89 WRITTEN ARITHMETIC. CHAPTER I. NUMERATION. SECTION 1. THE UNIT, which is the first thing to be considered in numeration, signifies One. The figure 1 stands for one unit; 2, for two units; 3, for three units; 4, for four units; 5, for five units; 6, for six units; 7, for seven units; 8, for eight units; 9, for nine units. The TEN is a number which is made up of ten units. One ten is expressed thus, 10; two tens, thus, 20; three tens, thus, 30; four tens, thus, 40; &c. The HUNDRED is a number which is made up of ten tens. One hundred is expressed thus, 100; two hundreds, thus, 200; three hundreds, thus, 300; &c. Suppose the balls below, which are arranged in three places, to represent 8 units, 3 tens, and 1 hundred. Learn from the figures above, that the first or right hand figure expresses units, the second figure expresses tens, and the third figure expresses hundreds. H* The THOUSAND is a number, which is made up of ten hundreds. One thousand is expressed thus, 1000; two thousand, thus, 2000; three thousand, thus, 3000; &c. Observe, that a figure expresses thousands, when it stands in the fourth place from the right; therefore ten thousand is expressed thus, 10000; and a hundred thousand, thus, 100 000. Examine the following Numeration Table. Begin at the right hand, and observe, that every three figures may be viewed by themselves;- the first three express so many units, tens and hundreds; the second three, so many Thousands; the third three, so many Millions; the fourth three, Billions; the fifth three, Trillions.* To read the line of figures 841 526 in this table, begin with the left hand figure, and proceed as follows. This character, 0, called nought, or cipher, expresses nothing of itself-it stands only to occupy a place, where there is none of the denomination belonging to that place to be expressed. For example, in the number 240, there are no units; therefore a cipher stands in the units' place. In the number 407, there are no tens; therefore a cipher stands in the tens' place. * The old method of embracing six figures in a period, is of late abandoned, Note to Teachers. Require the learners to copy upon their slates the following figures expressing numbers. Then require them to read from their slates the several numbers expressed. 1 000 001 90 040 107 090 6 000 304 508 (19) (20) (21) (22) (5) 13 008 100 100 011 220 002 (8) 30 030 (26) 11 333 111 Note to Teachers. The following numbers written in words, are to ce written upon the slate in figures. If the learner meet with difficulty in denoting the larger numbers, he may be instructed to repeat the Numeration Table, from units up to the highest denomination in the number to be denoted; and, while repeating the table, he may make a dot for each denomination, arranging the whole in a line. Then, the figure to express the highest denomination may be written under the left hand dot, and there will be no difficulty in arranging the figures of other denominations under their respective dots. 1. Seventy. 2. Forty-eight. 3. One hundred and twenty-four. 4. Six hundred and nine. 5. Three thousand, and six hundred. 6. Two thousand, four hundred and fifty. 7. Nineteen thousand, and sixty-eight. 8. Five thousand, seven hundred and thirty-one. 9. Thirty-six thousand, seven hundred and forty. 10. Two hundred and sixty-eight thousand. 11. Nine hundred five thousand, and one hundred. 12. Eighteen thousand, seven hundred and thirty-five. 13 Seven hundred thousand and nine. 14. Thirteen million, sixteen thousand, and nineteen 15. One hundred five million, two thousand, and one. 16. Six billion, forty million, and six thousand. 17. Twenty-one billion, and one hundred million. 18. Five trillion, fourteen billion, seventy million, one thousand, two hundred and thirty-six. 19. One hundred twenty-two trillion, eight hundred and forty-seven thousand. 20. Ten billion, nine hundred eighty-seven thousand, seven hundred and thirty. 21. Seven hundred trillion, and thirty-six thousand. 22. Twelve billion, eight hundred forty-two thousand, seven hundred and eighty. 23. Twenty-nine trillion, eight hundred nine billion, one thousand, and eighteen. 24. Eight hundred twenty-three billion, ten million, eight thousand, and fifteen. Questions to be answered Orally. (1) What is a unit? (2) What is the greatest number, that can be expressed by one figure alone? (3) In what situation must the figure 9 stand, to express 9 tens? (4) What is the greatest number that can be expressed by two figures? (5) Recite the several denominations of numbers, from units to trillions, as they stand in the Numeration Table. (6) What denominations are expressed in the 1st. three places of figures? (7) What denominations are expressed in the 2nd. three places? (8) Where must the figure 7 stand to express 7 tens of thousands - that is, seventy thousand? (9) What denominations are expressed in the 3rd. three places? (10) Where must the figure 2 stand, to express two hundred thousand? CHAP. II. ADDITION. SECTION 1. 1. What is the whole sum of 6312 dollars, 8032 dollars, 501 dollars, and 7123 dollars? → Thousands Co Hundreds Tens Units 6312 8032 501 7123 21968 We first write the numbers under one another, so that all the units may stand in a We then add column on the right hand. the units thus-3 and 1 are four, and 2 are six, and 2 are eight; and we write 8 under the column of units. We next add the column of tens, and, finding their sum to be 6, we write 6 under the column. In the same manner we add the hundreds, and the thousands. Find the sum of the numbers in each of the following examples, by addition upon the slate. 1. Add the following numbers into one sum. 4638 and 216 and 8329 and 1212. Finding the sum of the units to be 25, or 2 tens and 5 units, we write only the 5 units, and presently add the 2 tens in with the column of tens. In adding the hundreds, we find their sum to be 13. Now if we should write down 13, the 3 would stand under the column of hundreds, and the 1, under the column of thousands; therefore we write the 3 only, and presently add the 1 in with the thousands. |