46. Bought 1085 bags of coffee for 9564 dollars, and sold them for 10453 dollars; what was gained by the transaction ?

47. In the year 1841, France, with a population of 31 millions, raised 547550440 bushels of grain; during the same period, the United States with a population of 17 millions, raised 533988970 bushels; what is the difference in population, and cereal productions?

48. In 1828, the votes given at the presidential election in the United States, were 1150508, in 1840, the number was 2388900. Required the increase.

49. A grocer purchased 185 hhds. of sugar, weighing 186480 pounds, and sold 97 hhds., weighing 98796 pounds. How many hhds. had he left, and what was their weight?

50. Charles Carroll, the last surviving signer of the Declaration of Independence, died A. D., 1832, aged 95 years; in what year was he born?

51. The first complete treatise on Practical Arithmetic, in which the numerals now in use were employed, was published A. D. 1556. How many years since? (A. D. 1845.)

52. Sold goods to the amount of 29648 dollars, and gained 4749 dollars; what was the prime cost of the goods? 53. How much must you add to 1001 to make 100000? 54. The total population of the United States is 17068666, that of Great Britain, 26270151. Required the difference?

55. A Liverpool merchant shipped merchandize to the amount of 63484 dollars, but during a storm the captain threw overboard a part, valued at 13697 dollars. What was the value of the remainder?

56. Mount Sorato, the highest point of the Andes, rises 25400 feet above the level of the sea, and 9732 feet higher than Mount Blanc, the highest point of the Alps. What is the height of Mount Blanc ?

57. A person bought goods to the amount of 17468 dollars, on a credit of three months, but preferring to pay the cash, an allowance of 269 dollars was made. What was the

amount paid?

58. The number of inhabitants in the Middle States, in 1830, was 3664412; by the census of 1840, the number was 4604345. Required the difference in population?

59. The value of the imports at Philadelphia for the year 1842, was 7381788 dollars; the value of the domestic ex

ports for the same time, was 3770729 dollars. What is the difference in value between the imports and exports?

EXERCISES IN ADDITION AND SUBTRACTION.

1 Subtract the sum of 56604, 4155, 4516, 3774, 2162 from 2514817?

2. Subtract 35637 from the sum of 250165, 92635, and 99097 ?

3. Subtract from 129601862, the sum of 40732359, 19221328, 6291808, and 9364965.

4. From the sum of 6544654, 1407736, 9477343 and 32708, subtract the sum of 361558, 11615769, 1485360 and 681979 ?

5. From 258037 subtract the sum of 111, 999, 88, 666 and 108050?

6. From 1724033 subtract the sum of 908744 and 815289.

7. Subtract from the sum of 188625 and 175574, the sum of 61617, 32500, 2705, 61, 727 and 24007.

8. What is the difference between the sum of 23583, 16872, 21891, and 22977; and the sum of 4226, 24531, 27873, 30699, and 23506?

9. The population of the Eastern States was, in 1840, as follows: Maine, 501793; New Hampshire, 284574; Vermont, 291948; Massachusetts, 737699; Rhode Island, 108830; and Connecticut, 309978. Of the Middle States, the population of New York was 2428921; of New Jersey, 373306; of Pennsylvania, 1724033; and of Delaware, 78085. How many more inhabitants were there in the Middle than in the Eastern States?

10. Give the difference between the total population of the Southern and the Western States in 1840, from the following list. Southern States: Maryland, 470019; Virginia, 1239797; North Carolina, 753419; South Carolina, 594398; Georgia, 691392; Alabama, 590756; Mississippi, 375651; Louisiana, 352411. Western States: Ohio, 1519467; Kentucky, 779828; Tennessee, 829210; Michigan, 212267; Indiana, 685866; Illinois, 476183; Missouri, 383702; Arkansas, 97574.

11. The value of the imports into New York state from October, 1841, to October, 1842, in American vessels, amounted to 51523055 dollars; in foreign vessels, to 6352549 dollars. Pennsylvania imported during the same period, in Ame

C

rican vessels, 6757228 dollars; in foreign vessels, 628630 dollars. How much greater was the total value of the imports of New York than that of the imports of Pennsylvania ?

12. Louisiana exports, in one year, foreign produce to the amount of 976727 dollars; domestic produce, 27427422 dollars. The total value of the exports, domestic and foreign, of New York, is 27576778 dollars. How much greater is the exporting trade of Louisiana than that of New York?

13. The imports of New York, from October, 1841, to October, 1842, were 57875604 dollars; of Pennsylvania, 7385858 dollars; of Louisiana, 8033590 dollars; and of Massachusetts, 17986433 dollars. What is the difference between the sum of the imports of these four states and the sum of those of the whole United States, which were for the same period 100162087 dollars?

14. The number of militia men and officers in the Eastern States, is stated to be, in Maine, 43352; New Hampshire, 32471; Massachusetts, 87215; Vermont, 27536; Rhode Island, 14995; and Connecticut, 46470. Of the Western States, the number in Tennessee, is 71252; Kentucky, 77276; Ohio, 180258; Indiana, 53913; Illinois, 83234; Missouri, 59689; Arkansas, 2028; and Michigan, 12786. How many more enrolled militia men are there in the Western than in the Eastern States?

15. The exports of the United States from October, 1841, to October, 1842, were as follows: Of products of the sea, 2823010 dollars; of the forest, 5518262; of agriculture, 73688113; of manufactures, 10940611. The total value of the imports for the same period, was 100162087 dollars. How much did the total value of the imports exceed that of the exports?

16. From the sum of 609458, 870406, 9004879, 23460401, and 7894763; subtract 21869909.

17. A person owed a merchant 1074 dollars, he paid him 695 dollars, and purchased goods to the amount of 598 dollars. How much did he then owe?

18. A merchant bought at one time 657 barrels of flour for 2625 dollars, at another time 956 barrels for 4025 dollars; he sold 845 barrels for 4235 dollars. How many barrels had he left, and what was their value?

19. The population of Philadelphia county in 1840, was 258037, of which the Northern Liberties contained 34474; Spring Garden, 27849; Kensington, 22314; Southwark,

27548; Moyamensing, 14573; and the townships, 37614. What was the remaining population, being that of the city?

20. A wholesale merchant purchased 6 hogsheads of sugar, weighing as follows: No. 1, 976 pounds; Nos. 2 and 3, each 1019 pounds; Nos. 4 and 5, each 1146 pounds; and No. 6, 1085 pounds; he sold to one person 2498 pounds, to another 1947 pounds, and to a third 763 pounds. How many pounds had he left?

21. In the city and districts of Philadelphia, for 1843, the assessed valuation of property, subject to county taxation, was as follows: the City, 58688499 dollars; Northern Liberties, 9224409 dollars; Spring Garden, 8862404 dollars; Kensington, 4023668 dollars; Southwark, 5578619 dollars; Moyamensing, 2330341 dollars; townships, 10613941 dollars. How much more was the city assessed than the districts?

22. In 1843, there were raised in the state of New York, 12479499 bushels of wheat; 24907553 bushels of oats; 3677222 bushels of rye; 2398354 bushels of buckwheat; and 15574590 bushels of corn. In Pennsylvania, 12215230 bushels of wheat; 19826938 bushels of oats; 9429637 bushels of rye; 2408508 bushels of buckwheat; and 15857431 bushels of corn. How many more bushels of grain did Pennsylvania raise than New York?

23. The first landing of settlers in Pennsylvania, under Penn's charter, occurred in 1681, at Upland, now Chester; the boundary line between Pennsylvania and Maryland, after long and serious difficulties between the two colonies, was finally established by Mason and Dixon, in 1768. How many years elapsed between these two dates? And how many years between each of these dates and the year. 1845?

24. How many years elapsed from the discovery of America, in 1492, to the Declaration of the Independence of the United States, in 1776? To the death of the author of that Declaration, Thomas Jefferson, in 1826? How many to 1845?

25. What is the difference between the population of New York, 312710, and that of Philadelphia, 258037? Between Philadelphia and New Orleans, 102103? Between New Orleans and Cincinnati, 46338? Between Cincinnati and Charleston, 29261? Between Charleston and Norfolk, 10920? Between Norfolk and Lexington, 6977 ?

MULTIPLICATION.

§ 5. Multiplication is that operation by which we increase one of two given numbers as often as there are units in the other; and is a compendious method of performing addition. Q. What does multiplication mean?

A. It means the repetition of one number as many times as is expressed by another number, and showing to how much the repetition amounts.

Q. Must there always be two numbers given in every case of multiplication?

A. There must always be two numbers given, the one of which represents the number that is to be repeated, and the other the number of repetitions.

Q. What names are given to those numbers?

A. That which is to be multiplied is called the multiplicand; and the other, the multiplier. Both the multiplicand and multiplier are called terms, or factors.

Q. Is there any difference in these numbers?

A. The multiplicand is a number, or a number meaning things of any kind; but the multiplier means a number of times.

Q. What are the prime factors?

A. The prime factors of any number are those prime numbers by whose continued multiplication the number is formed. Thus, 2 and 3 are the prime factors of 12, for 2 multiplied by 2 gives 4, which multiplied by 3 is equal to 12.

Q. Is multiplying the same as adding equal numbers together?

A. It is; if we write down the multiplicand as often as there are units in the multiplier, and add the whole together, it is the same as multiplying.

Q. How can this long labour be avoided, and produce the same effect?

A. By the operation of multiplying, the result of which is called a product.

Q. What preparation is required, before you can perform the operation of multiplying?

A. That of committing the multiplication table carefully to memory.

Q. What is meant by the sign ×?

A. This sign, when written between numbers, means that they are to be multiplied together. Thus, 4x3.