1 NOTATION AND NUMERATION...... 144 83 MEASURES OF WEIGHT................. 101 REDUCTION OF DENOM. INTEGERS... 209 ..... N. B.-Editions of this book are bound with, and without, the As a science, Arithmetic treats of the nature and properties of numbers. As an art, it teaches how to apply a knowledge of numbers to practical and business purposes. 2. A Unit is one, or a single thing; as one, one boy, one year, one dozen. 3. A Number is a unit, or a collection of units; as one, three, five boys; it answers the question, How many? 4. An Integral Number or Integer is a number which expresses whole things; as seven, four days. 5. The Unit of a Number is one of the collection of units which constitute the number. Thus, the unit of twelve is one, of twenty dollars is one dollar. 6. A Concrete Number is a number that is applied to a particular kind of object, or quantity; as three houses, four dollars, five minutes. 7. An Abstract Number is a number that is not applied to any object; as four, seven, eight. 8. Like Numbers are such as have the same kind of unit, or express the same kind of quantity. They may be either concrete or abstract; as eight and nine, six days and ten days, two rods five feet, and five rods three feet. 9. Unlike Numbers are such as have different kinds of units, or express different kinds of quantity; as ten months and eight miles; seven dollars and five barrels. 10. A Scale in Arithmetic, is a succession of units, increasing and decreasing according to a certain law, or rule. Scales are uniform or varying. 11. A Uniform Scale is one in which the law of increase and decrease is the same throughout the entire succession of units. 12. A Varying Scale is one in which the law of increase and decrease is not the same throughout the entire succession of units. 13. A Decimal Scale is one in which the law of increase and decrease is uniformly TEN. EXERCISES. 14. 1. How many units in two? In five cents? In six dollars? In seven acres? 2. What is the unit of six cents? Of nine books? 3. Are two trees and five trees like or unlike numbers? 4. Are they concrete or abstract? Why? 5. What kind of numbers are seven and nine? Are five acres and seven cords? Are four coats and six coats? 6. Name two numbers that are like and abstract. 7. Name two numbers that are like and concrete. 8. Name three numbers that are unlike and concrete. NOTATION AND NUMERATION. 15. In representing numbers, objects are regarded as arranged in groups of tens; hence we have single things, or units; next, groups containing ten units, or ten; next, groups containing ten tens, or one hundred; and again, groups containing ten hundreds, or one thousand, etc. 16. This method of grouping is called the Decimal System, from the Latin word decem, which signifies ten. 17. Notation is a method of writing, or representing numbers by characters. 18. Numeration is a method of reading numbers represented by characters. |