Ratios - South Seattle College

Math 110

Ratios

Worksheet #4

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:

2 pounds 1 pound

Crisscross multiply. (This can be

n ounces = 16 ounces

done ONLY with proportions).

n * 1 = 2 * 16 -1-

Math 110

Therefore, 2 pounds is equivalent to 32 ounces.

Worksheet #4

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 Again, because this is a proportion, we can use the

n pounds

1 pound

crisscross multiplication.

40 * 1 = n * 16

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 48

Notice the units: left side= pound per sauage = pound sausage

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Math 110

n * 8 = 4 * 150

8 * n = 600

Worksheet #4

the right side = 1

= pound

sausage/pound sausage

8 * n = 600 88 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

128 * n = 360

Notice the units:

left side= gallon per ounce = gallon

ounce

right side = 1 = gallon

ounce/gallon

ounce

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

n = 24 You have 24 8-ounce servings of milk on hand.

Worksheet #4

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

n = 12

(Check that the units are the same on each side.)

10 832

n*832 = 10*12 832n = 120

832n = 120 832 832 n = .1442

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Math 110

Therefore, large elbow macaroni costs $.144 per portion.

Worksheet #4

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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