24. The product of two numbers is 2350275 tons, and the multiplier is 6. What is the multiplicand?

25. Find the quotient of seven million, twenty thousand, nineteen divided by seven; by six; and by nine.

26. Divide ten million, fifty thousand, four hundred by three; by five; by seven; and by nine.

Find one of the 27. 4 equal parts of 12505. 28. 6 equal parts of 23457. 29. 5 equal parts of 35790.

30. 7 equal parts of 46790. 31. 8 equal parts of 56789. 32. 9 equal parts of 13579.

33. The sum of the eight equal parts of a number is 287650 dollars. What is one of the parts?

34. If 8 miles of railroad cost $135000, what was the average cost per mile? If they cost $250000?

35. How many barrels of flour can be made from 2570250 bushels of wheat, if 5 bushels make one barrel?

36. A grain-dealer shipped 125000 bushels of wheat in 4-bushel sacks. How many sacks did he fill?

37. When sugar is worth $9 a hundred, how many hundred pounds can be bought for $135135?

38. The national debt of the United States was at one time $2300000000. How much would have been required each year to have paid it in 7 equal yearly payments?

LONG DIVISION.

Problems.

Find the quotient of—

1. 8070624; 50607 ÷ 26; 6050428; 40506 ÷ 30. 2. 9700533; 75003 ÷ 35; 53001 ÷ 37; 31009 ÷ 39. 3. 908060708; 807060809; 706050 ÷ 908.

4. 50000 yards ÷ 53; 70000 acres ÷ 57; $9000 ÷ 63.

5. 200304 pounds 234; 500790 barrels ÷ 567.

6. 305006 miles

456; 406335 cattle 789.

How many times is

7. 68 contained in 6985? In 60985? In 160985?

8. Find the quotient of 40500 divided by 89; by 809. 9. What remains after dividing $304005 by 876? 10. 4005006 square feet 890 gives what remainder? 11. Divide 608040 by 56; by 67; by 78; by 89. 12. Divide 6008004 by 506; by 607; by 708.

13. Find the quotient of thirty-two thousand, ninety-eight divided by nine hundred eighty-seven.

14. How many times does four million, four hundred thousand, contain one thousand, fourteen?

15. What is the quotient of thirty million, thirty thousand, thirty divided by two thousand, thirty-four?

16. How many remain after dividing sixty million, sixty thousand, six hundred by three thousand, fifty-six?

Find the quotient of

17. 20405 200; 90087 ÷ 400; 30560 ÷ 600. 18. 80076230; 45006 ÷ 340; 76050 ÷ 560. 19. 357000 pounds 2000; 1357090 tons

9000.

20. 246809 divided by 30, by 450, by 506, by 6700. 21. What is one-tenth of 375? One-hundredth of 7965? 22. What number is equal to 79500 ÷ 4000? 23. A carriage-maker received $15000 for light carriages at $200 each. How many carriages did he sell? 24. There are 480 sheets in a ream. How many reams will 259200 sheets make? How many will 242880 sheets

make?

25. 640 acres make a square mile. How many square miles in Pennsylvania, which contains about 29440000 acres?

26. How many regiments averaging 750 men will make an army of 45000 men? An army of 64125 men?

27. At $1750 per car, how many cars can a railroad company buy with $52500? With $78750?

28. How many city lots at $2500 each can be bought for $227500? How many for $267500?

29. A cord of wood contains 128 solid feet. How many cords are in a pile containing 12750 solid feet?

30. The earth moves round the sun at the rate of about 11491200 miles in 168 hours. What is the rate per hour? 31. The average daily receipts of a ferry-boat are $275. In how many days will the receipts amount to $50000?

32. If 245 bushels of wheat weigh 14945 pounds, what is the average weight per bushel?

33. Mount Everest in Asia is about 29000 feet high. How many miles high is it, each mile being 5280 feet?

34. Divide 400070009 by 5607; by 6708; by 7809? 35. Divide 20030040 by 60708; by 70809; by 90705. 36. Divide 560780900 by 69584; by 72839; by 89076. 37. The product of two numbers is 99876540, and one of the numbers is 98765. What is the other?

38. The dividend is 8705003750, and the quotient is 96075. What is the divis?

SECTION VI.

Miscellaneous Problems.

1. To 4 add 8, subtract 3, multiply by 5, divide by 9, subtract 5. What remains?

2. From 14 take 5, add 2, multiply by 6, divide by 3, subtract 7, multiply by 6. What is the result?

3. Divide 49 by 7, multiply by 6, subtract 7, add 15, divide by 10, add 8. Result?

4. The quotient is 10, the remainder is 8, and the divisor is 12. What is the dividend?

5. A grocer bought 7 barrels of flour at $6 a barrel. For how much a barrel must he sell it to gain $14 on the lot?

6. If you earn 9 dollars a week, and pay 5 dollars for board, and 2 dollars for other expenses, how much will you lay up in 8 weeks? How much in 12 weeks?

7. A trader bought 12 pairs of shoes at $3 and 6 hats at $4, and paid for them in 5-dollar bills. How many did it take? How many 10-dollar bills would it have taken?

8. If 5 oranges are worth 25 cents, and 6 lemons are worth 42 cents, how much more is a lemon worth than an orange. How much are an orange and a lemon worth?

9. A furniture-dealer bought 8 tables for $40, and sold them at $6 each. How much did he clear?

10. How many pounds of rice at 10 cents a pound will cost as much as 6 pounds of sugar at 15 cents?

11. If 5 masons lay a wall in 12 days, how many men would be required to lay it in 3 days? In 4 days?

12. What is the cost of 18 quarts of milk, at the rate of 40 cents for 5 quarts? The cost of 25 quarts?

13. A miller bought 10 bushels of wheat for $20, and I bought 12 bushels at the same rate. How much did I pay?

14. If 5 barrels of flour will pay for 10 bushels of wheat

at $3 a bushel, what is the flour worth per barrel?

15. How many 4-quart cans of milk can be filled from five 8-quart cans? From six 12-quart cans?

16. In how many days can 7 men earn as much as 5 men can earn in 14 days? As much as 4 men in 21 days?

17. If four 10-dollar bills are paid for 8 yards of cloth, what is the price per yard?

18. A butcher bought 2 calves at $9 each, and one calf for $12. What was the average cost?

Find the value of19. 54X (9-6).* 20. (54) X 8-5. 21.43X (8-5).

22. 7(193) X (4-3). 23. 719-34-3.*

24. 719-3X4-3.

25. Find the sum of 65 X 76 and 6764 ÷ 89.
26. From 752476 take 8765 - 8678.
27. Multiply 7865+ 5678 by 139725

405.

28. Find the value of (75 + 25 × 25 — 50) × 205. 29. What is the result of 174225 ÷ 345 + 20 × 75? 30. Divide the product of 98 times 765 by the sum of 1865 and 2035 less 3543.

31. Divide 13230 by 98, subtract the quotient from 76 times 67, and to the remainder add one-sixth of 258.

32. From 7531 take 1357, multiply the remainder by 25, and divide the product by 725.

33. A man bought 75 acres of land at $90 an acre, paid $325 for improvements, and then sold it for $8675. How much did he gain per acre?

34. A and B started on a journey, A traveling 29 miles

NOTE. When figures are enclosed in parenthesis marks, as (9—6) Ex. 19, or marked with a vinculum or line over them, as 19-3, Ex. 23, the operation indicated is to be performed and the result used instead of the original figures thus, in Ex. 19 (96) 3, and the example will then stand 5 + 4 X 3. Operations of multiplication and division must be performed before those of addition and subtraction, unless parenthesis indicate otherwise (see Notes pp. 14 and 18).

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