dollars; and in the fourth, 209 dollars: how many dollars does the fifth contain ? Ans. 234 dollars.

5. America was discovered by Christopher Columbus in the year 1492. What number of years has since elapsed?

6. George Washington was born in the year 1732, and died in 1799: how old was he at the time of his death? Ans. 7. The declaration of independence was published July 4th, 1776: how many years to July 4th, 1838 ? Ans. 62 years.

8. By the census of 1840, it appeared, that the white population of the United States was 14,189,108, and the number of blacks 2,873,458: how much did the white population exceed the black? Ans. 11,315,650.

9. In 1840 there were in the State of New York 2,428,921 inhabitants, and in the State of Pennsylvania 1,724,033 inhabitants: how many more inhabitants were there in New York than in Pennsylvania? Ans. 704888.' 10. The revolutionary war began in 1775; the late war in 1812: what time elapsed between their commencements? Ans. 37 years.

11. In 1840 there were in New York, which is the largest city in the United States, 312,710 inhabitants, and in Philadelphia, the next largest city, 258,037: how many more inhabitants were there in New York, than in Philadelphia ? Ans. 54,673. 12. A man dies worth 1200 dollars; he leaves 504 to his daughter, and the remainder to his son: what was the son's portion?

Ans.

13. Suppose a gentleman has an income of 3090 dollars a year, and pays for taxes 150 dollars, and expends besides 253 dollars: how much does he lay up ?

Ans. 2687 dollars. 14. A merchant bought 500 barrels of flour for 3500 dollars; he sold 250 barrels for 2000 dollars: how many barrels remained on hand, and how much must he sell them for, that he may lose nothing?

Ans. 250 barrels remained, and he

must sell for 1500 dollars.

15. The tune of Yankee Doodle was composed by a doctor of the British army to ridicule the Americans in 1755: how many years to the present time?

16. Lord Cornwallis surrendered at Yorktown, and marched into the American lines in 1781 to the tune of Yankee Doodle: how many years was it after the tune was composed? Ans. 26.

17. There are 4338472 children in the United States, between the ages of 5 and 15, of this number 2477667 are in schools: how many are out of schools?

Ans. 1860805. 18. The circulation of the blood was discovered in how many years to 1839 ? Ans. 223. 19. Henry Hudson sailed up the Hudson river in 1609: how many years since?

1616

20. Pliny the historian died 17 years after Christ : how many years before the declaration of independence? Ans. 1759.

21. Potatoes were carried to Ireland from America in 1565: how many years was it before the settlement of Plymouth, in 1620 ?

Ans. 55.

22. If you have 35720 dollars and lose 9100: how many will you have left? Ans. 26620.

23. If you buy 8150 penknives, and lose 1634: how many will you have left? Ans. 6516. 24. The Mariner's Compass was discovered in England in the year 1302: how many years was this before the discovery of America in 1492? How many years to the present time? Ans. 190.

25. If you buy 1853 pounds of raisins, and give away 1370: how many pounds will you have left?

26. Subtract 4261 from 705684.

27. From 8473 take 1528.

28. Subtract 90462372 from 905106392.

Ans. 483.

Ans. 6945.

29. A merchant bought 1675 yards of cloth, for which he paid 5025 dollars; he then sold 335 yards for 1005 dollars: how much had he left, and what did it cost him ?

APPLICATIONS IN ADDITION AND SUBTRACTION.

1. A merchant buys 19576 yards of cloth of one person, 27580 yards of another, and 375 yards of a third; he sells 1050 yards to one customer, 6974 yards to another, and 10462 yards to a third: how many yards has he remaining? Ans. 29045. 2. A person borrowed of his neighbor at one time 355 dollars, at another time 637 dollars, and 403 dollars at another time he then paid him 977 dollars. How much did he owe him? Ans. 418. 3. I have a fortune of 2543 dollars to divide among my four sons, James, John, Henry, and Charles. I give James 504 dollars, John 600 dollars, and Henry 725: how much remains for Charles ?

Ans.

4. I have a yearly income of ten thousand dollars. I pay 275 for rent, 220 dollars for fuel, 35 dollars to the doctor, and 3675 dollars for all my other expenses: how much have I left at the end of the year ? Ans. 5795.

5. A man pays 300 dollars for 100 sheep, 95 dollars for a pair of oxen, 60 dollars for a horse, and 125 dollars for a chaise. He gives in return 100 bushels of wheat worth 125 dollars, a cow worth 25 dollars, a colt worth 40 dollars, and pays the rest in cash what amount of money does he pay? Ans. 390 dollars. 6. A man owing 3456 dollars, paid at one time 350, at another 456, at another 675: how much did he still owe ? Ans. 1975 dollars. 7. There are 12000 dollars in 6 boxes: the first contains 1240; 2d, 1346; 3d, 2012; 4th, 2101; 5th, 346: how much is contained in the 6th ?

8. Tell me the difference between 10000 and 44.

Ans. 9956. 9. The amount of the school fund in Virginia is

1551857 dollars, and in Connecticut 2027402: what is the difference? Ans. 475545 dollars.

10. There are about 805000000 inhabitants in the world. Of this number Asia contains 450000000, Europe 233500000, America 46500000, Oceanica 18000000 : how many in Africa? Ans. 57000000.

11. Suppose you gain 34568 dollars, then 12456; a second time you gain 2467 and lose 2365; and a third time you gain 41210 and lose 39300: how much will you have left?

12. A merchant owes 450120 dollars, and has property as follows: bank stock 350000 dollars, western lands valued at 225100, furniture worth 4000 dollars, and a store of goods worth 96000: how much is he worth? Ans. 224980 dollars. 13. How much greater is 1200, than 365 and 721 added together?

14. What other number with these four, viz., 2100, 3200, 1600 and 1200, will make 10000 ? Ans. 1900. 15. If a man's income is 3467 dollars a year, and he spends 269 dollars for clothing, 467 for house reut, 879 for provision, and 146 for travelling, how much will he have left at the end of the year? Ans. 1706.

16. A man gains 367 dollars, then loses 423; a second time he gains 875 and loses 912; he then gains 1012 dollars: how much has he gained in all ?

Ans. 919 dollars.

17. A merchant paid 39246 dollars for a cargo of molasses, and after selling it found that he had cleared 2406 dollars: for what did he sell it? Ans, 41652.

18. If I agree to pay a man 36 dollars for ploughing 25 acres of land, 200 dollars for fencing it, and 150 for cultivating it, how much shall I owe him after paying 331 dollars? Ans. 55 dollars. 19. A merchant bought 85 hogsheads of sugar for 28675 dollars, paid 1231 dollars freight, and then sold it for 1683 dollars less than it cost him how much did he receive for it?

20. There are 31769000 inhabitants in North America, 14731000 in South America, and in Europe 233500000: how many more in Europe than in the two Americas? Ans. 187000000.

21. If I buy 489 oranges for 912 cents, and sell 125 for 186 cents, and then sell 134 for 199 cents, how many will be left, and how much will they have cost me?

MULTIPLICATION OF SIMPLE NUMBERS.

21. If Charles gives 2 cents apiece for two oranges: how much do they cost him? Ans. 4 cents. If Charles gives 2 cents apiece for 3 oranges: how much do they cost him?

Ans.

If he gives 2 cents apiece for 4 oranges: how much do they cost him? Ans. 8 cents. The cost in each case, may be obtained by adding the price of the separate oranges; thus,

2+2=4 cents, the cost of 2 oranges,

2+2+2=6. cents, the cost of 3 oranges, 2+2+2+2=8 cents, the cost of 4 oranges.

In the first case 2 is taken two times, in the second case it is taken three times, in the third, four times; and in a similar manner any number may be taken as often as we please by adding it continually to itself.

MULTIPLICATION is a short method of taking one number as many times as there are units in another.

The number to be taken is called the multiplicand. The number denoting how many times the multiplicand is to be taken, is called the multiplier.

The number arising from taking the multiplicand as many times as there are units in the multiplier, is called the product.

The multiplicand and multiplier are called factors, or producers of the product.

The sign X, placed between two numbers, denotes that they are to be multiplied together. It is called, the sign of multiplication.

21. What is multiplication? What

the number called which

is to be taken? What does the multiplier denote? What is the product? In the case of the two oranges, which is the multiplicand? Which is the multiplier? Which is the product? In the case of three oranges, which is the multiplicand, which the multiplier, and which the product? What are the multiplicand and multiplier called? How do you denote that two numbers are to be multiplied together? What is the sign called?