been presented in an Appendix, so that they may be used or omitted, as desired in each case, without destroying the continuity of the other work. 4. The problems of the text have been drawn from the common field of everyday experience. The necessary arithmetical training is had from dealing with practical problems within the experience of the pupils. No unreal problems, or problems dealing with artificial situations, or problems treating of situations remote from the experiences of the average pupil in the grammar grades, are introduced. The text aims to teach arithmetic only. 5. The text contains an unusual amount of oral work, including oral problems under every topic treated. The oral problems are everywhere related to the written work. No additional text in "mental" arithmetic need be used in conjunction with this text. 6. The methods of the text are those commonly employed in business life. 7. The work in fractions and compound numbers is limited to the practical needs of life. Special attention is given in fractions to the use of those fractions which pupils must handle later on as the fractional equivalents of certain per cents. Commission, Taxes, Insurance, etc., are made part of the work in Percentage and are not treated as separate topics. The work in Interest has been considerably reduced, and but one method of finding interest is recommended. 8. A constant review of all previous work is maintained throughout the text. Finally, the aim of the authors has been to present a course in arithmetic that will secure a thorough knowledge of the essentials of this subject. CONTENTS The Decimal System - Notation and Numeration - Addition Subtraction - Multiplication - Bills and Accounts-Divi- Profit and Loss Commission Insurance - Taxes Customs and Duties - Trade Discount - Interest - Trade Discount- Partial Payments — Interest Table- Exact Interest-State and Local Taxes-Customs and Internal Revenue — Banking — Life Insurance - The Equa- tion-Proportion Surfaces and Solids - Measurement of ESSENTIALS OF ARITHMETIC PART I REVIEW OF INTEGERS AND DECIMALS 1. A unit is a single thing, or a group of things regarded as a single thing, as a book, an apple, a box of apples, etc. A unit is represented by the least whole 2. Point to several units of the same thing in your schoolroom. Can you think of a way by which you could tell your parents how many children there are in your 3. Any definite quantity used to measure quantity of the same kind is called a unit of measure. The unit of 6 is 1; of 6 cows is 1 cow; of 9 ft. is 1 ft. The inch, foot, yard, rod, and mile are units used to meas- ure length or distance. Name the units used to measure areas. What is the unit of 10? of $10? In finding the number of hats at $2 each that can be bought for $10, the unit of measure is $2. What is the unit of measure in finding the number of 4-ft. shelves that can be made from 5. In the number 111, the 1 at the right denotes some unit, and the 1 next toward the left denotes a unit ten times as great, and the 1 at the left denotes a unit ten times the second unit, or one hundred times the first unit. may be shown thus: one hundreds' unit This 100 10 1 6. In 236, the 6 represents 6 units; the 3 represents 3 units, each of which is ten times each of the units represented by 6; and the 2 represents 2 units, each of which is ten times each of the units represented by 3, or one hundred times each of the units represented by 6. 7. Tell what each figure represents in 125, 47, 352. 8. In 30, the O shows that there are no units of ones; and the 3 represents 3 units of tens. What does each figure represent in 60, 600, 405, 530, 203, 478, 700, 520? 9. In 324, the units represented by 4 are called units of the first order, or of units' order; the units represented by 2 are called units of the second order, or of tens' order; and the units represented by 3 are called units of the third order, or of hundreds' order. 10. Our number system is a decimal system. Decimal means tens. A decimal system is one in which ten units of one order are equal to one unit of the next higher order. The decimal system is believed to have had its origin in the practice of using the fingers for counting. |