the same as the units on the right side of the proportion.
Example 1: using a proportion to change units
To convert from 2 pounds into an equivalent number of ounces
n ounces = 16 ounces
Crisscross multiply. (This can be
2 pounds
1 pound
done ONLY with proportions).
n * 1 = 2 * 16
Therefore, 2 pounds is the same as 32 ounces.
OR:
1 pound
2 pounds
n ounces = 16 ounces
Crisscross multiply. (This can be
done ONLY with proportions).
n * 1 = 2 * 16
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Math 110
Worksheet #4
Therefore, 2 pounds is equivalent to 32 ounces.
Example 2: using a proportion to change units
n pounds
1 pound
40 ounces = 16 ounces
Remember, crisscross multiplication can
be done only with proportions.
n * 16 = 40 * 1
16*n = 40
To undo the multiplication of 16, we divide both sides by 16.
16*n = 40
16
16
Cancel the 16s. (This is why we chose to divide by 16.)
n = 2.5
Therefore, 40 ounces are equivalent to 2.5 pounds
OR
40 ounces = 16 ounces
n pounds
1 pound
40 * 1 = n * 16
Again, because this is a proportion, we can use the
crisscross multiplication.
This is exactly the same as the above problem.
40 = 16*n
To undo the multiplication of 16, we divide both sides by 16.
40 = 16*n
16
16
Cancel the 16s. (This is why we chose to divide by 16.)
2.5 = n
Therefore, 40 ounces are the same as 2.5 pounds.
One of the most useful proportions in your field of study is the following proportion. As
usual, the units on the left side of the proportion must be the same as the units on the right
side of the proportion.
quantity needed = portions needed
portion size
purchase size
Example 3: using a proportion to find quantity needed
Link sausages must be ordered in pounds. Say one portion consists of 4 sausages (links) and
you are serving 150 people. If 8 sausages are in each pound, how many pounds must you
order?
First, identify the information:
quantity needed = ?? pounds
portion size = 4 sausages
number of portions needed = 150
purchase size = 8 sausages (per pound)
so
n = 150
4
8
Notice the units:
left side= pound per sauage = pound
sausage
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Math 110
Worksheet #4
n * 8 = 4 * 150
the right side =
=
1
sausage/pound
pound
sausage
8 * n = 600
8 * n = 600
8
8
n = 75
You need to order 75 pounds of link sausages.
Example 4: using a proportion to find the quantity needed
Say you need 60 servings of 6-ounce glasses of milk. Milk comes in gallons. (128 fluid
ounces = 1 gallon) How much milk must you order?
quantity needed = ?? gallons
portion size = 6 ounces
number of portions needed = 60
purchase size = 128 ounces (per gallon)
so
n = 60
6 128
n * 128 = 6 * 60
Notice the units:
left side= gallon per ounce = gallon
ounce
right side =
1
= gallon
ounce/gallon
ounce
128 * n = 360
128 * n = 600
128
128
n = 2.8
You need to order 3 gallons of milk.
Sometimes you want to know how many serving you have available. A slightly altered form
of the previous proportion will give you the way to find your information. As always, the
units on the left side of the proportion must match the units on the right side.
quantity available = portions available
portion size
purchase size
Example 5: using a proportion to find the number of servings
If you have 1.5 gallons of milk in the refrigerator and you are serving the adults in 8 ounce
glasses, how many servings do you have? (Remember, 128 fluid ounces = 1 gallon.)
quantity available = 1.5 gallons
portion size = 8 ounces
number of portions needed = ??
purchase size = 128 ounces (per gallon)
so
1.5 = n
8
128
1.5 * 128 = 8 * n
192 = 8 * n
left side = gallons
ounce
right side =
1
= gallons
ounces/gallons ounces
192 = 8 * n
8
8
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Math 110
Worksheet #4
n = 24
You have 24 8-ounce servings of milk on hand.
There is one more proportion to examine. Again, it is a proportion that will help find the cost
of one serving or portion. It is important to know how much a serving costs, you that an
appropriate menu cost can be determined. Here we will just find the cost of one portion, the
cost per portion. As always, the units need to be the same.
portion cost = AP cost
portion size
EP size
(Review Worksheet #3 if you have
forgotten AP and EP)
Example 6: using a proportion to find the cost per portion
A 15-pound case of bacon slices cost $18. On the average, there are 20 slices of bacon in a
pound. If one serving consists of three slices of bacon, what is the cost per serving of bacon?
portion cost = $??
portion size = 3 slices
Notice the AP size and the EP size are the same
AP cost = $18
since bacon slices are measured by slices and
EP size = 15*20=300 slices
not the weight of each slice after cooking.
n = 18
3
300
n * 300 = 3 * 18
left side = $ per slice or dollars
slice
right side = $ per slice or dollars
slice
300*n = 54
300n = 54
300 300
n = .18
Therefore, one serving of three bacon slices costs $.18.
Example 7: using a proportion to find the cost per portion
Say a 20-pound box of large elbow macaroni costs $12. One portion of cooked macaroni is
about 10 ounces. However, cooked macaroni weighs about 2.6 times as much as the raw
macaroni.
portion cost = $??
portion size = 10 ounces
AP cost = $12.00
(Notice you must find the EP size in ounces)
EP size = 20 pounds * 2.6 = 5.2 pounds
= 52 pounds * 16 ounces = 832 ounces
1 pounds
(Check that the units are the same on each side.)
n = 12
10
832
n*832 = 10*12
832n = 120
832n = 120
832
832
n = .1442
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Math 110
Worksheet #4
Therefore, large elbow macaroni costs $.144 per portion.
Note: If you were pricing the total meal (plate cost), you would find the cost of one portion
for each item to the nearest mill. You add these costs to find the total meal cost and then
round to the nearest penny.
Problems
Here are a few standard unit conversions.
16 tablespoons = 1 cup
2 cups = 1 pint
2 pints = 1 quart
4 quarts = 1 gallon
8 ounces = 1 fluid cup
16 ounces = 1 pound
1. Use the standard unit conversions given above to fill in the following:
43 tablespoons = ________cups
3 fluid cups = ________ ounces
5 pins = _______ quarts
.75 gallons = _________cups
420 ounces = _________pounds
2. Sour cream is sold in 5-pound tubs. The Book of Yields says 1 pound of sour cream =
1.874 cups. How many cups of sour cream are in one tub?
3. World’s Finest Coffee (Decaf) is sold by the case where one case contains 48 6-ounce
packages. A restaurant uses 36 pounds of this coffee each month. How many cases must be
ordered per month?
4. If one 6-ounce package of the coffee mentioned in problem #3 makes about 18 servings of
coffee, how many servings are in a case?
5. A recipe for Brioche Parisienne (in Mastering the Art of French Pastry, page 201) uses
approximately 2 ounces of pate a brioche for each portion. If you are serving 65 people, how
many pounds of pate a brioche are required for this recipe?
6. Blanched, slivered almonds come in 3-pound cans and cost $56.92 per can. Pate d’
Amandes (almond paste) requires 10 ounces of these almonds to make about 2.25 pounds of
the paste. How many cans of blanched, slivered almonds are needed to make 12 pounds of
pate d’ amandes?
7. A #10 can of blueberries provides about 55 ounces of drained berries. One can costs
about $9.60. One ten-inch blueberry pie serves 8 people. If each pie uses 11 ounces of
blueberries, what is the portion cost of the blueberries?
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Math 110
Worksheet #4
8. A shipment of forty pounds of fresh, drawn (gutted) salmon is purchased for $4.50 per
pound. The filet yield of this fish is 27.2 pounds of salmon. If each portion consists of an 8ounce filet, what is the cost per portion?
9. Suppose you need 300 ounces of boneless, skinless half breasts of chicken. Suppose you
order untrimmed half breasts for $2.16 per pound. Each pound of untrimmed half breast of
chicken yields about 10.1 ounces of boneless, skinless half breasts. How many pounds of the
untrimmed chicken must you order?
10. A boneless, skinless half-breast of chicken weights about 5.3 ounces. What is the
portion cost of one half breast of chicken from problem #9?
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