ELEMENTARY ARITHMETIC PART II. DEFINITIONS. 1. A Unit is a single thing; as, a book, a man, an hour. 2. A Number is a unit, or a collection of units; as, one hat, ten birds, twenty-five dollars. 3. An Abstract Number is one whose unit is not named; as, 3, 10, 21. 4. A Concrete Number is one whose unit is named; as, 6 pens, 7 days, 10 dollars. All abstract numbers have the same unit; hence, the value of an abstract number depends entirely upon the number of its units. Concrete numbers do not all have units of the same value, and therefore the value of a concrete number depends both upon the value of its unit and upon the times its unit is repeated. A five-dollar bill is more valuable than a two-dollar bill, for five repetitions of the unit, one dollar, give a greater value than two repetitions. Five dozen eggs is a greater number than five eggs, for, while the repetitions of the unit are the same, the unit, one dozen eggs, is greater than the unit, one egg. Hence, the Unit of a Number is the measure of the number, and determines its value. 5. Arithmetic explains numbers and teaches methods of using them. 6. In writing numbers, characters called Figures are used, and also certain Capital Letters. 7. The writing of numbers with figures or with letters is called Notation. 8. The reading of numbers is called Numeration. EXERCISES. 1. What is a unit? How many units are there in eight? 2. Compare eight pounds with eight pounds. Have these numbers the same unit? Has each the same number of units? Then, if you are asked why eight pounds. equal eight pounds, what answer can you give? 3. In like manner compare the following: Ten ounces and six ounces. Ten dozen eggs and ten eggs. Twelve feet and ten inches. 4. Name the unit in each of the following, and tell which are concrete and which abstract: 1. The system of notation employing figures is called the Arabic System; that employing letters is called the Roman System. The one was introduced into Europe by the Arabs; the other was used by the ancient Romans. 2. The Arabic system employs ten figures to represent numbers. 0, 1, 2, 3, 4, 5, 6, Names: Naught, one, two, three, four, five, six, 7, 8, 9. seven, eight, nine. Naught is also called zero and cipher. The rest are called significant figures. Because we have ten fingers, these ten figures are sometimes called digits. [Latin, digitus, finger.] 3. The following are correct forms for these digits: 1 2 3 4 5 6 7 8 9 Slant Script Figures. 1 2 3 4 5 6 7 8 9 0 Vertical Script Figures. 90 EXERCISES. Make the best Arabic forms you can for the following: 1. Naught, one, two, three, four, five, six, seven, eight. 2. Two, three, four, five, six, seven, eight, nine. Numbers from Ten to Twenty. 1. The number next above nine is called ten (10). 2. Notation forms numbers into groups of ten each. The first group is: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. 3. The second group of ten numbers is formed as follows: 11, named eleven, one and ten. 20, named twenty, twice ten (ty means ten). 2. Eleven, nineteen, seventeen, eleven. 3. Twelve, fifteen, twenty, eighteen. 4. Thirteen, twelve, sixteen, twenty. Each of the above numbers consists of two figures: the figure on the right expresses units; the figure on the left, tens. 3. Point out the number of tens and units in 11, 17, 19, 15, 20. Numbers from Twenty to One Hundred. The numbers from one to one hundred form ten groups. The first two groups we have shown you. Third group: 21, 22, 23, etc., named twenty-one, twenty-two, etc. Fourth group: 31, 32, 33, etc., named thirty-one, thirty-two, etc. Fifth group: 41, 42, 43, etc., named forty-one, fortytwo, etc. Sixth group: 51, 52, 53, etc., named fifty-one, fiftytwo, etc. Seventh group: 61, 62, 63, etc., named sixty-one, sixty-two, etc. Eighth group: 71, 72, 73, etc., named seventy-one, seventy-two, etc. Ninth group: 81, 82, 83, etc., named eighty-one, eighty-two, etc. Tenth group: 91, 92, 93, etc., named ninety-one, ninety-two, etc. NOTE. The last number of the tenth group is called one hundred (100). EXERCISES. 1. Write in figures, and read, the ten numbers of the third group. |