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CASE II.

77. When the multiplier is greater than twelve.

1. Multiply 465 by 37.

SOLUTION. We write the multiplier under the multiplicand, units under units, tens under tens, etc. Since 37 equals 7 units and 3 tens, it is evident that 37 times a number equals 7 times the number plus 3 tens times the number. Seven times 465 equals 3255; 3 times 465 equals 1395, hence 3 tens times 465 equals 1395 tens. Taking the sum of the partial products we have 17205. Hence, etc.

OPERATION.

465

37

3255

1395

17205

Rule.-I. Write the multiplier under the multiplicand, placing terms of the same order in the same column, and draw a line beneath.

II. Begin at the right, and multiply the multiplicand by each term of the multiplier, writing the first term of each product under the term of the multiplier which produces it.

III. Add the partial products, and their sum will be the entire product.

Proof. Multiply the multiplier by the multiplicand; if the work is correct this product will equal the first product. NOTES.-1. When there are ciphers between the significant terms of the multiplier, pass over them and multiply by the significant terms alone. 2. We begin at the right to multiply, so that when any product exceeds nine we may add the number expressed by the left hand figure to the next product.

2. Multiply 247 by 24; also by 204.

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1. If a steamer sails 235 miles in 1 day, how far will she sail in 37 days?

SOLUTION.-If a steamer sails 235 miles in 1 day, in 37 days she will sail 37 times 235 miles, or 8695 miles.

OPERATION. 235

37

1645

705

8695

2. How many bushels of potatoes can be raised on 56 acres of land, if each acre produces 196 bushels? Ans. 10,976. 3. How many oranges in 59 boxes, if each box contains 275 oranges? Ans. 16,225 oranges.

4. If a clerk deposits $575 annually in a savings bank, how much will he deposit in 25 years? Ans. $14,375.

5. Mr. Gibbs bought a farm of 95 acres at $187 an acre; what was the cost of the farm?

Ans. $17,765.

6. What will a hogshead of wine, containing 63 gallons,

cost at the rate of $4.25 a gallon?

Ans. $267.75.

7. I bought 356 sacks of Liverpool salt at $2.50 per sack: what did I pay for the whole amount?

Ans. $890.

8. Sold 265 barrels of mess pork at $16.50 a barrel; what did I receive for the whole? Ans. $4372.50.

9. If a locomotive-wheel revolves 478 times in going 1 mile, how often will it revolve in 248 miles? Ans. 118,544. 10. When the market-price of butter is 18 cents a pound, what must I pay for 256 pounds? Ans. $46 08.

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NOTE. In this and similar problems we multiply by the smaller number, using both numbers abstractly, though in the explanation we should use the proper number as the multiplier.

11. If a barrel of flour is worth $8, how much are 596 barrels worth at the same rate?

Ans. $4768. 12. A dealer bought 2875 bushels of potatoes at 37 cents a bushel; what was the cost? Ans. $1063.75.

13. A Western fariner sold 9876 bushels of wheat at 85 cents a bushel; what did he receive? Ans. $8394.60.

14. Henry earned $28 a week and paid $5 for his board; how much could he save in 52 weeks?

Ans. $1196.

15. A travels 25 miles a day, and B 36 miles a day; how far will both travel in 286 days? Ans. 17,446 miles. 16. The President's cabinet consists of 7 members, who receive a salary of $8000 each; what is the amount of their salaries? Ans. $56,000.

17. A dealer shipped 2396 bushels of apples at 87 cents a bushel, and the same quantity of potatoes at 56 cents a bushel; what was the value of both? Ans. $3426.28.

18. A bought 2960 acres of prairie land at $38 an acre, and the same number of acres of woodland at $45 an acre; what did he pay for all? Ans. $245,680.

19. In a row of houses there are 46 rooms, in each room 4 windows, and in each window 12 panes of glass; how many panes in all the houses? Ans. 2208 panes.

20. If Thomas sells 48 papers a day, and Henry 72 papers, how many more papers does Henry sell in 94 days than Thomas? Ans. 2256 papers.

21. In 1852, 157,548 Irish immigrants arrived in the United States; at this rate what would be the number of immigrants from the beginning of 1852 to the end of 1875 Ans. 3,781,152.

22. If two persons should start from the same place and travel in opposite directions, one at the rate of 45 miles a day and the other at the rate of 67 miles a day, how far will they be apart in 67 days? Ans. 7504 miles.

23. A planter put up his cotton into 275 bales, averaging 576 pounds each, and sold it at 15 cents per pound; what I did he receive for the whole? Ans. $23,760.

24. Mr. Angell's annual income is $9750, and his average daily expenditure is $9.75; what can he save in a year of 365 days? Ans. $6191.25.

25. A bank teller receives $2500 saiary, and spends $520 for board, $475 for clothing, $112.65 for books, and $117.25 for other expenses annually; how much will he save in 5 years? Ans. $6375.50.

26. How many miles will a railroad conductor travel in a year if he makes a trip from Harrisburg to Philadelphia (106 miles) and back, every day except Sundays, reckoning 52 Sundays to a year? Ans. 66,356 miles.

27. A shoe-dealer bought 35 cases of French calf boots, each case containing 12 pairs, at $6.50 a pair; what did the bill amount to? Ans. $2730. 28. A division consisted of 4 regiments, each regiment of 9 companies, and each company of 98 men; how many men in the division? Ans. 3528 men.

29. In a block of houses there are 45 buildings, each building containing 32 windows, and each window 12 panes of glass; how many panes of glass in the whole block of buildings? Ans. 17,280 panes.

30. If it requires 124 tons of iron worth $72 a ton to builJ one mile of a railroad, what will be the cost of iron enough to build a railroad 236 miles long? Ans. $2,107,008.

31. A field contains 5076 rows of corn, each row containing 4005 hills, and each hill 4 stalks; how many stalks of corn in the field? Ans. 81,317,520 stalks.

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