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## Unit 5: Culinary Math and Recipes

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**Unit 5: Culinary Math and Recipes**The heart of many chefs in the kitchen 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.**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.**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.**Calculations**• Common denominator • Reducing fractions • Common fraction • Improper fraction • Mixed numbers American Culinary Federation: Culinary Fundamentals.**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.**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.**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.**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.**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.**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.**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.**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.**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.**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 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.**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.**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.**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.