RUDIMENTS OF ARITHMETIC. DEFINITIONS. 1. Quantity is any thing that can be increased, diminished, or measured; as distance, space, weight, motion, time, 2. A Unit is one, a single thing, or a definite quantity. 3. A Number is a unit, or a collection of units. 4. An Abstract Number is a number used without reference to any particular thing or quantity; as 3, 4, 756. 5A Concrete Number is a number used with reference to some particular thing or quantity; as 21 Lours, 4 cents, 230 miles. 6. A Simple Number is either an abstract number, or a concrete number of but one denomination; as 48, 52 pounds, 36 days. 7. A Compound Number is a concrete number expressed in two or more denominations; as 4 bushels 3 pecks, 8 rođs 4 yards 2 feet 3 inches. 8. An Integral Number, or Integer, is a number which expresses whole things; as 5, 12 dollars, 17 men. 9. A Fractional Number, or Fraction, is a number which expresses equal parts of a whole thing or quantity; as, of a pound, of a bushel. 10. Like Numbers have the same kind of unit, or express the same kind of quantity. Thus, 74 and 16 are like numbers; so are 74 pounds, 16 pounds, and 12 pounds; also, 4 weeks 3 days, and 16 minutes 20 seconds, both being used to express units of time. 11. Unlike Numbers have different kinds of units, or are used to express different kinds of quantity. Thus, 36 miles, and 15 days; 5 hours 36 minutes, and 7 bushels 3 pecks. 12. Arithmetic is the Science of numbers, and the Art of computation. 13. The Five Fundamental Operations of Arithmetic are, Notation and Numeration, Addition, Subtraction, Multiplication, and Division. NOTATION AND NUMERATION. 14. Notation is a method of writing or expressing numbers by characters; and, 15 Numeration is a method of reading numbers expressed by characters. -the 16 Two systems of Notation are in general use— Roman and Arabic. 18. The Roman notation is founded upon the following principles: 1st. Repeating a letter repeats its value. Thus, II represents two, XX twenty, CCC three hundred. 2d. If a letter of any value be placed after one of greater value, its value is to be united to that of the greater. Thus, XI represents eleven, LX sixty, DC six hundred. 3d. If a letter of any value be placed before one of greater value, its value is to be taken from that of the greater. Thus, IX represents nine, XL forty, CD four hundred. 4th. If a letter of any value be placed between two letters, each of greater value, its value is to be taken from the united value of the other two. Thus, XIV represents fourteen, XXIX twenty-nine, XCIV ninety-four. 19. Employs ten characters or figures to express numbers. Thus, 9 0 1 2 3 4 5 6 7 8 Names and naught, one, two, three, four, five, six, seven, eight, nine. values, cipher, or 20. The first character is called naught, because it has no value of its own. The other nine characters are called significant figures, because each has a value of its own. 21. As we have no single character to represent ten, we express it by writing the unit, 1, at the left of the cipher, 0, thus, 10. In the same manner we represent 20; 30; 40; 50; 60; 22. When a number is expressed by two figures, the right hand figure is called units, and the left hand figure tens. We express the numbers between 10 and 20, thus: eleven, twelve, thirteen, fourteen, fifteen, sixteen, seventeen, eighteen, nineteen. 11, 12, 13, 14, 15, 16, 19. 17, 18, In like manner we express the numbers between 20 and 30, thus: 21, 22, 23, 24, 25, 26, 27, 28, 29, &c. The greatest number that can be expressed by two figures is 99. 23. We express one hundred by writing the unit, 1, at the left hand of two ciphers; thus, 100. In like manner we write two hundred, three hundred, &c., to nine hundred. Thus: one three four two five six seven eight nine hundred, hundred, hundred,hundred, hundred, hundred, hundred, hundred, hundred. 100, 200, 300, 400, 500, 600, 700, 800, 900. 24. When a number is expressed by three figures, the right hand figure is called units, the second figure tens, and the left hand figure hundreds. |