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 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. of ten HUNDRED TENS UNITS 138 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.* Hundreds of trillions Hundreds of billions Tens of millions Tens of thousands THOUSANDS Tens 47 2 1 5 6 7 9 5 8 4 1 5 2 6 To read the line of figures in this table, begin with the left hand figure, and proceed as follows. 472 5 6 795 841 5 2 6 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 siz figures in a period, is of late abandoned, (5) 103 32) Note to Teachers. Require the learners to copy upon their slates the fol. lowing figures expressing numbers. Then require them to read from their slates the several numbers expressed. (Ex. 1.) 508 (19) 1 000 001 (2) 3361 (20) 90 040 (3) 1 050 (21) 107 090 (4) 27 400 (22) 6 000 304 13008 (23) 77 010 000 29 111 (24) 100 100 011 112 600 (25) 220 002 (8) 30 030 (26) 11 333 111 (9) 206 209 (27) 216 090 900 (10) 500 083 (28) 10 000 004 (11) 7 432 040 (29) 8 000 000 500 (12) 200 005 (30) 50 000 000 036 (13) 9 070 638 (31) 1 000 700 007 (14) 3018 103 8 400 052 000 600 (15) 16 974 036 (33) 8 631 008 000 (16) 340 007 140 (34) 22 000 004 (17) 31 031 032 (35) 919 000 000 060 (18) 9 908 000 (36) 86 000 001 100 018 SECTION 2. Note to Teachers. T'he 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: 9. Thirty-six thousand, seven hundred and forty. 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. 4 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 th 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, 3032 dollars, 501 dollars, and 7123 dollars ? We first write the numbers under one another, so that all the units may stand in a column on the right hand. We then add the units thus— 3 and 1 are four, and 2 6 31 2 are six, and 2 are eight; and we write 8 8032 under the column of units. We next add 501 the column of tens, and, finding their sum 7123 to be 6, we write 6 under the column. In the same manner we add the hundreds, and 2 1 968 the thousands. Find the sum of the numbers in each of the following examples, by addition upon the slate. (2). 51 (3). 733 (4). 6243 (5). 24031 4 120 4123 1320 60 12 40214 34314 00 Os Thousands er o w Hundreds SECTION 2. 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, 4 6 38 we find their sum to be 13. Now if we 216 should write down 13, the 3 would stand 8 329 under the column of hundreds, and the 1, 1212 under the column of thousands; therefore 14395 we write the 3 only, and presently add the 1 in with the thousands. A Thousands Hundreds |