1. ARITHMETIC. SCIENCE. 2. NUMBERS. ART. COMPUTATION. OPERATION. 13. Addition. Subtraction. Multiplication. Division. Reduction. Solution. 14. Problem. 15. Explanation. TERMS. 16. Principle. 17. Example. 18. Analysis. 19. Rule. SIGNS. CLASSIFICATION. Integers. Fractions. Denominate Numbers. Percentage. Ratio and Proportion. Involution and Evolution. Progressions. Mensuration. NO VINU CHAPTER I. INTEGERS SECTION I.-DEFINITIONS. 1. Arithmetic is the science of numbers and the art of computation. 2. A Number is a unit, or a collection of units, and answers the question "How many?” 3. A Unit is one, or a single thing; as, one, one dollar, one house, one bushel, one peck, one half. (5, NOTE, and 150.) Numbers are classified as to object into Concrete and Abstract. 4. A Concrete Number is one that is applied to some particular object; as, three books, four dollars, five miles. 5. An Abstract Number is one that is not applied to any object; as, three, four, five. Numbers are classified as to their unit into Integral, Fractional, and Mixed. 6. An Integer is a whole number; as, one, five, ten. 7. A Fraction is a number expressing one or more of the equal parts of an integer; as, one half, five tenths. 8. A Mixed Number is composed of an integer and a fraction; as, six and one half, nine and five tenths. Numbers are classified as to their nature, into Like and Unlike. 9. Like Numbers are those which express the same kind of units; as, two cents and four cents, six hats and one hat. 10. Unlike Numbers are those which express different kinds of units; as, two cents and six hats, four cents and one hat. Numbers are classified as to the number of kinds of units, into Simple and Compound. 11. A Simple Number is a number expressing one kind of unit; as, four pounds. 12. A Compound Number is a number expressing more than one kind of unit; as, four pounds five ounces. The terms used in computations in Arithmetic are Solution, Problem, Explanation, Principle, Example, Analysis, and Rule. 13. A Solution is a process of computation used to obtain a required result. 14. A Problem is a question for solution. 15. An Explanation is a statement of the reasons for the manner of solving a problem. 16. A Principle is a general truth upon which a process of computation is founded. 17. An Example is a problem used to illustrate a principle, or to explain a method of computation. 18. An Analysis is a statement of the successive steps in a solution. 19. A Rule is a direction for performing any computation. OUTLINE OF NUMERATION AND NOTATION. 20. NUMERATION, and 21. NOTATION. 22. ARABIC. 43. ROMAN. TERMS. 40. TABLE. 41. PRINCIPLES. 42. RULES. Order. 34. Hundreds. &c., &c., &c. 36. Units. 37. Thousands. 35. Period. 38. Millions. 39. Billions. &c., &c., &c. 44. ORIGIN. 46. Names. 47. Alone. 45. CHARACTERS. 48. Repeated. 49. Following. Values. 50. Preceding. 53. USES. 51. Between. 52. Horizontal Line. 20. Numeration is a method of reading numbers represented by characters. 21. Notation is a method of writing, or representing numbers by characters. There are two methods of reading and writing numbers, viz.: the Arabic and the Roman. 22. In the Arabic Method numbers are expressed by means of ten characters. 23. The Arabic method of expressing numbers had its origin in India, but was introduced into Europe by the Arabs. 24. The Characters used in this system of expressing numbers are called figures. 25. The figures used and their names are as follows: Printed, 1 2 3 4 5 6 7 8 9 0 Written, 1 2 3 4. 678 567 9 0 Named, One, Two, Three, Four, Five, Six, Seven, Eight, Nine, Naught. 26. The first nine are called significant figures, because each always expresses a number. They are sometimes called digits, from the Latin digitus, a finger; it being once customary to count upon the fingers. |