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**Unit 5: Culinary Math and Recipes**

The heart of many chefs in the kitchen American Culinary Federation: Culinary Fundamentals.

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**American Culinary Federation: Culinary Fundamentals.**

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**American Culinary Federation: Culinary Fundamentals.**

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 American Culinary Federation: Culinary Fundamentals.

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**American Culinary Federation: Culinary Fundamentals.**

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 American Culinary Federation: Culinary Fundamentals.

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**American Culinary Federation: Culinary Fundamentals.**

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 American Culinary Federation: Culinary Fundamentals.

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**American Culinary Federation: Culinary Fundamentals.**

Calculations Common denominator Reducing fractions Common fraction Improper fraction Mixed numbers American Culinary Federation: Culinary Fundamentals.

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**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 American Culinary Federation: Culinary Fundamentals.

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**American Culinary Federation: Culinary Fundamentals.**

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 American Culinary Federation: Culinary Fundamentals.

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**American Culinary Federation: Culinary Fundamentals.**

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 American Culinary Federation: Culinary Fundamentals.

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**American Culinary Federation: Culinary Fundamentals.**

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) American Culinary Federation: Culinary Fundamentals.

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**American Culinary Federation: Culinary Fundamentals.**

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 American Culinary Federation: Culinary Fundamentals.

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**American Culinary Federation: Culinary Fundamentals.**

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 American Culinary Federation: Culinary Fundamentals.

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**American Culinary Federation: Culinary Fundamentals.**

Converting To change a fraction to a decimal: 1/8 is 1 ÷ 8 = 0.125 To change a decimal to a fraction: .125 × 1000 = 125 125/1000 (125 ÷ 125)/(1000 ÷ 125) = 1/8 American Culinary Federation: Culinary Fundamentals.

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**American Culinary Federation: Culinary Fundamentals.**

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 American Culinary Federation: Culinary Fundamentals.

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**American Culinary Federation: Culinary Fundamentals.**

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 American Culinary Federation: Culinary Fundamentals.

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**Calculating Food Cost Applying 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 American Culinary Federation: Culinary Fundamentals.

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**American Culinary Federation: Culinary Fundamentals.**

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 American Culinary Federation: Culinary Fundamentals.

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**American Culinary Federation: Culinary Fundamentals.**

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 American Culinary Federation: Culinary Fundamentals.

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**American Culinary Federation: Culinary Fundamentals.**

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 American Culinary Federation: Culinary Fundamentals.

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**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 American Culinary Federation: Culinary Fundamentals.

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