© 2006, Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. American Culinary Federation: Culinary Fundamentals. Unit 5: Culinary Math.

American Culinary Federation: Culinary Fundamentals. © 2006, Pearson Education, Upper Saddle River, NJ

07458. All Rights Reserved.

Unit 5: Culinary Math and Recipes

The heart of many chefs in the kitchen





What Is Culinary Math?

• The same as any other math

• Used in the culinary world to make databases and spreadsheets, calculate yield percentages, and figure menu prices, labor costs, business costs, and profit and loss statements

• Involves fractions, ratios, and decimals



Whole Numbers

• Have a place value that allows us to indicate a large number

• Placed in specific sequence• Ones, tens, hundreds,

thousands, etc.• Used for subtraction,

addition, multiplication, and division



Fractions

• Break something (whole numbers) into pieces• Each piece is a part or a fraction of the whole• The number on top (numerator) is the fraction• The number on the bottom represents the whole

(denominator)• Used to measure ingredients• Crucial in scaling recipes



Calculations

• Common denominator

• Reducing fractions

• Common fraction

• Improper fraction

• Mixed numbers



Addition/Subtraction

• Common denominator• Example: ½ + ⅓ = ?• Multiply the values of numerator and denominator on

one side of the equation by the denominator of the other: 1 × 2 = 2, 3 × 2 = 6

• Repeat the process using the original denominator• 1 × 3 = 3• 2 × 3 = 6• Rewrite the equation, add the fractions, come up with

the answer• 2/6 + 3/6 = 5/6



Multiplication

• Multiplying is a form of adding • 1 × 1 = 1• 2 × 3 = 6• Common denominator is not needed for

this operation• Multiplying whole numbers must be

converted into improper fractions• After practice, this is very easy, as you will

do it for every recipe



Dividing

• Dividing is a form of subtraction

• Mixed numbers converted to improper fractions

• Reverse the numerator and denominator

• Or, invert the fraction

• Example ½ ÷ ¾ must be rewritten as ½ × 4/3 = 4/6



Reducing Fractions

• The last frame showed an answer of 4/6

• Reducing that fraction would be accomplished by dividing by the largest whole number that divides evenly

• In this case it is 2 (4/6 ÷ 2 = ⅔)



Ratios• A fraction is a ratio• Ratios are used to make work simpler• Many are standard throughout the industry• Vinaigrette: 3 parts oil, 1 part vinegar is the most

common ratio for this dressing• A fraction of ½ would be expressed as 1 part to 2 parts:

1-1 would be 50/50 or equal amounts• 2/3 would be 2 parts to 3 parts• Basic rice pilaf calls for 1 part rice, 2 parts hot stock, or

½ ratio• Also, 4 parts to 6 parts can be reduced to 2 parts to

3 parts• 1 part carrots, 1 part celery, 2 parts onion would be

written as 1:1:2



Decimals and Percents

• Numbers to the left of a decimal point are whole numbers

• Numbers to the right of the decimal point are parts of a whole number

• Numbers to the right are also called decimals and/or fractions

• To perform calculations, you must perform the operations of :– Decimals to fractions– Fractions to decimals



Converting

• To change a fraction to a decimal:1/8 is 1 ÷ 8 = 0.125

• To change a decimal to a fraction:1. .125 × 1000 = 125

2. 125/1000

3. (125 ÷ 125)/(1000 ÷ 125) = 1/8



Percentages

• A percent (%) is part of 100

• 100 percent means all of something

• A percent less than 100 means how many out of that whole

• 35 percent is 35 parts of 100 parts



To Calculate a Percent

• Begin with a decimal

• Move the point two places to the right

• Add the word or symbol for percent (%)

• To use this to calculate, turn it back to a decimal; divide the % by 100 or move the decimal point two places to the left

• Drop the word and/or symbol



Calculating Food CostApplying Math in the Kitchen

• Recipes is most obvious use

• You will either increase or decrease recipes

• Involves multiplication or division

• May involve fractions, decimals, ratios

• Goal is to generate a profit



Factors to Account for

• Salaries, rent, utilities, advertising, insurance

• Controlling these costs is crucial

• Cost of specific recipes includes every element needed to serve the dish

• Must have knowledge to convert from one measurement to another



Yield Percent

• This is commonly a pitfall that is unaccounted for

• It is “how much of an ingredient is available to use” after trimming, cooking, carving

• The lower the yield percent, the more the food actually costs to serve your guests

• “Relatively inexpensive” can be deceiving after preparation



Food Cost Percentage

• Most kitchens have established food cost percentages

• Total food cost is all the food and drink purchased to produce all the menu items

• Calculated to a predetermined schedule

• Useful as a monitoring tool for the kitchen

• Improves bottom line and efficiency



Food Cost Calculation Formula

• Probably one of the most important formulas in the industry

• Divide the total cost of food by the total sales

• $50,000 ÷ $200,000 = 25% food cost

© 2006, Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. American Culinary Federation: Culinary Fundamentals. Unit 5: Culinary Math.

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