30. A drover paid 300 dollars for 100 sheep, 525 dollars for 150 sheep, and 1000 dollars for 250 sheep. How many did he buy? What did the whole cost?

31. What is the sum of two million, five hundred thirty-one thousand, one hundred and twenty-fourteen thousand, thirty thousand and twenty-four,-five hundred and sixty, and seven hundred and two?

32. The inhabitants of the British Islands are stated thus: England, 11 260 555; Wales, 717 103; Scotland, 2092014; Ireland, 6 846 949; Army and Navy, 310 000; Isle of Man, 40 981; Guernsey, 20 827; Jersey, 28 600; Scilly Isles, 2 614. What is the whole number?

33. The inhabitants of the United States, by the census of 1840, were stated thus: Maine, 501 793; New Hampshire, 284 574; Massachusetts, 737 699; Rhode Island, 108 830; Connecticut, 309 978; Vermont, 291 948; New York, 2428 921; New Jersey, 373 306; Pennsylvania, 1724 033; Delaware, 78 085; Maryland, 470 019; Virginia, 1 239 797; North Carolina, 753 419; South Carolina, 594 398; Georgia, 691 392; Alabama, 590756; Mississippi, 375 651; Louisiana, 352 411; Tennessee, 829 210; Kentucky, 779 828; Ohio, 1 519 467; Indiana, 685 866; Illinois, 476 183; Missouri, 383 702; Arkansas, 97 574; Michigan, 212 267; Florida, 54 477; Wiskonsan, 30 945; Iowa, 43 112; District of Columbia, 43 712. What was the whole number?

Questions to be answered Orally.

(1) When you have several numbers to add together, in what order do you write them? (2) Which column do you add first? (3) Do you add all other columns in the same manner that you add the first? (4) When the sum of any column is less than 10, where is it to be written? (5) When the sum of any column is more than 9, what is to be done? (6) Why do we carry as many ones to the next left hand column, as there are tens in any column that we have added? (7) Recite the rule for addition.

CHAP. III.

SUBTRACTION.

SECTION 1.

1. Subtract 632 from 1847; that is, take 632 from 1847, and find what number remains.

1847 632 1215

We first write the smaller number under the greater. Then, take 2 units from 7 units, 3 tens from 4 tens, 6 hundreds from 8 hundred, and nothing from 1 thousand.

Subtract the smaller number from the greater in each of the following examples.

(4). 4258 (5). 705684

3215

4261

6. A farmer having 359 sheep, sold 136 of them, and kept the remainder. How many did he keep?

7. A trader having 2748 dollars, laid out 2616 dollars for goods. How many dollars had he remaining?

8473 1528 6945

SECTION 2.

1. Subtract the number 1528 from the number 8473. We unite 1 of the 7 tens with the 3 units, making 13 units, and say, 8 from 13, leaves 5. Then, having used 1 of the 7 tens, we take 2 tens from 6 tens. In the same way we take 5 hundreds from 14 hundreds. Do not pass from the above example without understanding it. Whenever an upper figure is smaller than the figure under it, we use 1 from the next upper figure, and this 1 becomes 10 when considered with the right hand figure. Arithmeticians commonly call this process, borrowing 10; and, instead of reckoning the figure from which they hay borrowed to be 1 less than it stands, they pay 1 to the figure under it-reckoning the lower figure to be 1 more than it stands.

I

Perform subtraction in the following examples. (2). 1853 (3). 5264 (4). 2657

1370

762

349

(5). 6807 4096

6. Subtract 1268 from 1503.

1503
1268

235

In subtracting the 8 units, we use a ten, that we obtain by supposing 1 of the 5 hundreds, (which is 10 tens,) to be where the O is. Then, naving used 1 of the 10 tens, we presently subtract 6 tens from 9 tens.

7. Subtract 1146 from 2601. 8. Subtract 5428 from 8019. 9. Subtract 258 from 34307.

RULE FOR SUBTRACTION.

Write the smaller number under the greater, placing units under units, &c. Begin with the units, and subtract each figure in the lower number from the figure over it. When a figure in the upper number is smaller than the figure under it, consider the upper figure to be 10 more than it is, and the next upper figure on the left hand, to be 1 less than it is.

PROOF. Add together the remainder and the smaller number: their sum will be equal to the greater number, if the work be right.

10. Find the difference between 39 and 64, by subtracting the smaller number from the greater.

11. What is the difference between 464 and 502? 12. What is the difference between 99 and 200?

13. What is the difference between 35720 and 9100? 14. Subtract 44 from 10000.

15. I deposited 1450 dollars in the bank, and I have since drawn out 835 dollars. How many dollars have I remaining in the bank?

16. Suppose a man owes 1634 dollars, and possesses property to the amount of 8150 dollars; how much will he have left, after paying his debts?

17. Subtract sixty-two thousand five hundred and seven, from one million eighty thousand and forty-four

18. The number of inhabitants in the city of London is 1 250 000; the number in the city of Paris is 750 000. How many more are there in London, than in Paris?

19. The population of Great Britain and Ireland is 21 500 000; the population of France is 32 000 000. How many more inhabitants are there in France, than in Great Britain and Ireland?

20. The Rocky Mountains, in North America, rise 12 500 feet above the level of the ocean; the Andes, in South America, rise 21440 feet. How many feet higher are the latter, than the former?

21. A merchant paid 13 745 dollars for a ship, and sold it for 15 150 dollars. What did he gain?

22. A farmer sold a piece of wood-land for 396 dollars, which was 78 dollars more than he gave for it How much did he give for the land?

23. Columbus discovered America in the year 1492. How many years is it since the discovery?

24. The United States declared Independence in the year 1776. How many years since the declaration?

25. A man bought 20 casks of wine, containing 2459 gallons, and sold 14 casks containing 1682 gallons. How many casks, and how many gallons were left?

26. There are two numbers, whose difference is 758; the greater number is 1524. What is the smaller number?

Questions to be answered Orally.

(1). How can you find what the difference is between two numbers? (2) When one number is to be subtracted from another, in what order must the numbers be written? (3) In what place do you begin to perform the subtraction? (4) When a figure in the upper number is smaller than the figure under it, what is to be done? (5) Where does the remainder appear, after the subtraction is performed? (6) Recite the rule for subtraction. (7) How can you prove that an operation in subtraction is performed correctly?

SECTION 3.

MISCELLANEOUS EXAMPLES.

1. A man owing 379 dollars, paid at one time 47 dollars, at another 23, at another 84, and at another, 143. How much did he still owe?

2. There are 1000 dollars in 4 bags; the first bag contains 230 dollars, the second 245, the third 270. What is contained in the fourth bag?

3. Suppose the world to have been created 4004 years before the Christian era, how old is it at this date? 4. A man having in his desk 2000 dollars, took out 120 dollars to pay a debt, and afterwards put in 75 dols. How much was there remaining in the desk?

5. A merchant bought a ship for 11 240 dollars, paid 305 dols. for repairing it, and sold it so that he lost 95 dols. For how much did he sell it?

6. What is the sum of 58, 45, and 70? Then, if you subtract 43 from this sum, what will be the remainder? 7. A merchant, who had 650 barrels of flour, sold 95 barrels to one man, 38 to another, and 225 to another How many barrels had he left?

8. A jockey bought a horse for 115 dollars; he exchanged him for a better horse, paying 23 dollars, and then sold the better one for 137 dollars. Did he gain or lose? and how much?

9. If 654 be subtracted from 10000, and then 29 670 be added to the remainder, what will be the sum?

10. A gentleman gave 972 dollars for a carriage and two horses; the carriage was valued at 525 dollars. What was the value of the horses?

11. Dr. Franklin died in the year 1790, and he was 84 years old when he died. In what year was he born?

12. A clerk went out with 240 dollars, to settle some accounts: he paid 126 dollars to one man, received 37 dollars from another, and paid 94 dollars to another How many dollars had he then?

13. Add together two hundred, sixteen thousand, thirteen million, and seven billion; and then subtract ten housand from the sum.