16. 361965384 + 2963 +1200+100200 + 2560 + - be presumed to be correct. See Example 18. 36, TABLE FOR PRACTICE IN THE FUNDAMENTAL OPERATIONS. 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 II-9 1 7 5 1 7 2 4 4 8 29 4 6 8 4 2 9 9 72 29 7 3- H 6 4 8- I 6 4 9 4 7 1 8 8 I 9 2 7 9 3 1 3 3 0 5 M-8 4 5 2 1 9 2 4 8 1 8 7 8 4 9 5 3 4 6 2 N-1 4 4 8 6 8 1 5 2 1 6 0 2 1 6 1 1 1 5 8 6- K L 7 1-M 4- N 3 6 4 3 8 7 2 1 9– V V-7 6 9 4 1 6 2 6 8 40 6 Add in the above Table (as units, tens, and hundreds) columans, 34. Paid $2400 (dollars) for my farm, $155 for my horse and tart, $26 for garden utensils, $86 for a mowing-machine, $10 for a horse-rake, and $108 for a pair of oxen. Required the amount. 35. A body of troops were furnished with 3622 Springfield rifled muskets, 7690 smooth-bores, and 13185 Enfield rifles. Required the amount. 36. J. R. bought of the Seneca Knitting Mills, 39600 pairs of socks; of Whitten, Hopkins & Co., 9782 pairs; of Pierce Brothers & Co., 9353 pairs; of Allen, Lane & Washburn, 5664 pairs; of George C. Bosson, 4296 pairs; of Cushing, Pierce & Co., 1315 pairs; of Samuel Dennis, 276 pairs. Required the amount. 37. Required the average number of pupils attending the Grammar Schools of Boston during the year 1859–60, the average number attending the Adams School being 493; the Bigelow School, 469; Bowdoin School, 538; Boylston, 941; Brimmer, 575; Chapman, 626; Dwight, for boys, 622; Dwight, for girls, 489; Eliot, 708; Franklin, 559; Hancock, 719; Lawrence, 761; Lincoln, 466; Lyman, 370; Mayhew, 367; Phillips, 549; Quincy, 720; Wells, 494; Winthrop, 933. 38. In the year 1861, Massachusetts furnished for the U. S. army, from her several counties, as follows: From Barnstable, 3 commissioned officers and 108 enlisted men; Berkshire, 21 officers, 614 men; Bristol, 59 officers, 1681 men; Dukes, 0 officers, 1 man; Essex, 148 officers, 4134 men; Franklin, 12 officers, 482 men; Hampden, 35 officers, 845 men; Hampshire, 15 officers, 575 men; Middlesex, 141 officers, 4200 men; Nantucket, 1 officer, 7 men; Norfolk, 70 officers, 2031 men; Plymouth, 44 officers, 1363 men; Suffolk, 278 officers, 4111 men; Worcester, 110 officers, 3464 men. Besides these, there joined her regi ments, 647 men whose residences were not given, and 20 officers and 955 men from other States. Required the whole number of enlisted men in her regiments; of commissioned officers; of both. 39. Massachusetts arished army shoes, 16649 + 4480 + 713932282022 +2336+2220 + 1000 +1200+1236 +1013240 pairs; cavalry boots, 336 +1008 +336+ 192 +160+168 +150 pairs. Required the number of pairs of boots; of shoes; of both. 40. She furnished hats, 12000 +4704; caps, 12130 + 2934 +2069450+251 +98 +160. Required the number of hats; of caps. 41. On commencing business a merchant had $7752 in cash, $7719 in real estate, goods valued at $9728, a lot of cattle valued at $6930, a ship valued at $16834; during the first year he was in trade he gained above all his expenses $3195. What was he worth at the end of the year? 42. What is the number of square miles in the British Isles, there being in Scotland 30000, in England 31200, in Wales 7200, and in Ireland 32500? 43. The United States contain 3284100 square miles more than the British Isles; required the area of the United States? 44. What is the length of the Grand Trunk Railway from Detroit to Portland, the distance from Detroit to Stratford being 143 miles; from Stratford to Georgetown, 59 miles; from Georgetown to Toronto, 30 miles; from Toronto to Coburg, 69 miles; from Coburg to Belleville, 44 miles; from Belleville to Kingston, 48 miles; from Kingston to Brockville, 47 miles ; from Brockville to Prescott, 12 miles; from Prescott to Cornwall, 46 miles; from Cornwall to Montreal, 67 miles; from Montreal to Richmond, 73 miles; from Richmond to Island Pond, 71 miles; from Island Pond to Gorham, 58 miles; from Gorham to Bethel, 21 miles; from Bethel to Danville, 42 miles ; from Danville to Portland, 28 miles? 45. How far is it from Detroit to Toronto? 46. How far from Toronto to Montreal? 47. How far from Kingston to Montreal? 48. How far from Montreal to Portland? 49. How far from Portland to Gorham? 50. From Boston to Portland is 111 miles; how far is it from Boston to Montreal? For Dictation Exercises, see Key. SUBTRACTION. 37. SUBTRACTION is the process of taking one number from another of the same kind, to find the difference. The number which is subtracted is called the subtrahend, from the Latin subtrahendus, to be taken from under, as that is the number taken away. The number from which the subtra hend is taken is called the minuend, from the Latin minuendus, to be made smaller, as that is the number to be diminished. The result is called the difference, or remainder. A short horizontal line, -, read minus or less, is the sign of subtraction, and, placed between two numbers, signifies that the number after it is to be taken from that before it; thus, 3 = 4, read, seven minus three equals four, shows that, if 3 be taken from 7, the remainder is 4. 7 ILLUSTRATIVE EXAMPLE, I. 38. From 267 take 135. OPERATION. Minuend, 267 133 Remainder, 132 Ans. For convenience, we write the subtrahend under the minuend, placing units under units, tens under tens, hundreds under hundreds, and draw a line beneath; 5 units from 7 units =2 units, which we write in the units' place, under the units ; 3 tens from 6 tens = 3 tens, which we write in the tens' place; 1 hundred from 2 hundreds = 1 hundred, which we write in the hundreds' place; and the result is 132, which is the difference between 267 and 135. 39. PROOF. If 132 is the difference between 267 and 135, it is evident that, if we add 132 to 135, the sum will equal 267. Hence, to prove subtraction, add the difference to the subtrahend. If the sum thus obtained is equal to the minuend, the work may be presumed to be correct. NOTE. The pupil should prove each example, till he is sure that he kes no mistakes. |