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MODULE 2 FOOD COSTING AND PRICING Prepared by: Prof. Rowena R. De Leon ENT 106: Pricing & Costing LESSON 1 BASIC BUSINESS MATH PRINCIPLES IN FOOD COSTING AND PRICING Prepared by: Prof. Rowena R. De Leon ENT 106: Pricing & Costing 1.1.Rounding Off Numbers At the end of the lesson, the students should be able to: 1. Apply the knowledge of place values in rounding off numbers; 2. Round of decimals and whole numbers; 3. Apply rounding off numbers I problem solving. 1.3 Rounding Off Numbers At the end of the lesson, the students should be able to: 1. Understand the concept of decimals; 2. Convert decimals to fractions and fractions to decimals.. 1.4 Rounding Off Numbers 1.2 Fractions At the end of the lesson, the students should be able to: 1. Identify the different types of fractions; 2. Simplify fractions; 3. Perform the fundamental operation with fractions. Prof. Rowena R. De Leon At the end of the lesson, the students should be able to: 1. Understand the concept of percent; 2. Convert decimal to percent and percent to decimals; and 3. Apply the knowledge in percentage in problem solving. ENT 106: Pricing & Costing 1.1 ROUNDING OFF NUMBERS Rounding off a decimal is a technique used to estimate or approximate values. Rounding is most commonly used to limit the amount of decimal places. Instead of having a long string of decimals places, or even one that goes on forever, we can approximate the value of the decimal to a specified decimal place. We can round to any place. After rounding, the digit in the place we are rounding will either stay the same, referred to as rounding down, or increase by 1, referred to as rounding up. Prof. Rowena R. De Leon When to Round Up Rounding up means that we increase the terminating digit by a value of 1 and drop off the digits to the right. If the next place beyond where we are terminating the decimal is greater than or equal to five (5, 6,7,8,9), we round up. For example, if we round 5.47 to the tenths place, it can be rounded up to 5.5. When to Round Down If the number to the right of our terminating decimal place is four less (4,3,2,1,0), we round down. This is done by leaving our last decimal place as it is given and discarding all digits to its right. For example, if we round 6.734 to the hundredths place, it can be rounded down to 6.73. ENT 106: Pricing & Costing Rounding is explained more simply in numbers in the following examples. Example 1.1: Round 4. 87315 to the nearest hundredth (or two places past the decimal point). The “7” occupies the final desired place, two places past the decimal point. 4.87315 The “3” is immediately to the right of the desired final place. Since 3 is less than 5, round down. Drop all of the numbers more than two places past the decimal point. The answer is 4.87 Prof. Rowena R. De Leon ENT 106: Pricing & Costing Rounding is explained more simply in numbers in the following examples. Example 1.1: Round 4. 87315 to the nearest tenth (or one places past the decimal point). The “8” occupies the final desired place, one places past the decimal point. 4.87315 The “7” is immediately to the right of the desired final place. Since 7 is greater than 5, round up. Drop all of the numbers more than one place past the decimal point. The answer is 4.9 Prof. Rowena R. De Leon ENT 106: Pricing & Costing Self-check #1 Direction: Round off the following numbers as indicated. 1. 15.7541 nearest hundredths 2. 469.6451 nearest tenths 3. 63.7635 nearest thousandths 4. 5,419.058 nearest tens 5. 172.54328 nearest ten thousandths 6. 9,017.53 nearest thousands 7. 8,720.127 nearest hundreds 8. 98,136.27 nearest units digit 9. 128.655 nearest hundredths 10. 561.0525 nearest thousandths Prof. Rowena R. De Leon ENT 106: Pricing & Costing 1.2 FRACTIONS A fraction is a quotient of numbers, the quantity obtained when the numerator is divided by the denominator. Each fraction consists of a denominator (bottom) and a numerator (top), representing (respectively) the number of equal parts that an object is divided into, and the number of those parts indicated for the particular fraction. Thus ¾ represents three divided by four, in decimals 0.75, as a percentage 75%. The three equal parts of the cake are 75% of the whole cake. Also, fractions are rational numbers, which means that the denominator and the numerator are integers. Prof. Rowena R. De Leon Fractions are numeric symbols of the relationship between the part and the whole. Common kitchen fractions used: 1/8, ¼, 1/3, ½, 2/3, 3/4 Fraction is part of a whole number. 3 out of 5 slices of pie could be represented by 3/5, (3 is the part, 5 is the whole amount) Also can be represented as a divisional problem 3÷5 ENT 106: Pricing & Costing Types of Fractions Proper (Common) Fraction Where the numerator is lower than denominator. For example: ½ or ¼ Mixed Number Is a whole number mixed with a fractional part Improper Fraction Where the numerator is greater than or equal to denominator. For example: 28/7, 140/70 and 28/28 Lowest Term Fraction The result of reducing a fraction so that the numerator and denominator no longer have any common factors. For example: 14 = 14 ÷ 14 = 1 28 28 14 2 Prof. Rowena R. De Leon ENT 106: Pricing & Costing Prof. Rowena R. De Leon ENT 106: Pricing & Costing Converting Fractions To convert a whole # to a fraction, simply place the whole number over 1. For Example: 5 = 5 1 Converting improper fractions to mixed numbers: Divide the numerator by the Denominator. The answer will be the whole # and the remainder (if any) will be place over the denominator of the original improper fraction to form the fractional part of the mixed number. For Example: 23 5 Prof. Rowena R. De Leon 43 5 4 5 ) 23 20 3 ENT 106: Pricing & Costing Converting Fractions To convert a mixed number to an improper fraction: (a) Multiply the whole number by the denominator; (b) Add the result to the numerator; and (c) Place the resulting number over the original denominator. For Example: 3 2 5 17 5 3x5=15+2=17 5 Prof. Rowena R. De Leon ENT 106: Pricing & Costing Addition and Subtraction of Fractions Fractions that are going to be added or subtracted together must have a common denominator. Another Example: Subtraction 3 - 1 = 9 -2 4 6 12 12 = 9–2 12 7 = 12 Prof. Rowena R. De Leon ENT 106: Pricing & Costing Multiplication of Fractions This process is done by simply: Multiply the Numerator x Numerator Multiply the denominator Denominator x Carry the numbers across for the new numerator and denominator. Alternative solution: by cancellation For Example: 2 1 x 4 = 7 x 4 3 3 5 5 = 7x4 3x5 Prof. Rowena R. De Leon = 28 15 or 1 13 15 ENT 106: Pricing & Costing Division of Fractions Invert the second fraction by placing denominator over the numerator. Next change the “÷” sign to “x” sign, then proceed with multiplying the problem. Convert any mixed numbers to improper fractions; Next, get the reciprocal of the divisor and proceed as in multiplication. For Example: 12 2 2 ÷ 2 = ÷ 2 5 3 3 5 6 26 3 or 2 = 12 x = 10 10 2 5 or 3 2 5 Prof. Rowena R. De Leon ENT 106: Pricing & Costing Self-check #2 Direction: Perform the indicated operations. 1. 1 + 2 2. 5 1 + 6 3. 12 + 2 + 9 4. 3 10 5. 5 6 8 1 8 1 4 1 3 1 8 3 24 = = 6. 5 8 = 7. 12x 3 5 = 8. = 9. = 2 3 x 41 = 4 3 3 1 + 2 10. 5 3 8 Prof. Rowena R. De Leon 1 = 3 + 6 = x 6 6 = 10 ENT 106: Pricing & Costing 1.3 DECIMALS Decimals are a place vale system based on the number 10. A decimal is the fractional part of a whole expressed in powers of ten. A point (.) called a decimal point, is used to indicate the decimal form of a number. .1 .01 .001 .0001 Prof. Rowena R. De Leon = = = = One Tenth One Hundredth One Thousandth One Ten-Thousandth ENT 106: Pricing & Costing Converting Decimals to Fractions Carry out the Division problem to the tenthousandths place and truncate. Truncate means to cut off a number at a given decimal place without regard to rounding. For example: 12.34567 Truncate to the hundredths place would be 12.34 •: Write down the decimal divided by 1, like this: decimal1 Example : 0.75 1 •Step 2: Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.) x100 •Step 3: Simplify (or reduce) the fraction Prof. Rowena R. De Leon ENT 106: Pricing & Costing Converting Decimals to Fractions •: Write down the decimal divided by 1, like this: decimal1 •Step 2: Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.) 1. Example : 0.75 1 2. x100 .75 1 = 75 100 x100 •Step 3: Simplify (or reduce) the fraction 3. ÷5 ÷ 5 Answer 75 = 15 = 100 20 ÷5 Prof. Rowena R. De Leon ÷ 3 4 3 4 5 ENT 106: Pricing & Costing Converting Decimals to Fractions Read the number as a decimal using place value. Examples: Write the number as a fraction. ⁴/₅ as a decimal is 4 ÷ 5 = 0.8 ⁷⁵/₁₀₀ as a decimal is 75 ÷100 = 0.75 ³/₆ as a decimal is 3 ÷ 6 = 0.5 Reduce the lowest terms Seventy-Five one-hundredths 75/100 = 3/4 Prof. Rowena R. De Leon ENT 106: Pricing & Costing Self-check # 3 A. Change the following fractions to decimals. 1. 7 10 2. 5 8 3. 350 1000 4. 27 11 5. 4 B. Change the following decimals to fractions or mixed numbers. Simplify to lowest term when possible. 1. 2. 3. 4. 5. 0.57 0.7 0.324 0.004 3.512 3 7 Prof. Rowena R. De Leon ENT 106: Pricing & Costing C. Change the following fractions to percent. 1. 2. 3. 4. 5. Prof. Rowena R. De Leon 3/8 5/6 4/5 5/9 2/5 D. Express the following percent to fractions or mixed numbers and simplify if necessary 1. 2. 3. 4. 5. 15% 2.3 % 0.74 % 0.218% 155% ENT 106: Pricing & Costing 1.4 PERCENT The term percentage means “part of a hundred”. The use of percentages to express a rate is common practice in the foodservice industry. For example, food and beverage costs, labor costs, operating costs, fixed costs, and profits are usually stated as percentage of establish standard control. To indicate that a number is a percentage, the number must be accompanied by a percentage sign (%). Converting Decimals to Fractions To convert a decimal to a percent, multiply the decimal by 100 then affix the % symbol. An easier way is just to move the decimal point two places to the right, then affix the % symbol. Prof. Rowena R. De Leon Examples: 1. 0.75 2. 1.5 3. 0.027 4. 0.93 5. 57.145 6. 1.02 7. 0.0038 = = = = = = = 0.75 x 100 1.5 x 100 2.7% 93% 5,714.5% 102% 0.38% = = 75% 150% ENT 106: Pricing & Costing Conversion of a Percent to a Decimal To convert a percent to a decimal, drop the percent sign then divide the number in percent by 100. The short cut is to simply move the decimal point two places to the left then remove the % symbol. Examples: 1. 25% 2. 5% 3. 2.5% 4. 98% 5. 135% 6. 0.15% Prof. Rowena R. De Leon = = = = = = 25/ 100 = 5/ 100 = 0.025 0.98 1.35 0.0015 0.25 0.05 If there is a fraction in the percentage, change the fraction to decimal, then divide the number by 100 or move the decimal point two places to the left. Examples: 1. ¾% 2. 20 ¼% = = 0.75% 20.25% = = 0.0075 0.2025 ENT 106: Pricing & Costing Percentage in the Kitchen In the kitchen, it is often necessary to work with percentages. Percentages may be used to calculate and apply a yield percentage or food cost percentage. The following formulas may be used: Part Percent = Whole Part = Whole = Whole x Percent Part Percent When using the formulas, the following tips might be helpful: The number or word that follows the word of is usually the whole number and the word is usually is 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 part. Prof. Rowena R. De Leon ENT 106: Pricing & Costing Illustrative Problem : 1. 40% of P7,000 is _____________. Solution: Part = Whole x Percent = P7,000 x 0.40 = P2,800 2. What is 25% of 40 kilos? Solution: Part = Whole x Percent = 40 kilos x o.25 = 10 kilos 3. 75 is ____________% of 375. Solution: Percent = = = Prof. Rowena R. De Leon Part = 75 Whole 700 0.2 20 % 4. How many percent of 700 is 100? Percent = Part 100 = Whole 700 = 0.1429 = 14.29% 5. 15 ml is 20% of ____________. Solution: Whole = Part Percent = 15 0.20 Percent is converted to decimal when used in the solution. ENT 106: Pricing & Costing Percent Meat Cuts Applying the formula, we can determine the percentage of different meat cuts. To determine the percentage of the different beef cuts, divide the weight of each part by the total weight then multiply by 100. 62 lb 26 lb 18 lb 24 lb 17 lb 52 lb Examples: Chuck Sirloin = 62lb = 0.2531 x 100% = 25.31% 245lb 19 lb 12 lb 15 lb = 24lb = 0.098 x 100% = 9.80% 245lb Prof. Rowena R. De Leon ENT 106: Pricing & Costing Self-check # 4 A. Convert each of the following percentage to decimal. 1. 12. 7% 2. 4 ¼% 3. 85% B. Convert the following decimals to percent. 1. 0.46 2. 0.05 3. 0.0356 Prof. Rowena R. De Leon C. Find the missing terms in each of the following problem. Round off to the nearest tenths. 1. 24.5% of P3,265 is __________ 2. 5 ½% of P2,575 is __________ 3. 80% of P6,700 is ___________ 4. 28 is ___________% of 120 5. 57 is ___________% of 85 6. 10 is ___________% of 150 7. P25 is 35% of ___________ 8. P205 is 45.6% of _________ 9. P2,460 is 86% of _________ ENT 106: Pricing & Costing D. Determine the percentage of the following pork cuts. 29 lb 15 lb 24 lb 14 lb 4 lb 9 lb 27 lb 18 lb 8 lb 2 lb Prof. Rowena R. De Leon ENT 106: Pricing & Costing ENT 106: Pricing & Costing THE END Prof. Rowena R. De Leon