Reading: Lesson 5 - Basic Math and Measurement Systems

7.5.A - Basic Math and Measurement Systems

1. BASIC MATHEMATICS OPERATIONS

1. Consumers use mathematics every day. A debit card purchase might require a quick calculation to ensure there is enough money in the account to cover the purchase. When a restaurant server presents the bill after a meal, the amount of the tip must be determined. Comparing prices of frozen and fresh-squeezed orange juice requires calculating the cost per serving. A store display announcing 30 percent off the regular price requires the shopper to figure out the price of the merchandise after the discount is taken. Businesspeople also encounter situations where math skills are needed. A salesperson must quickly recalculate the price of an order after the company approves an additional discount for an important customer. An accountant tries to find an error when two columns in a balance sheet show different totals. When discussing benefits with a new employee, a human resources staff member compares the out-of-pocket costs of two different health care options.
   
2. A starting point for effectively using mathematics in business is understanding and applying basic arithmetic operations. Arithmetic involves addition, subtraction, multiplication, and division. Furthermore, managers need to understand, use, and convert fractions, decimals, and percentages. Businesses have two expectations of employees when using math on the job: calculations must be accurate and they must be completed quickly. Managers need to be comfortable and confident in their use of basic math skills.
   
3. The structure and terminology of addition and subtraction equations are shown in the Figure below. Many of the numerical situations faced in business that require addition and subtraction involve large numbers in the thousands or even millions and may include decimals or fractions and percentages. Frequently, many numbers need to be added or subtracted in sequence. People who regularly encounter more complex addition and subtraction problems as a part of their jobs typically use spreadsheets or calculators. Using these electronic tools may quicken the calculation but does not ensure accurate results. When encountering a series of small numbers or only a few numbers that need to be added or subtracted, people should be confident they can complete the problem mentally. 
   

   
   

4. Remember the following when adding numbers:
   
   • The order of the addends does not matter. The sum is the total of all addends.
   
   • Check answers by adding the numbers again in the reverse order they were added originally.
   
   • Both positive and negative numbers can be added. However, adding a negative number reduces the sum.
   
   • A way to simplify the addition of large numbers is to add each column of numbers separately and then add the column sums together. Remember the following when subtracting numbers:
   
   • Only two numbers can be subtracted at a time. However, a series of numbers can be subtracted one after the other.
   
   • The order of numbers in subtraction is important. The subtrahend must be subtracted from the minuend.
   
   • A larger number can be subtracted from a smaller number. If the subtrahend is larger than the minuend, the result—called the difference—will be a negative number.
   
   • Check subtraction problems by adding the difference and the subtrahend. The correct answer is the minuend.
   

5. Multiplication and division are used frequently in business. The Figure above shows the structure and terminology of multiplication and division equations. Remember the following when multiplying numbers:
   
   • Count the number of decimal places in the multiplicand and the multiplier. The total will be the number of decimal places in the product.
   
   • To check the accuracy of multiplication, divide the product by the multiplier. The correct answer is the multiplicand. Remember the following when dividing numbers:
   
   • When dividing whole numbers using long division, make sure the decimal in the quotient is aligned with the decimal in the dividend. If the divisor contains a decimal, the decimal in the quotient will be located the number of positions to the right of the decimal in the dividend as it took to make the divisor a whole number.
   
   • To check the accuracy of division, multiply the quotient by the divisor. The correct answer is the dividend.
   

6. Fractions, ratios, decimals, and percentages are frequently used in business. A fraction is a part of a whole number expressed as a proportion. For example, the fraction 3/5 represents three parts of five. If $3,000 of a $5,000 weekly advertising budget is spent on radio ads, 3/5 of the total budget is allocated to radio. The top number in the fraction is the numerator while the bottom number is the denominator. A ratio is the relationship between two quantities. If a department has 4 supervisors and 60 employees, the ratio of supervisors to employees is 1:15. There is one supervisor for every 15 employees in the department. A ratio is similar to a fraction. In the same example of employees and supervisors, four of the 64 total personnel in the department are supervisors so 4/64, or 1/16, of the total department workforce are supervisors. A percentage is a part of a whole expressed in hundredths. In the advertising example above, 3/5 of the advertising budget was used to pay for radio ads. When 3 is divided by 5, the percentage of radio advertising is .60 or 60%. A percentage uses a decimal, which is a fraction that has a denominator of a power of ten and is expressed with digits and a decimal point rather than as a fraction. For example, the fraction 1/10 is equal to the decimal 0.1 or 10%, and the fraction 238/1,000 is equal to the percentage 23.8% or 0.238. You calculate the percentage represented by a fraction by dividing the numerator by the denominator.
   

2. MEASUREMENT SYSTEMS IN BUSINESS

1. Precise measurement is critical in business. When a product is assembled, every one of the many parts must fit together perfectly for the product to operate. If a part is damaged and must be replaced, the replacement must be identical to the original part. If a house or factory is being designed, measurements must be exact for walls to meet, floors to be level, and the building to withstand weight and weather conditions. Customers expect exact measures in products they purchase, whether it is the quantity of cereal in a package or the tons of wheat in a shipment of grain from a farm to a food processor. With the growth of international business, products move back and forth from one country to another. Many manufacturers produce products and parts that will be sold to consumers or other businesses in more than one country. Consumers purchase products for their personal use, rarely considering where they were manufactured. Businesses must be able to develop products that meet the standards and expectations of customers in any country in which they choose to do business. Understanding standards of measurement has become very important for businesspeople. The common measures used in business are length, mass, and volume.
   
2. Measurement units in the United States are different from most other countries. The U.S. system was developed from the traditional English system. The standard units of measurement in the U.S. system appear in the Figure below. Several centuries ago, because there was no need for precise measurement, units of measure were based on common, but general, standards. For example, the foot was the length of a man’s foot and the inch the width of a thumb or the first joint of a forefinger. Some have stated the mile was the approximate distance a Roman soldier could stride in 1000 paces—mille is Latin for thousand. As the need for precision became greater, governments began to impose specific standards on the traditional measures. The U.S. federal government first created the Office of Standard Weights and Measures in 1824 to develop standards for commerce. However, it was 1901 before a national research laboratory was created with responsibility for the scientific development of exact measures. Today the National Institute of Standards and Technology (NIST), part of the U.S. Department of Commerce, maintains thousands of standards for precise measurement, quality, safety, and performance. 
   

   
   

3. There have been efforts in the United States as early as the 1800s to make the metric system the official measurement system for the country. However, continued resistance has hindered the conversion. Congress passed the Metric Conversion Act of 1975 to support a ten-year voluntary conversion to the use of metrics. When that effort failed to gain general acceptance, the Omnibus Trade and Competitiveness Act of 1988 designated the metric system as the “preferred system of weights and measures for United States trade and commerce.” Since that time, most products produced and sold in the United States carry both metric and U.S. measures. The U.S. now uses metric standards to define the traditional U.S. measures. For example, the yard is 0.914 meters and the pound is 0.454 kilograms. The Figure below shows conversions of common measures between the U.S. and metric systems.