Notation and Numeration,...... General Principles of Division,... United S:ates or Federal Money, Notation and Numeration of L. S. Muncy,.. Roduction of U.S. Moncy,....... Multiplication of U. S. Money,. Promiscuous Examples in U.S. Money,... Reduction of C:mpound Numbers,... To find the Area of a Rectangle,. Sulid or Cubic Measurc,........ Promiscuous Examples in Reduction, Addition of Compound Numbers,.. Subtraction of Compound Numbers..... To find the period of Time between any two Dates,.. Multiplication of Compound Numbers........ Examples for Practice,...... 125 First Method, by Factoring, ..... First Method, by Factoring,..... Origin and Nature of Fractions,.. To reduce a fraction to its lowest terms, To reduce an improper fraction to a whole or mixed number,......... 143 To reduce a whole or mixed number to an improper fraction.......... 144 To reduce compound to simple fractions,...... To reduce ccm and to simple fractions by Cancellation,..... 147 To reduce fractions to a common denominator, To reduce fractions to the least common denominator................... 10 Division of Fractions........... Fractional Excrcises in Compound Numbers,.. Reduction of Fractional Compound Numbers..... Addition and Subtraction of Fractional Compound Numbers, 174 Promiscuous Examples,............ Origin and nature of Decimals......... Decimal Numeration and Notatior.............. Addition of Decimals,......... Picmiscuous Examples,....... 29. PERCENTAGE AND ITS APPLICATIONS. To find any per cent. of a Number ....... To find what per cent. one Number is of another,... Another method for Interest,... Problems in Interest,.......... American Dutics,........ Extraction of the Square Root,...... Applications of the Squarc Root,.. Extraction of the Cubo Root,... Measurement of Surfaces....... Plasterers', Painters', and Carpenters' Work,... Measurement of Bodies or Solid:,. Masons' and Bricklayers' Work,... PROMISCUOCS QUESTIOXS......... OBSERVATIONS TO TEACHERS. INTELLECTUAL ARITHMETIO should be thoroughly studied by all, and especially by the young, before commencing PRACTICAL. For this purpose, attention is called to “Ray's Arithmetic, Second Book,” which has been carefully prepared, and is now published with important improvements. When admissible, pupils studying Arithmetic should be taught in classes ; the presence of the class being a stimulus to both teacher and pupil. This arrangement also economizes time, since the same oral illustrations, necessary for the instruction of a single pupil, serve for a class. The time occupied at each recitation ought not to be less than thirty minutes, nor more than one hour. The class should not be too large; and, if possible, the attainments of its members equal. Every school should have a blackboard, on which pupils can solve the questions and explain the method of solution. A prime object in recitations is to secure attention; to do this, the exercises must be interesting, and all must be kept employed. Let as many be called out as can obtain positions at the blackboard, and let ail solve the same question at once. When the solutions are completed, let some one be called on to esplain the process, giving the reason for each step of the operation. Exercises thus conducted animate the class; and by requiring the learner to explain every process, and assign a reason for every step, he Icarns to rely on his owr. reasoning powers. In assisting pupils to overcome difficulties, it is preferable to do it indirectly, by making such suggestions, or asking such questions, as will enable the learner to accomplish the object. Frequent Reviews will be found of great benefit. The pupil should be rendered familiar with the answers to the questions in the Review at the foot of the page. This review is intended to aid the teacher, but not to prevent his asking other questions, or presenting different illustrations. (8) ARITHMETIC. 1. A Unit, or one, is a single thing of any kind; as one apple, one dollar, one pound. 2. Number is a term signifying one or more units; as, one, five, seven cents, nine men. 3. Numbers are expressed by ten characters, called Figures; as, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0. 4. Arithmetic treats of numbers, and is the art of computing by them. The fundamental rules are five; Notation and Numeration, Addition, Subtraction, Multiplication, and Division. are six; .. I. NOTATION AND NUMERATION. tico; 2 Two units and one more, arc three; 3 6 7 Seven units and one more, are cight; 8 Eight units and one more, are nine; Art. 2. These nine characters are called digits, or significant figures, because they denoto something. The character, 0, called cipher, naught, or zero, is cmployed to denote nothing: ihus, to show that there are no cents in a purse, write, the number of cents is 0. REMARK.—The cipher is sometimes termed an auxiliary digit, because it helps the other digits in expressing numbers. Review.-ART. 1. What is a single thing? What are one unit and one more of the same kind? Two units and one inore, &c. ? 2. What are these ninc characters callou ? Why? What does naught, or zero denote? Rex. What is the cipher termed ? Why? |