# Chapter 2 Numbers, symbols of operations, and the mill.

OBJECTIVES

At the completion of this chapter, the student should be able to:

2. Identify the symbols for the four basic operations of addition, subtraction, multiplication, and division.

3. Identify the mill and use it in solving problems.

4. Understand the reasoning for rounding up in a food service operation.

KEY WORDS

whole numbers

unit

numerals

digits

period

symbols of operations

cent

mill

rounding up

The information presented in this chapter is intended to refresh your knowledge of basic mathematical terms and principles that you learned in your early school years but may not have put into practice often enough to retain. These terms and principles are important to all math functions. They will be used throughout the book, and they need to be fully understood for you to increase your math skills and function effectively in the workplace.

The food service industry, in the 21st century, will continue to require employees to possess math skills. The industry is extremely competitive, and controlling costs (e.g., food, beverage, labor, etc.) is vital to the survival of any business venture.

Math skills start with the understanding of terms such as whole numbers, units, numerals, and digits.

You may feel you fully understand all these terms, but it is still important that you study this chapter, if only to adjust your attitude to a more enthusiastic approach toward refreshing your math skills.

NUMBERS

Whole numbers are numbers such as 0, 1, 2, 3, 4, 5, b, 7, 8, and 9 that are used to represent whole units rather than fractional units. A unit is a standard quantity or amount. Units, of course, are not limited to manufactured products. A unit may be a single quantity of like products, such as a case of apple juice. Units are often established by producers or manufacturers. The unit they establish is usually a quantity that is convenient for both the consumer and producer. Some convenient and sensible units for individuals could include a quart or gallon of milk, a pound of butter, a pint or quart of strawberries, or a dozen oranges. In the food service industry, convenient and sensible units might include a 10-pound can of fruit or vegetables, a 100-pound bag of flour, or a 5-pound box of bacon. Convenient and sensible units also help a manufacturer or business keep track of inventories.

Numerals are used to represent or express numbers. For example, 8, 21, 450, II, and X are numerals, because they express numbers. The individual numbers on a clock are numerals as well.

Digits are any of the numerals that combine to form numbers. There are 10 digits, as shown in Figure 2-1, with names that you should be quite familiar with.
```Figure 2-1 Digits.

0     1   2    3    4     5   6    7    8     9
zero one two three four five six seven eight nine
```

[FIGURE 2-2 OMITTED]

Digits can be combined in various ways to produce different numbers. For example, 457 and 745 are both combinations of the digits 7, 5, and 4. The value of each digit depends on where it is placed in the combination of numbers. For example, the 4 in the number 457 is valued at 400. However, the 4 in the number 745 is valued at 40. Each place has a different name and therefore a different value, as shown in Figure 2-2.

In large groups of numbers made up of four or more digits, the digits are placed into groups of three. Each of these groups is called a period, as shown in Figure 2-2. Periods are separated with commas. (In the metric system, to be discussed later in this text, periods are separated by spaces rather than commas.) The value of each digit is determined by its position in the place value columns. In Figure 2-2, the digit 5 is used twice. When it appears in the tens place of the ones period, the 5 represents 50. When it is used in the hundreds place of the millions period, it represents 500 million. As you can see, place is very important when numbers are grouped.

In the food service industry, the billions and trillions periods are very seldom or ever required. These periods are used by big business and our government when discussing budgets and the national debt. Major restaurant chains and some popular restaurant establishments will present and use figures in the millions place, but that is usually the extent of profit or loss figures.

Commas are used to separate periods. They are used for financial records, such as profit and loss statements and balance sheets. Commas are also used when writing checks, both professionally and personally.

Readers should be aware that in many non-English-speaking countries, spaces or periods are used to separate numeric periods in place of commas. For example, an invoice from France for toothpicks may be shown as 1 500 or even 1.500 instead of 1,500.
```TIPS ... To Insure Perfect Solutions

When placing commas, start at the right, then count three places
and insert a comma.
```

A chef/owner--or, for that matter, any person--must know how to write a bank check to pay bills. For most people, daily, monthly, or weekly checks are generally written in the hundreds of dollars. But there will be times when a person must write a check in the ten thousands and maybe even in the hundred thousands. Summary Reviews 2-1 and 2-2 will allow the student to practice check-writing techniques using both numbers and words.

SUMMARY REVIEW 2-1

Rewrite the following numbers by adding commas in the correct place(s).

1. 4956 --

2. 10495 --

3. 245620425 --

4. 26495 --

5. 218873296 --

6. 48973 --

7. 210000000 --

8. 41213728 --

9. 97822732642 --

10. 8725351280 --

As stated before in this chapter, most food service professionals will have to write checks with smaller numbers, such as \$195.23. This would be written as one hundred ninety five and 231100 dollars. When writing words or numbers on a check, always start at the far left. If not, unscrupulous merchants may add an extra number or word. Figure 2-3 illustrates the correct way to write a check, while Figure 2-4 illustrates the improper way to write a check.

[FIGURE 2-3 OMITTED]

[FIGURE 2-4 OMITTED]

[FIGURE 2-5 OMITTED]

Large numbers are also expressed with the names shown in Figure 2-5. The digit 0 in the ones column is needed to hold a place and to give the other digits their proper value. The digit b in the tens place would be b, not 60, without the zero. The complete number shown in Figure 2-3 is read "eight billion nine-hundred twenty-five million four-hundred fifty-one thousand two-hundred sixty." Zeroes are not read. The number 149,000,000 is read "one hundred forty-nine million." The word "and" is not used in reading whole numbers.

REVIEW 2-2

Write out the words for the following dollar amounts. For example, \$195.23 would be written as one hundred ninety five and 231100 dollars.

1. \$1,956.12 --

2. \$20,495.25 --

3. \$35.32 --

4. \$492.49 --

5. \$52,678.52 --

6. \$63,682.63 --

7. \$781.75 --

8. \$8.88 --

9. \$92.91 --

10. \$105.16 --

SYMBOLS OF OPERATIONS

There are four basic arithmetic operations: addition, subtraction, multiplication, and division. Math symbols are used to indicate which of these four operations is required in any given transaction or arithmetic problem. The importance of math symbols can be demonstrated by selecting two numerals and setting up problems using each of the four basic math symbols. The problems appear to be similar until the symbol is added.

(a) 10 + 2/12

(b) 10 - 2/8

(c) 10 x 2/20

(d) 10/2 = 5

or 10/2 = 5

or 10/2 = 5

As you can see, the math symbol used will yield different results and dictates the direction the problem will take.

Example (a), of course, is addition, (b) is subtraction, (c) is multiplication, and (d) is division. Figure 2-b provides the names, meanings, and some examples of the symbols commonly used in the food service industry.

SUMMARY REVIEW 2-3

In the problems or statements following, the symbol of operation has been omitted. In each instance, determine the symbol that should be placed in the blank.

1. Meaning by the hundredths. --

2. Used to indicate price of each unit. --

3. Used to separate the numerator from the denominator when dealing with fractions. --

4. Indicates the beginning of a decimal fraction. --

5. A symbol placed before a monetary figure. --

6. 24 -- 15 = 360

7. 284 -- 4 = 71

8. He purchased a dozen -- \$1.99 per dozen.

9. 28 x 2 -- 56

10. A waitress is usually tipped 15 -- of the total bill.

11. 1540 -- 5 = 308

12. 1850 -- 360 = 1490

13. 2075 -- 190 = 2265

14. The food cost for the month was 38

15. The restaurant purchased six cases of sliced apples -- \$12.50 per case.

THE MILL

When dealing with monetary numbers, cent is used to represent the value of one hundredth part of a dollar. The third place to the right of the decimal is called a mill and represents the thousandth part of a dollar, or one-tenth of one cent.

When the final result of a monetary number includes a mill, it is usually rounded to a whole number of cents. To round a number to the nearest cent, the third digit (the mill) is dropped if it is less than 5. If that digit is 5 or more, another cent is added to the digit before it. For example:

\$4.626 rounded to the nearest cent is \$4.63 because 6 mills are more than 5.

\$4.623 rounded to the nearest cent is \$4.62 because 3 mills are less than 5.

\$4.625 rounded to the nearest cent is \$4.63 because the digit 5 means another cent is added to the digit before it.

The mill is an important figure in the food service industry because the production cost of an item and the cost of menu food items are figured to the mill to obtain the exact cost of the item. The exact cost is very important when figuring a menu or selling price. For example, when producing rolls, it is necessary to know that each roll may cost \$0.043 to produce, making the cost of one dozen rolls \$0.516, or \$0.52. In the case of a menu item, the manager must determine the cost of a serving before he or she can determine a selling or menu price.
```TIPS ... To Insure Perfect Solutions

Find the answer to the problem. The LAST step is rounding to
the mill.
```

SUMMARY REVIEW 2-4

1. How many mills are contained in one cent? --

2. How many mills are contained in 10 cents? --

3. How many mills are contained in \$1.00? --

4. What is the rule to follow if the mill is 4 or less? --

Five or more? --

Change the following amounts to the nearest cent using the mill.

5. \$0.045 --

6. \$0.591 --

7. \$0.058 --

8. \$0.052 --

9. \$0.073 --

10.\$0.074 --

11. \$0.012 --

12.\$0.134 --

13. \$638.514 --

14. \$8,425.793 --

15. \$542.247 --

The value of rounding up

In the food service industry, it is essential to make intelligent financial decisions in order to have a profitable business or maintain a budget in a nonprofit organization. Industry leaders often say, "Don't step over pennies to pick up nickels." Instead of stepping over pennies, pick them up and use them to make a profit or balance a budget! Those pennies that are picked up will assist in having a financially successful operation. For instance, an owner of a quick service operation selling french fries determines that each portion of fries costs 0.134 cents to produce. The owner--now that the raw food cost is determined--can set the menu price. Even though it is mathematically incorrect to round up when the hundredth place (the mill) is 4 or less, it makes sense business-wise to round up. Rounding off correctly, mathematically, would result in each portion of fries costing 13 cents. Business-wise, the quick service owner decides to round up the portion of fries to 14 cents, and sets the desired food cost percentage as 20%. As stated in Chapter 1, the formula to determine the menu price is: raw food cost divided by the desired food cost percentage. Mathematically correct, the 13-cent portion of fries divided by 20% would create a menu price of 65 cents for each portion of fries. But if the owner rounds up to the next penny (14 cents), the menu price is now determined to be 70 cents. Selling a million orders of french fries would result in an income gain of \$50,000!

Chez Sez ...

George R. Goldoff

Vice President of Food and Beverage

Beau Rivage Resort and Casino

Biloxi, Mississippi

Mr. Goldoff oversees the success of the 14 restaurants and outlets that serve food, along with the four bars and five service bars at this prestigious hotel, resort, and gaming complex. Revenue from food and beverage sales is \$75,000,000 (yes, that's right, 75 million dollars). Beau Rivage employs 275 cooks and 1,100 food and beverage employees. Among the restaurants that Mr. Goldoff is responsible for is the Port House. This restaurant has won the Best Award of Excellence from Wine Spectator magazine, is a four-diamond award winner from AAA, and has earned the prestigious Distinguished Restaurants of North America (DiRbNA) award. The Beau Rivage Resort and Casino has been named by Travel and Leisure magazine one of the top 500 hotels in the world.
```Figure 2-6 Mathematical
symbols.

Symbol   Name             Meaning                   Examples

+      plus sign        add to, or increase by    8 + 99 = 107
2 + 19 = 21
361 + 12 = 373

-      minus sign       subtract tram, take       17 - 9 = 8
away from, decrease by,   23 - 5 = 18
or less                   49 - 9 = 40

x      multiplication   multiply by, or the       2 x 12 = 24
or *    or times sign    product of                9 x 3 = 27
5 * 25 = 125

/      division sign    divided by                4/2 = 2
or /                                               27 / 9 = 3
100 / 20 = 5

-      fraction bar     separates numerator       6/3 = 2
and denominator           10/5 = 4
20/5 = 4

.      decimal point    indicates the beginning   0.321
of a decimal fraction     1.877
117.65

%      percent sign     parts per 100, by the     15%
hundredths                12%
6%

=      equal sign       the same value as, or     1 = 1
is equal to

\$      dollar sign      the symbol placed         \$12.00
before a number to
indicate that it stands
for dollars

@      at or per        used to indicate price    5 doz. doughnuts
or weight of each unit    @ \$1.15/doz.
when there is a           25 bags of potatoes
quantity of a unit        @ 10 lb./bag
100 ice cream cones
@ \$0.25 per cone
```