Culinary Math Principles and Applications 3rd Ed by American Technical Publishers

Michael J. McGreal Linda J. Padilla

Culinary Math Principles and Applications contains procedures commonly practiced in the foodservice industry. Specific procedures vary with each task and must be performed by a qualified person. For maximum safety, always refer to specific manufacturer recommendations, insurance regulations, specific facility procedures, applicable federal, state, and local regulations, and any authority having jurisdiction. The material contained is intended to be an educational resource for the user. American Technical Publishers assumes no responsibility or liability in connection with this material or its use by any individual or organization.

Cover Photo Credits: Rolandas Grigaitis/Shutterstock.com

American Technical Publishers Editorial Staff Editor in Chief: Peter A. Zurlis Director of Product Development: Cathy A. Scruggs Assistant Production Manager: Nicole D. Burian Technical Editor: Sara M. Marconi Supervising Copy Editor: Catherine A. Mini Copy Editor: Dane K. Hamann Editorial Assistants: Erin E. Bello Alex C. Tulik

This book is printed on recycled paper.

Art Supervisor: Sarah E. Kaducak Cover Design: Bethany J. Fisher Illustration/Layout: Bethany J. Fisher Digital Media Manager: Adam T. Schuldt Digital Resources: Cory S. Butler James V. Cashman Tim A. Miller

Acknowledgments About the Authors Michael J. McGreal, M.Ed., CEC, CCE, CHE, FMP, CHA, MCFE, is the Culinary Arts Department Chair at Joliet Junior College. He has received many honors over his 38 years of foodservice experience including, the American Culinary Federation Presidential Medallion. Chef McGreal is also the author of Culinary Arts Principles and Applications and 50 Effective Knife Techniques.

Linda J. Padilla taught mathematics at Joliet Junior College for over 30 years. She holds degrees in mathematics, education, and counseling. Linda has extensive experience collaborating with other disciplines and has developed curriculum strategies and applications for math in the culinary arts. Her work on math applications in the culinary field has also been featured at national conferences.

Technical Reviewers The authors and publisher are grateful for the technical reviews provided by the following individuals: Bridget English Former Chef Instructor Erie Community College, North Campus (NY)

Adrienne O’Brien, CCE Former Culinary Arts Instructor Luna Community College (NM)

Kyle Haak Hospitality Management Instructor Erie Community College, City Campus (NY)

Janelle Pease Culinary Arts Instructor Western Technology Center (OK)

Tom Hickey, CEC, CCE, CFE, HOGT Former Chef Ambassador Sullivan University (KY)

Christopher Plemmons, CEC, AAC Chef Instructor Olympic College (WA)

Anthony Lowman, CCC, CCE, ACE Chef Instructor St. Johns Technical High School (FL)

Marivic Schrage Assistant Professor Guam Community College (HI)

Kyle A. Mitchell Culinary Arts Instructor Kalamazoo Valley Community College (MI)

Peter B. Sproul, CEC Program Director Culinary Arts Institute, Utah Valley University (UT)

Stephen J. Moir, CEC Culinary Arts Instructor Perth Amboy Tech (NJ)

Katie Street Former Math Instructor Lorain County Joint Vocational School (OH)

Rebecca Norwood Director of Education New Orleans Culinary & Hospitality Institute (LA)

Acknowledgments (continued) The authors and publisher are grateful for the images provided by the following companies, organizations, and individuals: American Metalcraft, Inc. • Beef Checkoff • Browne Foodservice • Calculated Industries • Carlisle FoodService Products • Charlie Trotter’s • Classic Party Rentals • Cooper-Atkins Corporation • Cres Cor • Daniel NYC • Detecto, A Division of Cardinal Scale Manufacturing Co. • Edlund Co. • Edward Don & Company • Eloma Combi Ovens • Florida Department of Agriculture and Consumer Services • Fluke Corporation • Idaho Potato Commission • Lauren Frisch • Lavu, Inc. • MacArthur Place Hotel, Sonoma • McCain Foods USA • National Chicken Council • National Honey Board • National Turkey Federation • Perdue Foodservice, Perdue Farms Incorporated • The Spice House • Sullivan University • Tanimura & Antle® • U.S. Apple® Association • The Vollrath Company, LLC • Vulcan-Hart, a division of the ITW Food Equipment Group LLC • Wisconsin Milk Marketing Board, Inc. •

Contents Chapter

Using Math in Foodservice Operations Section 1-1 How Math Is Used in Food Service

1 2

Pricing Menu Items • Ordering Food and Supplies • Measuring Recipe Ingredients • Preparing Food • Serving Food • Storing Food and Supplies • Processing Money • Scheduling and Payroll • Tracking Income and Expenses Checkpoint 1-1

Section 1-2 Performing Basic Math Calculations

Adding Whole Numbers • Subtracting Whole Numbers • Multiplying Whole Numbers • Dividing Whole Numbers Checkpoint 1-2

Math Exercises

Chapter

Measuring in the Professional Kitchen

Section 2-1 Using Standardized Measures

Checkpoint 2-1

Section 2-2 Measuring Volume

Fluid Ounces Versus Ounces • Volume Units and Equivalents • Calculating Customary Volume Equivalents • Calculating Metric Volume Equivalents • Tools for Measuring Volume Checkpoint 2-2

Section 2-3 Measuring Weight

Weight Units and Equivalents • Calculating Weight Equivalents • Tools for Measuring Weight Checkpoint 2-3

Section 2-4 Measuring Time and Temperature

Checkpoint 2-4

Section 2-5 Measuring Distance

Checkpoint 2-5

Math Exercises

Contents Chapter

Calculating Measurements

Section 3-1 Whole Number Measurements

Adding and Subtracting Measurements • Multiplying and Dividing Measurements Checkpoint 3-1

Section 3-2 Fraction Measurements

Adding and Subtracting Fractions • Multiplying Fractions • Dividing Fractions Checkpoint 3-2

Section 3-3 Decimal Measurements

Rounding Decimals • Adding and Subtracting Decimals • Multiplying Decimals • Dividing Decimals • Converting Between Fractions and Decimals Checkpoint 3-3

Section 3-4 Calculating Area, Volume, and Angles

Calculating Area • Calculating Volume • Calculating Angles Checkpoint 3-4

Section 3-5 Basic Statistics

Creating Data Tables • Graphing Data Checkpoint 3-5

Math Exercises

Chapter

Converting Measurements and Scaling Recipes Section 4-1 Converting Measurements

99 100

Converting Within the Customary or Metric System • Converting Between Customary and Metric Measurements • Converting Between Volume and Weight Measurements • Using a Kitchen Calculator Checkpoint 4-1

Section 4-2 Scaling Recipes

107

Standardized Recipe Elements • Scaling Based on Yield • Scaling Based on Product Availability • Multiplying Scaling Factors • Additional Scaling Considerations Checkpoint 4-2

Math Exercises

115

Chapter

Calculating Percentages and Ratios

127

Section 5-1 Calculating Percentages

128

Checkpoint 5-1

Section 5-2 Using Yield Percentages

132

Calculating Yield Percentages • Calculating As-Purchased Amounts • Calculating Edible-Portion Amounts • Factors Affecting Yield Percentages Checkpoint 5-2

Section 5-3 Using Baker’s Percentages

138

Converting Units of Measure • Calculating Baker’s Percentages Checkpoint 5-3

Section 5-4 Calculating Ratios

143

Checkpoint 5-4

Section 5-5 Using Ratios

145

Checkpoint 5-5

Chapter

Math Exercises

147

Calculating Costs and Menu Prices

159

Section 6-1 Identifying As-Purchased Costs

160

Checkpoint 6-1

Section 6-2 Calculating Unit Costs

161

Calculating As-Purchased Unit Costs • Calculating Edible-Portion Unit Costs Checkpoint 6-2

Section 6-3 Calculating As-Served Costs

164

Checkpoint 6-3

Section 6-4 Calculating Food and Beverage Cost Percentages

166

Menu-Item Cost Percentages • Overall Cost Percentages • Target Cost Percentages Checkpoint 6-4

Section 6-5 Calculating Menu Prices

169

Food and Beverage Cost Percentage Pricing • Perceived Value Pricing • Contribution Margin Pricing Checkpoint 6-5

Section 6-6 Using Pricing Forms

175

Checkpoint 6-6

Math Exercises

179

Contents Chapter

Calculating Revenue and Expenses

191

Section 7-1 Calculating Revenue

192

Processing Guest Checks • Calculating Sales Revenue Checkpoint 7-1

Section 7-2 Calculating Expenses

202

Calculating Capital Expenses • Calculating Cost of Goods Sold • Calculating Operating Expenses • Variable Expenses Versus Fixed Expenses Checkpoint 7-2

Math Exercises

Chapter

211

Analyzing Profit and Loss

223

Section 8-1 Making a Profit

224

Maximizing Revenue • Minimizing Expenses Checkpoint 8-1

Section 8-2 Standard Profit and Loss

233

Gross Profit Versus Net Profit • Standard Profit and Loss Statements • Estimating Profit and Loss Checkpoint 8-2

Section 8-3 Special Event Profit and Loss

241

Planning Special Events • Calculating Special Event Profit and Loss Checkpoint 8-3

Math Exercises

249

Checkpoint Answers

261

Appendix 271 Math Formulas Reference Tables Forms

272 278 283

Glossary 285

Index 289

Online Learner Resources Culinary Math Principles and Applications includes access to online learner resources that enhance and reinforce the content of the text/workbook. • Quick Quizzes® • Flash Cards • Master Math® Applications • Forms and Tables • Media Library • Internet Resources

Book Features Culinary Math Principles and Applications demonstrates how and why foodservice workers use math in the professional kitchen. This full-color, third edition includes access to digital resources that reinforce how math is used in culinary and hospitality settings. Whether this text/workbook is used in a college course, an apprenticeship program, or in a career and technical education classroom, learners will benefit from its well-illustrated and engaging style. Each chapter is divided into sections to allow maximum teaching and learning ﬂexibility. Additionally, each section ends with a checkpoint consisting of short-answer review questions. There are 50 math exercises at the end of each chapter for a total of 400 real-world culinary math problems. Leaf icons next to 80 of these problems indicate a culinary math problem with a sustainability focus. Checkpoint answers are located at the end of the book and the appendix contains all of the culinary math formulas used in the book plus reference tables and forms.

Chapter Objectives identify the main concepts addressed in each section of the chapter.

Key Terms are listed on each chapter opener. All vocabulary terms are italicized and deﬁned at ﬁrst use.

Formulas are shown with variables, text, and illustrations to support varied learning styles and reinforce meaning.

Guides provide a brief summary of math concepts that are applied in foodservice settings.

Math Exercises give learners the opportunity to apply the math skills covered in the chapter. Leaf Icons indicate a math problem with a sustainability focus.

Problem-Solving Steps present key math applications in a clear, step-by-step format. Detailed Illustrations provide visual clarity and context for math principles and applications. Checkpoints at the end of each section serve as a review and apply the concepts covered to reinforce learning. Checkpoint answers are provided at the end of the book.

Online Resources Culinary Math Principles and Applications includes access to online learner resources that reinforce content and enhance learning. These interactive resources can be accessed using either of the following methods: • Key atplearningresources.com into a web browser and then enter access code • Use a Quick Response (QR) reader app on a mobile device to scan the QR code located on the opening page of each chapter.

LEARNER RESOURCES The Culinary Math Principles and Applications Learner Resources are self-study tools that reinforce the content covered in the text/workbook. Learner resources include the following: • Quick Quizzes® that provide 10 interactive questions for each chapter, with embedded links to highlighted content within the text/workbook and to the Illustrated Glossary. • Flash Cards that provide a review tool to match terms and definitions and/or identify symbols, tools, and equipment. • Master Math® Applications that provide two key review tools. Master Math® Worksheets provide opportunities to review math principles and then apply those math skills. Master Math® Problems present 20 common foodservice calculations in a step-by-step format for easy comprehension. • Forms and Tables that consist of a comprehensive listing of all of the math formulas used in the book, provided in pdf format for easy printing. Reference tables from the appendix are also provided in pdf format. A pricing form and a daily sales record are provided in an interactive format to facilitate learning of math applications. • Media Library that consists of videos and animations that reinforce and expand upon content found in the book. • Internet Resources that provide links to online reference materials that support continued learning.

Online Resources (continued) INSTRUCTOR RESOURCES The Culinary Math Principles and Applications Instructor Resources provide instructional tools to help implement a comprehensive instructional program. The Instructor Resources include the following: • Culinary Math Principles and Applications ATPWebBook™ that allows access to content anytime, anywhere, using any internet-connected device. • Instructional Guide that explains how to make the best use of various instructional tools and includes a detailed instructional plan for each chapter and section of the text/workbook. • Premium PowerPoint ® Presentations that review the objectives, key content, and review questions for each chapter and section of the book. Instructor notes are provided. • Assessments that provide sets of questions and answers based on objectives and key concepts from each chapter of the book and include a Pretest, a Posttest, and Test Banks. • Answer Keys that list answers to the Text/Workbook Math Exercises and Master Math® Worksheets. • Learner Resources are included as part of the Instructor Resources for ease of use.

To obtain information on other related training materials, visit atplearning.com. The Publisher

Converting Measurements and Scaling Recipes

Recipes are often changed to produce more or less food to meet the demands of a particular kitchen. Foodservice employees need to be able to calculate new ingredient measurements to account for those changes in recipes. Often, measurements may need to be converted to different units of measure. Factors such as cooking times and temperatures also need to be taken into account when recipes are changed. By using solid math skills and paying close attention to detail, accurate changes can be made to recipes while maintaining the quality of the food prepared. Section 4-1: CONVERTING MEASUREMENTS • Convert measurements within the customary or metric measurement system.

• Convert measurements between the customary and metric measurement systems. • Convert between volume and weight measurements. Section 4-2: SCALING RECIPES • Identify the most common elements of a standardized recipe.

Key Terms • • • • • •

converting cancelling scaling yield portion size scaling factor

• Calculate scaling factors based on recipe yield. • Calculate scaling factors based on product availability. • Explain how other scaling considerations of a recipe are affected when the yield is changed.

Learner Resources

atplearningresources.com access code

All-Clad Metalcrafters

Section 4-1 CONVERTING MEASUREMENTS

Photo Courtesy of Perdue Foodservice, Perdue Farms Incorporated

With a working knowledge of the standard units of measure used in the professional kitchen and an understanding of how measurements are calculated, foodservice employees can convert measurements. Converting is the process of changing a measurement with one unit of measure to an equivalent measurement with a different unit of measure. There are three different types of measurement conversions performed in the profession kitchen. • Converting volume or weight measurements within the customary or metric system. Converting gallons to quarts, pounds to ounces, liters to milliliters, and kilograms to grams are examples of this type of conversion. • Converting between customary and metric measurements. Converting quarts to liters and ounces to grams are examples of this type of conversion. • Converting between volume and weight measurements. Converting cups to ounces, gallons to pounds, and teaspoons to grams are examples of this type of conversion. These conversions are unique because volume-to-weight equivalents are approximations and differ depending on the ingredient being measured. Converting Within the Customary or Metric System

To convert a measurement to a different unit within the same measurement system, the measurement is first written as a fraction. For example, to convert 8 quarts to gallons, the first step is to write the original measurement as a fraction. 8 qt 1

The next step is to identify the conversion factor that the original measurement can be multiplied by to convert quarts to gallons. In this case, the common equivalent of 4 quarts = 1 gallon can be used. The equivalent can be written as a fraction in two ways, just like it is equally correct to say that “1 gallon is equivalent to 4 quarts” or “4 quarts are equivalent to 1 gallon.” 1 gal. 4 qt or 4 qt 1 gal.

Then, the original measurement is multiplied by the equivalent, which is written so that the unit in the denominator is the same as the unit in the original measurement. 8 qt 1 gal. × 1 4 qt

100

CULINARY MATH PRINCIPLES AND APPLICATIONS

When multiplied, the unit in the numerator of the original measurement (8 qt) cancels the matching unit in the denominator of the written equivalent (4 qt). Cancelling is the process of crossing out and eliminating matching units in the numerators and denominators of fractions in a conversion calculation. Cancelling is shown by drawing a line through the matching units. In this example, the quarts cancel each other. 8 qt 1 gal. 8 1 gal. × = × 1 4 qt 1 4

When multiplying fractions, the numerators are multiplied by each other and the denominators are multiplied by each other. 8 × 1 gal. 8 gal. = 1× 4 4

Then, the numerator is divided by the denominator to obtain the final answer.

Cancelling Guide Convert 4 pints to quarts. Step 1: Write the measurement and the conversion factor as fractions in a multiplication calculation. 4 pt 1 qt × 1 2 pt Step 2: Cancel the matching units in the numerators and denominators and then multiply the resulting fractions. 4 pt 1 qt 4 1 qt 4 qt × = × = 1 2 pt 1 2 2 Step 3: Divide the numerator by the denominator to obtain the final answer. 4 qt ÷ 2 = 2 qt

8 gal. ÷ 4 = 2 gal.

The cancelling method works for any measurement conversion within the same measurement system as long as the appropriate conversion factor is known. For example, 20 ounces of chocolate can be converted to pounds of chocolate. See Figure 4-1. Converting Weight Measurements Within the Customary System ORIGINAL MEASUREMENT

Example: Convert 20 ounces of chocolate to pounds of chocolate. 1. Write the original measurement as a fraction with the measurement as the numerator and 1 as the denominator.

20 oz 1

2. Identify the equivalent between the original measurement and the desired measurement and write as a fraction with the original measurement unit in the denominator.

1 lb 16 oz

3. Set up a multiplication calculation with the measurement and the equivalent. Cancel the matching units in the numerators and denominators of the calculation.

20 oz 1 lb × 1 16 oz

CANCEL MATCHING UNITS

20 20 lb 1 lb 20 × 1 lb × = = 1 16 16 1 × 16

4. Multiply the resulting fractions. 5. Divide the numerator by the denominator to obtain the final answer. Answer:

TO CONVERT OUNCES TO POUNDS

20 lb ÷ 16 = 1.25

1.25 lb

Figure 4-1. Converting measurements involves expressing measurements and equivalents as fractions and cancelling the matching units of measure.

Chapter 4 — Conver ting Measurements and Scaling Recipes

101

Converting Between Customary and Metric Measurements

Measurements can also be converted between customary and metric units of measure. However, the equivalents between customary units and metric units are seldom whole numbers. For example, 1 liter is equivalent to 1.06 quarts and 1 kilogram is equivalent to 2.2 pounds. See Figure 4-2.

Customary and Metric Unit Equivalents Volume

1 LITER SLIGHTLY LARGER THAN QUART

1 gallon (gal.) = 3.79 liters (L) 1 quart (qt) = 0.95 liters (L)

1 liter

1 cup = 236.6 milliliters (mL) 1 fluid ounce (fl oz) = 29.6 milliliters (mL)

500 milliliters 250 milliliters

1 teaspoon (tsp) = 5 milliliters (mL) 1 liter (L) = 1.06 quart (qt) 1 liter (L) = 33.8 fluid ounces (fl oz)

1 quart

1 cup

1 KILOGRAM SLIGHTLY LARGER THAN TWO POUNDS

Weight 1 pound (lb) = 0.454 killograms (kg) 1 pound (lb) = 454 grams (g) 1 ounce (oz) = 28.4 grams (g)

1 pound (454 grams)

1 kilogram (2.2 pounds)

1 kilogram (kg) = 2.2 pounds (lb)

Figure 4-2. Equivalents between customary and metric units of measure for volume and weight are used to perform calculations in the professional kitchen.

The process for converting between customary and metric measurements is the same as for other conversions. For example, to convert 800 grams to pounds, the first step is to write 800 grams as a fraction. 800 g 1

The second step is to identify the equivalent between grams and pounds. The equivalent 1 pound = 454 grams is found in Figure 4-2. This equivalent is written as a fraction with grams in the denominator so that the grams will cancel each other. 800 g 1lb 800 1lb × = × 1 454 g 1 454

102

CULINARY MATH PRINCIPLES AND APPLICATIONS

Next, the numerators of each fraction are multiplied by each other and the denominators of each fraction are multiplied by each other. 800 × 1lb 800 lb = 1× 454 454

Then, the numerator is divided by the denominator to obtain the final answer. 800 lb ÷ 454 = 1.76 lb

When converting between customary and metric measurements, it is common to calculate answers as decimals. Decimal answers are rounded based on the degree of accuracy required for that ingredient in the recipe. In some instances, two measurement equivalents will need to be used in one conversion calculation. For example, if a restaurant has 2 liters of soy sauce in storage and a recipe requires 3 pints of soy sauce, is there enough soy sauce to make the recipe? To answer this question, two equivalents are required. The first equivalent is used to convert liters to quarts and the second equivalent is used to convert quarts to pints. See Figure 4-3.

Converting Between Customary and Metric Measurements Example: If a restaurant has 2 liters of soy sauce in storage and a recipe requires 3 pints of soy sauce, is there enough soy sauce to make the recipe? 1. Write the original measurement as a fraction. 2. Identify the equivalents between the original measurement and the desired measurement and write as fractions with the original measurement unit in the denominator. 3. Set up a multiplication calculation with the measurement and the equivalents. Cancel the matching units in the numerators and denominators of the calculation.

2L 1

ORIGINAL MEASUREMENT

TO CONVERT LITERS TO QUARTS

2 pt 1 qt and 1 qt 0.95 L 2 pt 2L 1 qt × × 1 qt 1 0.95 L

TO CONVERT QUARTS TO PINTS CANCEL MATCHING UNITS

CANCEL MATCHING UNITS

1 2 pt 2 4 pt × × = 0.95 1 1 0.95

4. Multiply the resulting fractions. 5. Divide the numerator by the denominator to obtain the final answer (rounded to the tenths place). Answer:

4 pt ÷ 0.95 = 4.2

Yes, there are 4.2 pints of soy sauce.

Figure 4-3. Volume measurements in metric units can be converted to volume measurements in customary units.

Chapter 4 — Conver ting Measurements and Scaling Recipes

103

Converting Between Volume and Weight Measurements Volume vs. Weight Units Blueberry Pie Yield: 1 (9-in. pie) Ingredients

24 oz 6 oz 6 fl oz 2 tsp

Blueberries, fresh Sugar, granulated Water Lemon Juice

Recipe Calls for Ounces

Product Sold in Pints

Converting between volume and weight measurements is often necessary because food products cannot always be purchased in the same units that are called for in a recipe. See Figure 4-4. Equivalents between volume and weight units are approximations based on how much a given volume of an ingredient will weigh on a scale. Two ingredients of the same volume may not weigh the same due to differences in density. For example, 8 fluid ounces of water will weigh 8 ounces, but 8 fluid ounces of all-purpose flour will only weigh about 4.5 ounces, while 8 fluid ounces of honey will weigh about 12 ounces. Volume-to-weight equivalents tables can be referenced as needed. See Appendix. It is important to remember that volume-to-weight equivalents are approximate and care must be taken to reference the most appropriate entry in an equivalents table. For example, there may be more than one volume-to-weight equivalent listed for grapes depending on whether the grapes are sliced or if the grapes are whole. A cup of sliced grapes will weigh more than a cup of whole grapes because the sliced grapes will fill the cup more compactly. See Figure 4-5. Volume-to-weight equivalents can be used to convert volume measurements to weight measurements. For example, how many ounces of frozen peas are there in 10 cups of frozen peas? The first step is to write the original measurement as a fraction.

Figure 4-4. Food products are not always sold in the same units as the units used in a recipe.

10 c 1

Volume-to-Weight Equivalents

Volume-to-Weight Equivalents Ingredient Grapes sliced whole

Volume

Weight

1c 1c

5³⁄₄ oz 3³⁄₄ oz

1 Cup Grapes, Sliced

1 Cup Grapes, Whole

Figure 4-5. When referencing volume-to-weight equivalents, there may be more than one entry for an ingredient.

104

CULINARY MATH PRINCIPLES AND APPLICATIONS

Based on the equivalents table, the volume-to-weight equivalent for frozen peas is 1 cup = 3.5 ounces. This equivalent is written with cups in the denominator so the cups will cancel each other. 10 c 3.5 oz 10 3.5 oz × = × 1 1c 1 1

The numerators of each fraction and denominators of each fraction are then multiplied by each other. Then, the numerator is divided by the denominator to obtain the final answer. 10 × 3.5 oz 35 oz = = 35 oz 1× 1 1

Volume-to-weight equivalents can also be used to convert weight measurements to volume measurements. Consider the example of a recipe that requires 24 ounces of fresh blueberries. If the blueberries are only available by the pint, how many pints should be ordered? To answer this question, 24 ounces of blueberries is converted to pints. See Figure 4-6.

Converting Between Volume and Weight Measurements Example: A recipe requires 24 ounces of fresh blueberries and fresh blueberries are purchased in 1-pint containers. How many pints of blueberries should be ordered? ORIGINAL MEASUREMENT

Tip: 1 cup of fresh blueberries weighs 7 ounces.

24 oz 1

1. Write the original measurements as a fraction.

TO CONVERT OUNCES TO CUPS

2. Identify the equivalents between the original measurement and the desired measurement and write as fraction with the original measurement unit in the denominator. 3. Set up a multiplication calculation with the original measurement and the equivalents. Cancel the matching units in the numerators and denominators of the calculation.

1 c and 7 oz

1 pt 2c

1 pt 24 oz 1c × × 2c 1 7 oz

TO CONVERT CUPS TO PINTS

CANCEL MATCHING UNITS

4. Multiply the resulting fractions.

1 1 pt 24 24 pt × × = 7 2 1 14

5. Divide the numerator by the denominator to obtain the final answer. Answer:

24 pt ÷ 14 = 1.7

Since 1.7 pints are required, 2 pints should be ordered.

Figure 4-6. Weight measurements can be converted to volume measurements using approximate volume-to-weight equivalents.

Chapter 4 — Conver ting Measurements and Scaling Recipes

105

Using a Kitchen Calculator

A kitchen calculator can be used to quickly convert units of measure, scale recipes, and alter the number of servings for a recipe. See Figure 4-7. However, it is important to be able to mentally estimate answers to all conversion and scaling calculations even when a calculator is used. Otherwise, any error made by inputting an incorrect number or unit of measure or by pushing an incorrect key on the calculator keypad can result in one or more wrong answers. Kitchen Calculator Functions

Calculated Industries ®

Figure 4-7. A kitchen calculator can be used to quickly convert units of measure, scale recipes, and alter the number of servings for a recipe.

It is also important to remember that a calculator cannot be used to covert volume to weight nor weight to volume because of differences in density. Ounces can be used to measure both volume and weight, but with very different results. Ounces of liquids are typically measured by volume, but ounces of solids are best measured by weight. If a recipe lists 6 ounces of grated cheese, it means 6 ounces by weight. If grated cheese were poured into a measuring cup to the 6-ounce mark, the cheese would only weigh about 3 ounces. Once math concepts are understood in terms of when and how they are applied, a kitchen calculator can be an efficient tool.

106

CULINARY MATH PRINCIPLES AND APPLICATIONS

4-1

Checkpoint

1. Define cancelling. ________________________________________________________________________________ 2. Convert 6 cups to quarts. ________________________________________________________________________________ 3. Convert 4.25 kilograms to grams. ________________________________________________________________________________ 4. Convert 10 cups to liters and round answer to the tenths place. (Tip: 1 qt = 0.95 L ) ________________________________________________________________________________ 5. Why would it be important to distinguish between chopped pecans and whole pecans when looking up a volume-to-weight equivalent for pecans? ________________________________________________________________________________ ________________________________________________________________________________ 6. Why is it important to estimate calculations before using a kitchen calculator? ________________________________________________________________________________ ________________________________________________________________________________

Section 4-2 SCALING RECIPES

Converting measurements is often done when scaling recipes. Scaling is the process of calculating new amounts for each ingredient in a recipe when the total amount of food the recipe makes is changed. For example, a recipe that serves 4 people may be scaled for use in a restaurant that plans to make 50 servings of the recipe. Similarly, a recipe used by a banquet hall that normally serves 100 people may need to be scaled to make only 12 servings for a small party. A recipe may also need to be scaled based on the availability of one of the ingredients. For example, a recipe may require 20 pounds of ground beef but only 15 pounds of ground beef are available. A foodservice employee needs to know how to adjust all of the other ingredient amounts in a recipe to account for the available amount of a key ingredient. Foodservice employees not only need to know how to calculate new ingredient amounts when recipes are scaled, but also need to understand how scaling can affect other elements of a recipe. For example, depending on how significantly the recipe is scaled, the units of measure used for some ingredients may need to be converted to make measuring the ingredients more practical. In addition, cooking times or temperatures

C h a p t e r 4 — C o n v e r t i n g M e a s u r e m e n t s a n d S c a l i n g R e c i p e s

107

may need to be adjusted, or cooking equipment of a different size may be required. A well-written recipe will contain all of the information that needs to be considered when a recipe is scaled. Standardized Recipe Elements

The exact look and format of a standardized recipe will vary from one foodservice operation to another. However, most standardized recipes usually contain the following common elements. See Figure 4-8.

Standardized Recipe Elements

Yield: 10 Servings

Meatloaf

Cooking Temperature: 350°F Cooking Time: 1 hour

Portion Size: 6 oz Amount

Ingredients

Procedure

1 tbsp 3 oz 4 oz 2 fl oz 2 1c 1 tbsp 1¹⁄₂ tsp 1 tsp 3 lb

vegetable oil celery, small dice onion, small dice milk eggs breadcrumbs salt black pepper thyme ground beef

1. Heat oil in small sauté pan and sauté celery and onions until tender. Allow to cool. 2. Combine remaining ingredients and mix well. 3. Form mixture into a loaf and place in a greased bread pan. 4. Bake at 350°F for about 1 hour or until a thermometer inserted in the center of the loaf registers 160°F (to allow for carryover cooking). 5. Remove from oven, cover, and let rest for 15 minutes before slicing into 6-oz portions.

Nutrition info (per serving): 465.4 calories; 64% calories from fat; 32.7 g total fat; 149.2 mg cholesterol; 911.5 mg sodium; 503.2 mg potassium; 11.7 g carbohydrates; 0.9 g fiber; 4.0 g sugar; 28.6 g protein.

Figure 4-8. Most standardized recipes include the same common elements.

• Recipe Name. The name of a recipe should be descriptive of the dish being prepared and should reﬂect the name used on the menu. • Yield. Yield is the total quantity of a food or beverage item that is made from a standardized recipe. Yields can be expressed as a count, a total volume or weight, or a number of portions. For example, 24 cookies, 3 gallons, 50 pounds, and 36 portions, 8 ounces each, are all valid recipe yields.

108

CULINARY MATH PRINCIPLES AND APPLICATIONS

• Portion Size. Portion size is the amount of a food or beverage item that is served to an individual person. Portion size is related to yield. For example, a soup recipe that yields 1 gallon can also be said to yield 16 portions of 8 ﬂuid ounces each. See Figure 4-9. • Ingredients and Procedures. The amount of each ingredient used in the recipe is listed next to the name of the ingredient. If an ingredient is to be prepared in a certain way prior to being measured, such as minced, that information is also provided. The ingredients are usually listed in the order that they are incorporated into the recipe. Procedures are listed in sequential order. • Cooking Temperature. The temperature at which food is cooked greatly affects the outcome of the final product. • Cooking Time. Cooking times provided in standardized recipes are often guidelines. Many professional cooks rely on the appearance or feel of an item and on exact measurements, such as an internal temperature checked with a thermometer, to determine when a food item is done. • Nutrition Information. While nutrition information is not required to prepare a recipe, it is important information to have for menu planning and for customer inquiries.

Yield and Portion Size

Yield = 1 gal.

Scaling Based on Yield

The most straightforward examples of scaling a recipe are doubling the yield where all the ingredient amounts are simply multiplied by 2, or halving the yield by dividing all the ingredient amounts by 2. Scaling becomes more challenging when the yield is changed by a factor that is not as simple as doubling or halving the recipe. For example, a recipe that normally yields 3 gallons may need to be scaled to yield 10 gallons. Likewise, a recipe that makes 12 portions, 6 ounces each, may need to be scaled to make 30 portions, 9 ounces each. Regardless of the reason for scaling a recipe, the scaling process starts out by calculating a scaling factor. A scaling factor is the number that each ingredient amount and the recipe yield are multiplied by in order to increase or decrease a recipe. The formula for calculating a scaling factor based on yield is as follows:

Yield = 16 portions, 8 oz each Figure 4-9. A total recipe yield of 1 gallon can also be expressed as a number of portions and a portion size.

SF = DY ÷ OY

where SF = scaling factor

Scaling Factor =

Desired Yield Original Yield

DY = desired yield OY = original yield

Chapter 4 — Conver ting Measurements and Scaling Recipes

109

Scaling Based on Count. If a cookie recipe that makes 24 cookies is scaled to make 84 cookies, the scaling factor is calculated by dividing the desired yield (84 cookies) by the original yield (24 cookies). See Figure 4-10. SF = DY ÷ OY SF = 84 cookies ÷ 24 cookies SF = 3.5 Calculating Scaling Factors Scaling Factor = Type of Yield

Desired Yield Original Yield

Original Yield

Desired Yield

Scaling Factor

24 cookies

84 cookies

84 ÷ 24 = 3.5

8 gallons

3 gallons

3 ÷ 8 = 0.375

4 pounds

80 pounds

80 ÷ 4 = 20

12 portions, 5 oz each (12 × 5 oz = 60 oz)

30 portions, 8 oz each (30 × 8 oz = 240 oz)

240 ÷ 60 = 4

Count Yield

Volume Yield

ON ZERO

lb GROSS

TARE

OFF

NET GROSS

TARE

OFF

NET

Weight Yield

Portion Yield

Figure 4-10. When a recipe is scaled based on yield, the scaling factor is calculated by dividing the desired yield by the original yield.

Scaling Based on Volume. If a soup recipe that makes 8 gallons of soup is scaled to make 3 gallons of soup, the scaling factor is calculated by dividing the desired yield (3 gallons) by the original yield (8 gallons). SF = DY ÷ OY SF = 3 gal. ÷ 8 gal. SF = 0.375

110

CULINARY MATH PRINCIPLES AND APPLICATIONS

Scaling Based on Weight. If a potato salad recipe that makes 4 pounds of salad is scaled to make 80 pounds of salad, the scaling factor is calculated by dividing the desired yield (80 pounds) by the original yield (4 pounds). SF = DY ÷ OY SF = 80 lb ÷ 4 lb SF = 20

Scaling Based on Portion Size. If a fish recipe that makes 12 portions, 5 ounces each, is scaled to make 30 portions, 8 ounces each, the yields must first be converted to a total number of ounces. OY = 12 × 5 oz = 60 oz DY = 30 × 8 oz = 240 oz

Then the scaling factor formula can be applied. SF = DY ÷ OY SF = 240 oz ÷ 60 oz SF = 4

Scaling Based on Product Availability

In some cases, a recipe is scaled because the amount of one ingredient needs to be changed based on availability. For example, if a beef stew recipe that calls for 15 pounds of beef stew meat needs to be made with only 12 pounds of beef stew meat, the scaling factor is calculated by dividing the available ingredient amount by the original ingredient amount. SF = DY ÷ OY SF = 12 lb beef stew meat ÷ 15 lb beef stew meat SF = 0.8

Multiplying Scaling Factors

Once a scaling factor is known, every ingredient amount in the original recipe is multiplied by the scaling factor. See Figure 4-11. Using the new ingredient amounts will produce the desired yield of the scaled recipe. For example, a meatloaf recipe that normally yields 10 servings is scaled to make 80 servings. The scaling factor (based on count) is calculated first.

Paderno World Cuisine

SF = DY ÷ OY SF = 80 servings ÷ 10 servings SF = 8.0

Chapter 4 — Conver ting Measurements and Scaling Recipes

111

Multiplying Measurements by a Scaling Factor Meatloaf Recipe Scaled from 10 Servings to 80 Servings Scaling Factor = 80 ÷ 10 = 8 Yield = 10 Servings Amount and Ingredient

Scaling factor ×8=

1 tbsp vegetable oil

1 tbsp × 8 = 8 tbsp:

3 oz × 8 = 24 oz:

4 oz × 8 = 32 oz:

2 fl oz × 8 = 16 fl oz:

2 eggs × 8 = 16 1 c breadcrumbs 1 c × 8 = 8 c:

1 tbsp × 8 = 8 tbsp:

1¹⁄₂ tsp × 8 = 12 tsp:

eggs 2 qt breadcrumbs

2 qt

¹⁄₂ c salt =

8c = 16

3 lb × 8 = 24

¹⁄₂ c

4 tbsp black pepper

4 tbsp

4 tbsp thyme

1 tbsp 12 tbsp 12 tsp × = = 3 tsp 3 1

3 lb ground beef

1 pt

16 eggs, beaten

1 tbsp 12 tbsp 12 tsp × = = 3 tsp 3 1

1¹⁄₂ tsp thyme

2 lb

1 pt milk

8 tbsp 1 fl oz 1c × × 1 2 tbsp 8 fl oz

1¹⁄₂ tsp black pepper

2 lb onion, small dice

1 qt 8c 1 pt 8 qt × × = = 2 pt 1 2c 4

1 tbsp salt

1 lb 8 oz

16 fl oz 1c 16 pt 1 pt = × × = 1 8 fl oz 16 2c

2 eggs, beaten

¹⁄₂ c

1 lb 8 oz celery, small dice

1 lb 32 lb 32 oz × = = 16 oz 16 1

2 fl oz milk

¹⁄₂ c vegetable oil

24 lb 1 lb 24 oz × = = 1.5 lb = 1¹⁄₂ lb = 16 16 oz 1

4 oz onion, small dice

Amount and Ingredient

8 tbsp 1 fl oz 8c 1c × × = = 1 2 tbsp 16 8 fl oz

3 oz celery, small dice

Yield = 80 Servings

4 tbsp

24 lb ground beef

Figure 4-11. When recipe ingredients are multiplied by a scaling factor, it may be necessary to adjust the new measurements to a different unit of measure.

112

CULINARY MATH PRINCIPLES AND APPLICATIONS

Then, the new amount of each ingredient is calculated using the following formula: NA = OA × SF

New Amount = Original Amount × Scaling Factor

where NA = new amount OA = original amount SF = scaling factor

For example, the original meatloaf recipe requires 3 pounds of ground beef. The new amount of ground beef required is calculated as follows: NA = OA × SF NA = 3 lb × 8.0 NA = 24 lb

The new amounts for the remaining ingredients are then calculated using the same formula. Note: It may be necessary to convert some of the new ingredient amounts to a different unit of measure to make measuring the ingredients more efficient. In general, it is most efficient to measure ingredients using the largest appropriate unit of measure. For example, the original meatloaf recipe in Figure 4-10 calls for 1 tablespoon of vegetable oil. The new amount based on a scaling factor of 8 is calculated as follows: NA = OA × SF NA = 1 tbsp × 8.0 NA = 8 tbsp

However, measuring 8 tablespoons individually is time consuming. Instead, 8 tablespoons need to be converted to a larger unit of measure such as ounces. Measuring 4 ﬂuid ounces (or ¹⁄₂ cup) is more efficient than measuring 8 tablespoons. 8 tbsp 1

1 fl oz 2 tbsp

8 × 1 fl oz 1×2

8 fl oz 2

Barilla America, Inc.

= 8 fl oz ÷ 2 = 4 fl oz (¹⁄₂ ¹⁄₂ c)

Additional Scaling Considerations

When recipes are scaled, additional considerations must be taken into account before actually preparing the recipe. Addressing these considerations will help to ensure that the final product is the same quality as the original recipe. • Adjusting Measurements. If a new measurement is calculated that is not easily measured, such as 3.7 cups, the measurement will need to be adjusted to make measuring more practical. However, to avoid affecting the final result, the amount should only be adjusted slightly to ensure a quality product. For example, 3.7 cups should only be adjusted to 3³⁄₄ cups (3.75 cups).

Chapter 4 — Conver ting Measurements and Scaling Recipes

113

• Adjusting Cooking Temperature. In certain circumstances, such as when a recipe yield is significantly decreased, it may be necessary to reduce the cooking temperature to keep food from drying out. • Adjusting Cooking Time. The cooking time for a recipe may need to be increased or decreased. For example, if a larger roast is used for a recipe, a longer cooking time will be required. Likewise, if a cake recipe that makes cake layers is scaled to make one sheet cake, the thinner sheet of cake may cook faster than the thicker cake layers. 4-2

Checkpoint

1. List the elements found in most standardized recipes. ________________________________________________________________________________ ________________________________________________________________________________ 2. What is the yield of a recipe in quarts that makes 8 portions, 4 fluid ounces each? ________________________________________________________________________________ 3. If a standardized recipe that yields 2 quarts of soup is scaled to yield 2 gallons, what is the scaling factor? ________________________________________________________________________________ ________________________________________________________________________________ 4. If a standardized recipe for stew that yields 20 portions, 6 ounces each, is scaled to yield 10 portions, 8 ounces each, what is the scaling factor? ________________________________________________________________________________ ________________________________________________________________________________ 5. If a standardized recipe for chicken pot pie calls for 10 pounds of cooked chicken meat and is scaled to use 14 pounds of available cooked chicken meat, what is the scaling factor? ________________________________________________________________________________ ________________________________________________________________________________ 6. If a standardized recipe calls for 3 ounces of Cheddar cheese and the recipe is scaled by a scaling factor of 16, how many pounds of cheese are required? ________________________________________________________________________________ ________________________________________________________________________________ 7. How should a scaled measurement be changed to make measuring more practical? ________________________________________________________________________________ ________________________________________________________________________________

114

CULINARY MATH PRINCIPLES AND APPLICATIONS

Math Exercises

Work each problem in the space provided. Write the ﬁnal answer on the blank provided. Round any decimal answers to the hundredths places. Leaf icon indicates a math problem with a sustainability focus.

Example:

64 portions

If a soup recipe yields 3 gallons, how many 6-fluid-ounce portions will the recipe make? (Tip: 1 gal. = 128 fl oz )

3 gal. × 128 fl oz = 1 1 gal. 384 fl oz , then 384 fl oz × 1 portion = 384 portions = 64 portions 6 fl oz 6 1

1. How many 1-cup servings are in a lemonade recipe that yields 10 gallons?

2. If a soup recipe yields 20 gallons, how many 5-fluid-ounce portions will the recipe make? (Tip: 1 gal. = 128 fl oz)

3. How many 15-ounce jumbo chocolate chip cookies can be prepared from 75 pounds of cookie dough?

Chapter 4 — Conver ting Measurements and Scaling Recipes

115

Math Exercises

�� 4. If a stir-fry recipe requires ½ cup of teriyaki sauce per serving, how many servings of stir-fry can be made from 3 quarts of teriyaki sauce?

�� 5. If a chowder recipe yields 50 portions, 100 milliliters each, what is the total yield of the recipe in liters?

�� 6. If 25 milliliters of extra-virgin olive oil is drizzled over finished pasta dishes, how many pasta dishes can be finished from a 3-liter container of extra-virgin olive oil?

�� 7. How many 12-ounce bags of frozen peaches are needed to make peach sorbet that calls for 3 pints of frozen peaches. (Tip: 1 c of frozen peaches weighs about 6 oz.)

�� 8. What is the equivalent of 5 teaspoons of baking soda in ounces?

116

CULINARY MATH PRINCIPLES AND APPLICATIONS

Math Exercises

�� 9. How many grams of sugar are in a 4-pound bag of sugar? (Tip: 1 lb = 454 g)

�� 10. If a chef prepares 10 ounces of a poultry seasoning mix, how many grams of the seasoning mix has been prepared? (Tip: 1 oz = 28.4 g)

�� 11. A produce stand where fresh items are brought in daily uses day-old spinach and overripe bananas in their signature green smoothie recipe. If one serving of the green smoothie is 300 milliliters, what is one serving of the smoothie in cups? (Tip: 1 c = 236.6 mL. Round answer to one decimal place.)

�� 12. If a salad dressing recipe calls for 3.5 liters of olive oil, is 4 quarts of olive oil enough to make the salad dressing? (Tip: 1 qt = 0.95 L)

�� 13. If a meatball recipe calls for 10 pounds of ground beef, is 5 kilograms of ground beef enough to make the meatballs? (Tip: 1 kg = 2.2 lb)

C h a p t e r 4 — C o n v e r t i n g M e a s u r e m e n t s a n d S c a l i n g R e c i p e s

117

Math Exercises

�� 14. If 20 liters of lemon juice are needed and one case of lemons yields 4 quarts of lemon juice, how many cases of lemons are required? (Tip:1 qt = 0.95 L)

�� 15. How many ounces of cornstarch are there in a box containing 300 grams of cornstarch? (Tip: 1 oz = 28.4 g)

�� 16. Trimmed produce leaves are saved for composting and used for the flower beds in front of a deli. If 4.5 pounds of leaves are trimmed from produce every week, how many kilograms of trimmed leaves will be composted in a year? (Tip: 1 lb = 0.454 kg)

�� 17. If a brownie recipe yields 36 brownies, what scaling factor is needed to scale the recipe to yield 396 brownies?

�� 18. If a recipe yields 2 pounds of quinoa-kale salad, what scaling factor would be used to make 15 pounds of quinoa-kale salad?

118

CULINARY MATH PRINCIPLES AND APPLICATIONS

Math Exercises

�� 19. After picking apples at a local orchard, the owner of a bakery adds apple fritters to the menu. At the end of the day, 20 apple fritters are left to repurpose into bread pudding. If 6 fritters make one pan of bread pudding, what is the scaling factor that the other ingredients need to be multiplied by in order to use the 20 fritters for bread pudding? (Show as a mixed number.)

�� 20. If a tiramisu recipe yields 12 servings, what scaling factor would be used to make 156 servings?

�� 21. If a recipe yields 72 mini-muffins, what scaling factor would be used to make 45 mini-muffins?

�� 22. A chef with a nose-to-tail cooking approach purchases whole turkeys since it is cost-effective and helps eliminate food waste. The chef uses the bones for stock, various parts for gravy, and different cuts for entrées, including 87 pot pies. If the recipe for turkey pot pie yields 116 pot pies, what scaling factor would be used to make 87 turkey pot pies?

C h a p t e r 4 — C o n v e r t i n g M e a s u r e m e n t s a n d S c a l i n g R e c i p e s

119

Math Exercises

�� 23. If a pasta sauce recipe yields 4 gallons of pasta sauce, what scaling factor is needed to scale the recipe to yield 3 quarts?

�� 24. If a bread recipe yields 12 pounds of dough, what scaling factor is needed to scale the recipe to yield 50 pounds?

�� 25. A restaurant that serves roasted cauliflower as a side dish has five cauliflower heads left over. To use the leftover cauliflower, the chef will make crispy battered cauliflower bites for an appetizer the next day. If the recipe yields 20 servings, what scaling factor would be used to yield 30 servings?

�� 26. If a chicken fajita recipe yields 20 fajitas, 3 ounces each, what scaling factor is needed to scale the recipe to yield 50 fajitas, 4 ounces each?

120

CULINARY MATH PRINCIPLES AND APPLICATIONS

Math Exercises

�� 27. If a kombucha tea recipe yields 60 servings, 8 fluid ounces each, what scaling factor is needed to scale the recipe to yield 90 servings, 10 fluid ounces each?

�� 28. If a cream of asparagus soup recipe normally calls for 12 kilograms of asparagus, but the chef wants to use 18 kilograms of asparagus, what is the scaling factor that the other ingredients need to be multiplied by?

�� 29. A banquet facility where leftover food was a problem reduced waste and expenses by modifying and testing standardized recipes to ensure portion control. If their new minestrone soup recipe calls for 6-ounce portions, what scaling factor should be used to prepare 180 portions if the original recipe yielded 50 portions?

�� 30. To produce 12 pounds of egg noodles, 32 large eggs are required. What is the scaling factor that the other ingredients need to be multiplied by if only 24 large eggs are available?

C h a p t e r 4 — C o n v e r t i n g M e a s u r e m e n t s a n d S c a l i n g R e c i p e s

121

Math Exercises

�� 31. Instead of discarding 6 pounds of fresh carrots that were accidentally frozen and are no longer crisp, the chef will use them in a vegetable stock. If the stock recipe calls for 12 ounces of carrots to yield 1 gallon, what scaling factor should be used to prepare stock from the 6 pounds of carrots?

�� 32. If a smoothie recipe calls for 8 pints of mango juice but only 10 cups of mango juice are available, what is the scaling factor the other ingredients in the recipe need to be multiplied by?

�� 33. A café has leftover watermelon after a catered luncheon. To ensure the watermelon is used, the café features it in a watermelon-basil lemonade. If the original lemonade recipe yields 4½ cups, what scaling factor should be used to yield 4 gallons of the watermelon-basil lemonade?

�� 34. A donut recipe calls for 3 pounds of pastry flour and yields 60 donuts. If the recipe is scaled to make 200 donuts, how many pounds of pastry flour are required?

122

CULINARY MATH PRINCIPLES AND APPLICATIONS

Math Exercises

�� 35. If 1 pound of raw spaghetti noodles makes 5 cups of cooked spaghetti noodles, how many pounds of raw spaghetti noodles would be needed to make 30 cups of cooked noodles?

�� 36. How many gallons of bolognaise sauce can be made using 4.75 pounds of ground chuck if the original recipe yields 1 gallon and calls for 2.5 pounds of ground chuck?

�� 37. A restaurant with an on-site garden uses leftover coffee grounds as a medium for growing mushrooms. If 5½ pounds of coffee grounds grow enough mushroom spores to yield 3 pounds of mushrooms, how many pounds of coffee grounds are needed to yield 20 pounds of mushrooms? (Show as a mixed number.)

�� 38. A chili recipe calls for 12 ounces of finely diced onions and normally yields 2 gallons. If the recipe is scaled to make 2 quarts, how many ounces of finely diced onions are required?

C h a p t e r 4 — C o n v e r t i n g M e a s u r e m e n t s a n d S c a l i n g R e c i p e s

123

Math Exercises

�� 39. A puff pastry recipe calls for 18 ounces of butter and yields 4.5 pounds. How many ounces of butter are required to make 1.5 pounds of puff pastry?

�� 40. If 1 pint of cherry tomatoes weighs 300 grams, how many pints of cherry tomatoes are required for a recipe that calls for 6 kilograms of cherry tomatoes?

�� 41. A jalapeño Cheddar cornbread recipe that yields 9 servings requires 4 ounces of butter. If the recipe is scaled to yield 198 servings, how many pounds of butter are required?

�� 42. A sweet and sour pork recipe calls for 10 pounds of pork tenderloin, yielding 30 servings, 8 ounces each. If the recipe is scaled to yield 50 servings, 10 ounces each, how many pounds of pork tenderloin are required?

124

CULINARY MATH PRINCIPLES AND APPLICATIONS

Math Exercises

�� 43. If 15 pounds of ground bison meat yields 40 bison burger patties, 6 ounces each, how many pounds of ground bison meat are needed if the recipe is scaled to yield 90 bison burger patties, 8 ounces each?

�� 44. A recipe for soft pretzels calls for 2 teaspoons of salt and yields 36 pretzels. If the recipe is scaled to yield 324 pretzels, how many tablespoons of salt are required?

�� 45. A crab cake recipe calls for 2 ounces of diced celery and yields 20 crab cakes. If the recipe is scaled to make 320 crab cakes, how many pounds of diced celery are required?

�� 46. A gumbo recipe calls for 4 quarts of cooked rice and yields 80 servings, 6 ounces each. If the recipe is scaled to yield 12 servings, 5 ounces each, how many cups of cooked rice are required?

C h a p t e r 4 — C o n v e r t i n g M e a s u r e m e n t s a n d S c a l i n g R e c i p e s

125

Math Exercises

�� 47. If a chicken enchilada recipe calls for 2 pounds of shredded Cheddar cheese and yields 32 enchiladas, how many ounces of shredded Cheddar cheese are needed to yield 8 enchiladas?

�� 48. A restaurant with seasonal demand scales recipes down during slower months to reduce waste and costs. If the restaurant’s chicken marsala uses 6 pounds of cremini mushrooms to yield 48 portions, how many pounds and ounces of cremini mushrooms are needed to yield 12 portions?

�� 49. If a fruit tart recipe calls for 30 ounces of apricot filling and yields 24 tarts, how many kilograms of apricot filling would be required to yield 240 tarts? (Tip: 1 oz = 28.4 g)

�� 50. If a seafood bisque recipe calls for 1 pint of sherry and yields 4 gallons, how many liters of sherry would be required to yield 12 gallons of the bisque? (Tip: 1 L = 1.06 qt)

126

CULINARY MATH PRINCIPLES AND APPLICATIONS