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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.

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