2203.1 Basic Culinary Mathamatics

Written by Black Belt Chef CAIBOK on August 26, 2024. Posted in 2200 Cooking Brown Belt.

Math is important in culinary arts, affecting every aspect of kitchen operations from recipe formulation to portion control and scaling. Mastery of basic math—addition, subtraction, multiplication, and division—is crucial for chefs to ensure accuracy and efficiency in their culinary practices.

Helpful Resource

https://www.thecalculatorsite.com/cooking/cooking-calculator.php

Essential Arithmetic Skills

Addition and Subtraction: These basic operations are used daily for calculating ingredient quantities, adjusting recipes, and managing inventory. Addition helps in compiling total costs and combining ingredient measurements, while subtraction is used to determine the remaining ingredients or adjust stock levels.
Multiplication and Division: These are critical when altering recipes to serve more or fewer people than originally intended. Multiplication allows chefs to increase ingredient quantities in proportion, and division is used to decrease them accordingly without losing flavor balance.
Fractions and Decimals: Many culinary measurements are given in fractions (e.g., 1/2 cup, 3/4 tsp) or decimals (0.5 liters, 0.25 kilograms). Understanding how to convert these measurements and use them in calculations is essential for precision in recipe creation.
Percentage Calculations: Used for determining food costs, calculating profit margins, and modifying ingredient quantities based on weight or volume percentages.
Ratio and Proportion: Fundamental for maintaining the integrity of a dish when scaling recipes up or down, ensuring that all ingredients are increased or decreased in a cohesive manner.

Learning Arithmetic for Culinary Use

Developing strong arithmetic skills requires practice and application. Here are ways culinary professionals can enhance their math abilities:

Formal Education: Culinary schools typically include coursework in kitchen math as part of their curriculum. These courses focus on practical applications of arithmetic in a culinary setting.
Online Courses and Workshops: Many platforms offer specific courses on culinary math. Websites like Coursera, Khan Academy, or Udemy provide beginner to advanced math courses that can be applied in kitchen settings.
Practice in Daily Operations: Regularly applying math skills in everyday kitchen tasks is one of the best ways to improve. Calculating costs, adjusting recipes, or scaling dishes for service are practical ways to enhance these skills.
Tutorials and Guides: Numerous online tutorials explain and demonstrate culinary math concepts. YouTube channels such as [America’s Test Kitchen](https://www.youtube.com/user/americastestkitchen) and [ChefSteps](https://www.youtube.com/user/chefsteps) offer videos that include detailed explanations of math used in their recipes.

Fractions and Decimals

A fraction is a way of showing a relation between a “PART” and a “WHOLE”

For example: If you cut a pie into 4 equal pieces…
- And you ate 1 piece…
  - Then you ate ¼ of the pie.
    - The top number represents the “PART” of the pie you ate (1)
    - The bottom number represents how many pieces were in the “WHOLE” Pie (4)

The part is over the whole

1/2 would represent 1 piece of a pie that is cut into 2 equal pieces
2/8 would represent 2 pieces of a pie cut into 8 equal pieces

Equal Fractions

Fractions can be different… but equal

1/2 = 2/4 = 4/8

Imagine you have a chocolate bar, and you break it into 2 big pieces. If you take one of those big pieces, you have half of the chocolate bar, right? We write that as 1/2.

Now, let’s imagine a different chocolate bar, but this time you break it into 4 smaller pieces instead. If you take 2 of those smaller pieces, it still looks like you have half of the chocolate bar, just like before. We write this as 2/4.

What if you break another chocolate bar into 8 even smaller pieces? Taking 4 of these tiny pieces is still just like having half the bar. That’s 4/8.

So, 1/2, 2/4, and 4/8 all mean the same thing – they are all ways of showing that you have half of something, even though the number of pieces can be different. This is what we mean when we say fractions can look different but be equal.

Reducing Fractions

Let’s say you have some candy bars divided into pieces, and you want to make sure you have the smallest number of pieces that still shows the same amount of candy bar you started with. This is like making a big fraction smaller or “reducing” it.

For example, if you have a candy bar split into 4 pieces and you have 2 of those pieces, we write it as 2/4. But, you can make it simpler! If you can divide the top number (2) and the bottom number (4) by the same number, like 2, you make the fraction smaller but still keep the same amount of candy bar.

So, if you take 2/4 and divide both the top and the bottom by 2:

Divide the top 2 by 2, and you get 1.
Divide the bottom 4 by 2, and you get 2.
Now, it looks like 1/2, which is simpler but still means the same amount of candy bar!

Sometimes, you can tell what number to divide by:

If both numbers in the fraction end in even numbers (like 2, 4, 6, 8, 0), you can divide them by 2 to make the fraction smaller.
If both numbers end in 5 or 0, you can divide them by 5.

For instance, if you have 5/10, both numbers end in 5 and 0, so you can divide them by 5:

Divide the top 5 by 5, and you get 1.
Divide the bottom 10 by 5, and you get 2.

Now, it looks like 1/2, and it’s simpler!

So, reducing fractions is like finding the easiest way to show the same amount of something you have, using smaller numbers.

Mixed Numbers and Improper Fractions

Imagine you have some cookies. If you have a whole cookie and a half of another cookie, that’s what we call a mixed number. A mixed number has a whole part (like the whole cookie) and a little extra piece (like the half cookie). We write this as 1 1/2.

Now, think about a different way to look at cookies. If you had three halves of cookies, you could say you have 3/2. This is called an improper fraction because the top number (how many pieces you have) is bigger than the bottom number (how many pieces make a whole). So, 3/2 means you have more than one whole cookie because two halves make one whole cookie, and you have one extra half.

So, a mixed number like 1 1/2 is just another way of saying an improper fraction like 3/2. It’s all about different ways of showing how many cookies or parts of cookies you have!

To change a mixed number to an equivalent improper fraction

Think about your mixed number like a special kind of math problem where you have whole things and pieces of things. For example, if you have 1 and a half pies, it’s like saying you have 1 whole pie plus half of another pie.

Here’s how you can think of changing that into just a fraction, where it’s all about the pieces, not whole pies anymore:

You start with your whole pie. We call this the whole number. In your example, that’s the 1 in 1 and a half.
Next, you have your half pie. This half part is a fraction, and it has a top number and a bottom number. The bottom number (2) tells us it’s a half because the pie is cut into 2 pieces. We call this number the denominator because it names how many pieces the whole pie is divided into.
To figure out how many pieces you really have, first, think of your whole pie as pieces too. Multiply your whole pies (1) by how many pieces are in a pie (2 pieces because of the denominator). So, 1 pie times 2 pieces is 2 pieces.
Now, add the extra half pie piece. That’s just adding the top number of the fraction, which is 1 (we call this the numerator).
So, you add your 2 pieces (from step 3) and your 1 piece (the numerator) together: 2 + 1 = 3.
You don’t change the bottom number; it stays 2 because each pie is still cut into 2 pieces.

So, 1 and a half pies (1 1/2) is really the same as saying 3 halves of a pie (3/2) when you think about all of it in terms of pieces. This is what we call an improper fraction because it tells you have more than one whole pie in pieces!

Fractions to Decimals

The fraction sign means DIVIDE… it is telling you to divide the top number by the bottom number
- Example: 1/2 tells you to divide 1 by 2
  - On a calculator you put in the top number first … 1
  - Then push the divide sign … ÷
  - Then put in the bottom number … 2
    - The answer will always be the decimal form of that fraction… .5

Decimal Place Names

To the nearest 10th means to use only 1 number after the decimal point
- 1/2 = .5 or 1/3 = .3
To the nearest 100th means to use 2 numbers after the decimal point
- 1/2 = .50 or 1/3 = .33
To the nearest 1000th means to use 3 numbers after the decimal point
- 1/2 = .500 or 1/3 = .333

To change a decimal into a percentage

Let’s think about fractions like a way of sharing something. When you see a fraction like 1/2, it’s like saying you have one cookie and you want to split it into 2 equal parts. Each part is a piece of the whole cookie.

To understand how much one piece is compared to the whole cookie, you do a simple division:

The top number of the fraction (1 in this case) tells you how many pieces you have.
The bottom number (2 here) tells you into how many pieces the whole cookie is divided.

Here’s how you turn that fraction into a decimal:

If you have a calculator, you can type in the top number (1), which is the piece of the cookie you’re looking at.
Then you press the divide button (÷) because the fraction line means division.
After that, you type in the bottom number (2), which is how many pieces the whole cookie is divided into.
When you press the equals button, the calculator shows you a decimal (0.5), which means each piece is half (0.5) of the whole cookie.

So, the fraction 1/2 turned into a decimal becomes 0.5, showing that one piece is half of the whole thing. It’s just a way of showing the same thing in a different form, like using different words to tell the same story!

Multiplying Fractions

To multiply fractions you simply multiply the numbers straight across

1/2 X 2/4 = 2/8

If you have a mixed number you must first change it to an improper fraction before you multiply

Dividing Fractions

To divide fractions, we do something a little funny—we flip the second fraction upside down and then multiply. This is how you can do it:

Take the fraction that comes after the division sign and flip it upside down.
- Example: If you have 2/4 ÷ 8/3, you flip 8/3 to get 3/8.

Change the division sign (÷) to a multiplication sign (×).
- Now, your equation should look like this: 2/4 × 3/8.

Multiply the top numbers (numerators) together and the bottom numbers (denominators) together.
- Multiply the tops: 2 × 3 = 6.
- Multiply the bottoms: 4 × 8 = 32.
- So, you write your new fraction as 6/32.

Simplify the fraction if you can.
- You can divide both the top and the bottom by 2.
- 6 ÷ 2 = 3 and 32 ÷ 2 = 16.
- Your simplified fraction is 3/16.

This process is like flipping one pizza upside down to see how many pieces fit into the pieces of another pizza.

Remember if you have a mixed number you must first change it to an improper fraction before you multiply

Adding and Subtracting Fractions

To add or subtract fractions the bottom numbers must be the same (Called a common denominator)

To find a common denominator … you must find a number that both the denominators will divide into evenly
- Sometimes the higher of the two denominators can be used as a common denominator
  - Example: 1/2 + 7/8 = 4/8 + 7/8 = 11/8

Sometimes a new number has to be used as a common denominator

For example:

1/4 + 2/5 = (1 x 5/20) + (2 x 4/20) = 5/20 + 8/20 = 13/20

The term percent means “part of a hundred”. The use of percentages to express a rate is common practice in the food-service industry.

Example: If 34 percent of the customers in a restaurant favor nutritious entrées…

Percentages

The term percent means “part of a hundred”. The use of percentages to express a rate is common practice in the food-service industry. For example, food and beverage costs, labor costs, operating costs, fixed costs, and profits are usually all stated as a percentage to establish standards of control.

To indicate that any number is a percentage, the number must be accompanied by %.

Converting Decimals to Percentages

To convert any decimal to a percentage, multiply the number by 100 and add a percent sign.
A shortcut would be to simply move the decimal point two places to the right and add a percentage sign.

Converting Percentages to Decimals

To convert percentages to decimal form, divide by 100 and drop the percent sign.
A shortcut would be to simply move the decimal point two places to the left and drop the percent sign.

Chefs may use percentages to calculate and apply a yield percentage or food cost percentage.

Helpful Hints When Working with Percentages

First determine what you are looking for—part, whole, or percentage.
The number or word that follows the word “of” is usually the whole number, the word is usually connected to the part.
The percentage will always be identified with either the symbol % or the word percent.
The part will usually be less than the whole.
Now it’s time to put this knowledge to use.

Example Problem

The bakeshop has an order for 10 dozen rolls. Forty rolls have been baked. What percentage of the rolls still have to be baked?

1 dozen = 12 rolls
10 dozen rolls = 120 rolls
40 rolls have been baked
80 rolls still need to be baked

Percent = Part/Whole

To find the percentage:
- 1. Find the decimal equivalent of:
  - a) 9.99%
  - b) 0.5%
- 2. Change the following to a percentage:
  - a) 0.0125
  - b) 2/5
- 3. If you order 300 lobster tails and you use 32 percent, how many do you have left?
- 4. You have 60 percent of a bottle of raspberry syrup remaining. If 10 ounces were used, how many ounces did the bottle originally hold?
- 5. Mr. Smith purchased $125.00 worth of spices and herbs. Because this was such a large order, the supplier charged Mr. Smith only $95.00. What percent discount did Mr. Smith receive?

Answers 1. a) .0999 b) .005 2. a) 999% b) 40% 3. 204 4. 25 ounces 5. 24%

The Bridge Method

The bridge method is the “recipe” for converting from one unit of measure to another. It can be used to convert ounces to pounds, quarts to pints, tablespoons to cups, grams to ounces, volume to weight, and so on.

Example: teaspoons to cups
- Step 1: If the unit of measurement that you are converting is a whole number, put it over 1. If it is a fraction, first convert it to a decimal and then put it over 1.
- Step 2: Place a multiplication sign next to this.
- Step 3: Draw another fraction line.
- Step 4: Put in the units of measurement. The unit of measurement to be removed is written on the bottom. The unit of measurement to be converted to is written on top. The units diagonal to each other (that are the same) cancel each other out.
- Step 5: Enter the numbers to create the equivalency.
- Step 6: Multiply straight across.
- Step 7: Reduce the resulting fraction (if needed).

Convert the following using the bridge method

1. 5 gallons = ? qt 2. 78 cups = ? quarts 3. 18 tsp = ? cups 4. 2 pecks = ? gal 5. 9 tbsp = ? tsp

Answers 1. 20 qt 2. 19.5 quarts 3. .375 cups 4. 4 gal 5. 27 tsp

This conversion provides detailed steps and examples for performing unit conversions using the bridge method, critical in culinary measurements and recipes.

Resources for Further Learning

For those looking to expand their knowledge and proficiency in culinary arithmetic, the following resources can be particularly useful:

YouTube: Channels like [Khan Academy](https://www.youtube.com/user/khanacademy) provide free tutorials on basic and advanced math concepts.
Books: Books such as “Ratio: The Simple Codes Behind the Craft of Everyday Cooking” by Michael Ruhlman give insight into how ratios can simplify kitchen practices.