SELF-PROVING BUSINESS ARITHMETIC INTRODUCTION Arithmetic is a vital factor in every man's affairs. It enters every occupation, every profession, every business transaction. There is no commercial activity which does not involve calculation in some form. This book confines itself to the essential details of business arithmetic. Nothing in it is useless. The information contained herein is of constant use in business, and you will be required to use rapidly each item of knowledge that you secure from this book. Importance of obtaining correct results. To be usable, the result for every problem solved in the business world must be absolutely correct. The statement of the profit of a store for a whole year depends upon the accuracy of each individual computation made during the year. If any one is incorrect, the whole will be incorrect. An error in a bill sent to a customer may seem a small matter; but when we consider that if the error is against the customer, he immediately complains, and that if it is in his favor he may say nothing, we see that errors against us are usually discovered and those in our favor are seldom, if ever, found. Computation worth doing at all is worth doing correctly. Anything less than absolute accuracy is unsatisfactory. For these reasons you will be taught in this text how to solve and prove every problem you work. You must not only solve a given problem; you must know that it is right. Different methods of proof will be given as the work progresses. Chapter I presents the subject of common fractions, a mastery of which is essential to successful work in many lines of business. CHAPTER I COMMON FRACTIONS LESSON 1 Fractions in some form appear in nearly every business computation. Every division of an ounce, pound, or ton; of a quart, peck, or bushel; of a cent, dime, or dollar; of a pint, quart, gallon, or barrel; of an inch, foot, yard, rod, or mile; of a second, minute, hour, day, or year; and of all other units of measure, all are fractions of the divided unit. The principles presented in this chapter on Common Fractions form the foundation for nearly all the figuring you will ever have to do. A mastery of these principles is essential to an understanding of all the work which follows. Necessary Preliminary Operations with Whole Numbers FACTORING Definitions. Factoring is the process of finding all the prime numbers that are exact divisors of a given number. A digit is a single figure: 1, 2, 3, 4, 5, 6, 7, 8, 9, 0. A prime number is a number that can not be divided by any number except itself and the number 1; as, 2, 3, 5, 7, 11, etc. Prime numbers that exactly divide a given number are called prime factors of that number; thus, 2 and 3 are prime factors of 6. Necessity for learning factoring. You will need to know how to factor numbers in order to find the lowest common multiple of two or more numbers, which, in turn, is used in adding and subtracting fractions. Tests of divisibility. To be able to factor numbers readily, one should be familiar with the following tests of divisibility: Two is an exact divisor of any number ending in 0, 2, 4, 6, or 8; that is, of any even number. Three is an exact divisor of number if the sum of its digits is exactly divisible by 3; thus, 3 is an exact divisor of 417, because the sum of the digits 4, 1, and 7, or 12, is exactly divisible by 3. Four is an exact divisor of a number if the two right-hand figures express a number that is exactly divisible by 4; thus, 4 is an exact divisor of 37,924, because 24, the number expressed by the two right-hand figures, is exactly divisible by 4. Five is an exact divisor of any number ending in 0 or 5; thus, 5 is an exact divisor of 2730, 42,685, and 9900, because the right-hand digit in each case is a 0 or 5. Six is an exact divisor of any even number the sum of whose digits is exactly divisible by 3; thus, 6 is an exact divisor of 5814, because 5814 is an even number, and the sum of its digits, 5, 8, 1, and 4, or 18, is exactly divisible by 3. Eight is an exact divisor of a number if the three righthand figures express a number that is exactly divisible by 8; thus, 57,408 is divisible by 8, because 408, the number expressed by the three right-hand figures, is exactly divisible by 8. |