6. 94753+2847+793688+9386 +258 +3456. 7. 8289364275224+6875144+12897+7650368+94986347 +42682+3749286+7676. 8. 294796+489276+16759284+4938+5713245+3348675+ .9. 798426+9482+39867. 27515436+8937549 +37246375+48795+378+2863487+ 864937+3894+7863927+826957. 10. 9867594976346+29483+898647+3984753+6489778+ 57893+2468144+576989+498653. 11. 4683795+248675931+94986473 +2849758 +53388336 + 7788995+2137485+ 6758927 + 4926431 + 27729512 + 7842634949867+343216+78934. 12. Add together 9466495,375573735,754547,3789284, 29886799 992984,293675,2684487,3592873,8847599, 738873, 7849376 334486,123845,672849,73554,8674. 13. Required the sum of 978+749+4764+8967+79889294+ 7759286939723+864937+99375847+291886+94623 +924086+794867+935279423+9738413208+2468975 +945237+3834975. 14. 28674+39257+3834+92751+92503+86759 +394875+ 34938+375396+759394+2679346846+94657835+ 192648467319+2488+9357. 15. Add together seven thousand and ninety-four; two thousand, one hundred, and nine; eight thousand, nine hundred, and sixty; eighty-seven thousand and sixty-two; three hundred and seventy-five; nine thousand and thirty; thirty thousand and fortysix; fifty-four thousand, seven hundred, and seventy-five; seven thousand, eight hundred, and fifty-four. 16. Sir Isaac Newton was born in the year 1642, and died in his eighty-fifth year. In what year did he die? 17. William the Conqueror began his reign in England in the year 1066, and reigned 21 years; William II. reigned 13 years; Henry I. 15 years; Stephen, 39 years; Henry II. 35 years; Richard 1. 10 years; John, 17 years; Henry III. 56 years; Edward I. 35 years; Edward II. 20 years; Edward III. 50 years; Richard II. 22 years: in what year was this last prince dethroned? 18. In 1821, the population of the following towns in England, Scotland, Ireland, and France, (the three largest in each) were as follows: London,............. 1,274,800 | Glasgow,.... 147,043 133,788 Edinburgh,........... 138,235 Required the number of inhabitants contained in the three largest towns, in each country. 19. In the year 1810, the weight, in pounds of the cotton wool imported into England from the rest of Europe, was 16,725,708; from the United States, 55,194,616; from the British West Indies and conquered Colonies, 17,889,184; from foreign American Colonies, 22,137,397; from the East Indies, 23,144,907; from other sources, 1,478,291. Required the entire quantity. 20. The Pyramids of Egypt are thought to have been built 337 years before the founding of Carthage, Carthage to have been founded 49 years before the destruction of Troy, and Troy to have been destroyed 431 years before Rome was founded; Carthage was destroyed 607 years after the founding of Rome, and 146 years before the commencement of the Christian era; the Western empire of Rome ended in the year 476 of the Christian era, and 590 years before the Norman conquest; Constantinople was taken by the Turks 387 years after the Norman conquest, and 348 years before the union of Great Britain and Ireland in 1801. How many years elapsed between the first and last of these events? 21. Captain Cook, in his first voyage round the world, sailed from Portsmouth to the Madeiras, a distance of 1451 British miles; thence to the Canaries, 339 miles; from these to the Cape Verd islands, 985 miles; and thence to Rio Janeiro, 3058 miles; from that to Cape Horn, 2659 miles, and thence to Otaheite, 4919 miles; from Otaheite to the most southern point of the voyage, 1619 miles; and thence to Cook's strait in New Zealand, 1988 miles; from Cook's strait to Green Cape in New Holland, 1368 miles; and thence along the eastern coast of New Holland to the most northern point of that island, 2176 miles; thence to the straits of Sunda, 2487 miles; and thence to the cape of Good Hope, 5818 miles; from that cape to St. Helena, 1884 miles; and thence to Ascension island, 822 miles; from Ascension to Corvo in the Azores, 3462 miles; and thence to Portsmouth, 1598 miles. How far did he sail in all, exclusive of numerous deviations from these courses? 22. The following is the number of barrels of porter brewed in London by the twelve principal houses, between 5th July, 1814, and 5th July, 1815: what is the entire quantity? 337,621; 182,10+; 172,162; 161,618; 123,100; 119,333; 105,081; 72,080; 56,922; 51,294: 38,107; 32,256. 23. Required the entire population of England, from the fol lowing statement of the population of its several counties, according to the Census of 1821: Bedford,...... 83,710 Hertford,..... 129,714 Shropshire,.. 206,153 PROVINCE OF ULSTER. Acres. Population. Autrim,...... 387,200 269,856 Armagh,..... 181,450 136,971 Cavan, 196,577 301,000 194,330 249,483 ....... Louth,. 110,750 119,188 174,716 Queen's co.. 235,300 129,391 PROVINCE OF MUNSTER. Acres. Population. Clare,...... 476,200 209,595 Cork,........1,048,800 802,535 Kerry,........ 647,650 205,037 Limerick,.... 386,750 280,328 Tipperary,... 554,950 353,402 Waterford,... 262,800 154,466 *The acres are given from Beaufort, and the population from the Census of 1821, As that Census was, in some instances, in a slight degree defective, it is thought, that the population exceeded seven millions. The acres given above are Irish, 121 of which are equivalent to 195 of the standar4 acres now in use. 25. The number of inhabitants contained in the several counties of Scotland, in 1821, was as follows. Required the population of the whole kingdom: Argyle, 139,050 } 68,928 35,127 Renfrew,..... 112,175 Aberdeen,... 155,387| Elgin,......... 31,162 Orkney & Shetland. 53,124 97,316 Fife,........... 114,556 Peebles,...... 10,046 127,299 Forfar,........ 113,430 Perth,. 43,561 Haddington, Berwick,..... 33,385 Inverness, Bute,......... 13,797 Kincardine,.. Caithness,... 30,238 Kinross,...... Clackmannan, 13,263 Kirkcudbright, 38,903 Selkirk,... Dumbarton,. 27,317 Lanark,...... 244,387 Stirling,........ 65,376 Dumfries,... 70,878 Linlithgow,.. 22,685 Sutherland,... 23,840 Edinburgh,.. 191,514 Nairn,......... 9,006 Wigton,........ 33,240 6,637 SIMPLE SUBTRACTION. THE object of SUBTRACTION is to find the difference between two numbers. The number found in Subtraction is called the REMAINDER, the DIFFERENCE, or the EXCESS.* When the given numbers are of the same denomination, the process is termed SIMPLE SUBTRACTION. When the given numbers express quantities of the same kind, but of different denominations, the process is termed COMPOUND SUBTRACTION. Rule for Simple Subtraction. (1.) Place the less number below the greater, with units under units, tens under tens, &c. as in Addition. (2.) Beginning with the units, take, if possible, each figure in the lower line, from the figure above it, and set down the remainder. (3.) But if any figure in the lower line be greater than the figure above it, add ten to the upper; then subtract as before, and carry one to the next figure in the lower line. The sign, generally called minus, when set between two numbers, denotes, that the latter is to be taken from the former Thus, 16-9-7 denotes, that if 9 be taken from 16 the remainder is 7. The number to be subtracted is sometimes called the subtrahend; and that from which it is to be taken, the minuend. Methods of Proof. 1. Add the remainder and the less of the given numbers togegether: if the sum be equal to the greater, the work is correct. 2. Subtract the number found from the greater of the given numbers; if the remainder be equal to the less, the work is correct. Examples in Simple Subtraction. Ex. 1. From 7854 take 4513. Set the numbers as in the margin, and proceed thus:-3 from 4, and I remains; 1 from 5, and 4 remain; 5 from 8, and 3 remain; 4 from 7, and 3 remain: the remainder therefore is 3341. To prove the work, to the less of the given numbers add the remainder, and the sum will be 7854, the greater; or, as in the second method, subtract the remainder from the greater number, and the result will be 4513, the less. 7854 4513 Remainder, 3341 Proof, 7854 7854 4513 Remainder, 3341 Proof, 4513 From 3712 take 1831 Ex. 2. Required the difference of 3712 and 1831. In this example proceed thus:-1 from 2, and I remains; 3 from 11, and 8 remain; carry 1 to 8, and then 9 from 17, and 8 remain; carry 1, and then 2 from 3, and 1 remains. The difference, therefore, is 1881, and the operation would be proved in the same manner as before. Reason of the Rule. Remainder, 1881 The rule for Subtraction depends on the principle, that the differences of the several parts of two numbers are, when taken together, equal to the difference of the numbers themselves. The reason of placing units under units, tens under tens, &c. is, that figures may be subtracted from others of the same local value with more facility. By carrying one to the lower figure, we increase the lower line as much as we increased the upper, and thus the difference will be the same as if neither had been increased. Thus, in the second of the above examples, when in the tens' place we subtract 3 from 11, we thus add 10 to the 1 in the upper line; then the lower line is increased by the same quantity by adding 1 to the 8; because, by the nature of notation, I in the third columr is equivalent to 10 in the second. Thus, therefore, both the given numbers are equally increased, and consequently the difference must be the same as if they had received no increase. |