ELEMENTS OF ALGEBRA. CHAPTER I. QUANTITY AND NUMBER. 1. WHATEVER may be regarded as being made up of parts like the whole is called a Quantity. 2. To measure a quantity of any kind is to find how many times it contains another known quantity of the same kind. 3. A known quantity which is adopted as a standard for measuring quantities of the same kind is called a Unit. Thus, the foot, the pound, the dollar, the day, are units for measuring distance, weight, money, time. 4. A Number arises from the repetitions of the unit of measure, and shows how many times the unit is contained in the quantity measured. 5. When a quantity is measured, the result obtained is expressed by prefixing to the name of the unit the number which shows how many times the unit is contained in the quantity measured; and the two combined denote a quantity expressed in units. Thus, 7 feet, 8 pounds, 9 dollars, 10 days, are quantities expressed in their respective units. When a question about a quantity includes the unit, the answer is a number; when it does not include the unit, the answer is a quantity. Thus, if a man who has fifteen bushels of wheat be asked how many bushels of wheat he has, the answer is the number, fifteen; if he be asked how much wheat he has, the answer is the quantity, fifteen bushels. A number answers the question, How many? a quantity, the question, How much? NUMBERS. 6. The symbols which Arithmetic employs to represent numbers are the figures 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. The natural series of numbers begins with 0; each succeeding number is obtained by adding one to the preceding number, and the series is infinite. 7. Besides figures, the chief symbols used in Arithmetic are: +(read, plus), the sign of addition. (read, minus), the sign of subtraction. × (read, multiplied into), the sign of multiplication. ÷ (read, divided by), the sign of division. = = (read, is equal to), the sign of equality. 8. Any figure, or combination of figures, as 7, 28, 346, has one, and only one, value. That is, figures represent |