50. A drover bought 6 head of cattle at an average cost of $37.45 a head. How much did he pay for them?

51. Mr. A bought 8 acres of land at $45.75 per acre. How much did the land cost him?

52. If a firkin of butter costs $13.85, what must be paid for 5 firkins?

53. There are 5280 feet in a mile. How many feet are there in 6 miles ?

54. There are 3600 seconds in 1 hour. seconds are there in 8 hours?

How many

55. What will 7 tons of railroad iron cost at $64.25 a ton?

56. A merchant sold 9 bales of cotton at $37.60 a bale. How much did he receive for it?

57. At a public sale 8 tons of hay were sold for $7.85 per ton. How much was paid for the hay?

58. A party of 6 persons hired a schooner, paying $3.75 apiece for the use of it. How much did all pay?

59. What will be the cost of 7 organs, if each organ is worth $65.75 ?

60. At $75.35 each, what must be paid for 8 wagons? 61. At an average weight of 1267 pounds each, what will 7 oxen weigh?

62. How many bricks can be carried in 6 loads, if 1024 bricks are hauled at a load?

63. A lot cost $575. How much will 7 lots cost at the same rate?

64. A family of 3 persons boarded in Albany for 3 weeks at the rate of $4.75 a week for each person. What was the cost of their board for the whole time?

ORAL EXERCISES.

70. 1. How many are 10 times 5? 5 times 5?

2. Since 10 times 5 are 50, and 5 times 5 are 25, how many are (10+5), or 15 times 5?

3. How many are 10 times 8? 4. How many are 10 times 6? 5. How many are 10 times 7? 6. How many are 12 times 4? 7. How may a number be most conveniently multiplied by 15?

2 times 8?

12 times 8?

4 times 6?

14 times 6?

2 times 7?

12 times 7?

12 times 5?

12 times 3?

8. How many are 10 times 9 plus 2 times 9, or 12 times 9?

9. A foot contains 12 inches. How many inches are there in 12 feet?

10. A pound of sugar weighs 16 ounces. ounces do 12 pounds weigh?

How many

11. What will 12 dozen eggs cost at 17 cents per dozen? 12. The fare upon the railroad from a certain city to another is $18. How much will 12 tickets cost?

13. What will 18 tons of hay cost at $11 per ton?

14. What will 12 pounds of beefsteak cost at 18 cents a pound?

15. How much will 13 brooms cost at 22 cents each?

16. A farmer who owned 15 cows owned 15 times as many sheep. How many sheep did he own?

17. A man earned $18 per week for 16 weeks. How much did he earn in all?

18. A lady purchased 15 yards of cloth, paying 18 cents per yard for it. How much did she pay for the whole?

19. How many sheets of paper are there in 15 quires, since each quire contains 24 sheets?

20. What time will be required to walk 13 miles, if it requires 15 minutes to walk one mile?

21. A man deposited $15 per month in a savings bank. How much did his deposits amount to in a year?

22. A circular railroad is 18 miles in length. How far does a train run which makes the circuit 15 times in a day? 23. A stair has 15 steps. How many steps does a person take who goes up and down it 8 times per day?

24. How many are 10 times 5? 10 times 6? 10 times 7? 25. What is annexed to a number when it is multiplied by 10?

26. How many are 100 times 2? 100 times 3? 100 times 4?

27. What is annexed to a number when it is multiplied by 100?

28. How many are 1000 times 2, or 2 times 1000? 1000 times 5, or 5 times 1000? 1000 times 9, or 9 times 1000? 29. How is a number multiplied by 1000?

30. How is a number multiplied by 1 with ciphers annexed?

71. PRINCIPLE.

A number is multiplied by 10, 100, 1000, etc., by annexing to the multiplicand as many ciphers as there are in the multiplier.

7. What is the product of 3486 × 6000?

3486 6000 20916000

EXPLANATION. - Since 6000 is equal to 1000 times 6, 3486 is first multiplied by 6, giving a product of 20916, and then that result is multiplied by 1000 by annexing three ciphers.

EXPLANATION.

264

142

528 10560 26400

37488

- For convenience, the multiplier is written under the multiplicand, units under units, tens under tens, etc.

Since we cannot multiply by 142 at one operation, we multiply by the parts, and then add the products. The parts by which we multiply are 2, 4 tens, and 1 hundred.

2 times 264 equal 528, the first partial product; 4 tens, or 40, times 264 equal 10560, the second partial product; 1 hundred, or 100, times 264 equal 26400, the third partial product, and the sum of these, 37488, is the entire product.

EXPLANATION. -The ciphers at the right of the partial products may be omitted, the significant figures occupying their proper places without the ciphers.

264

142

528 1056

264

37488

RULE.

Thus, in multiplying by 4 tens, the lowest order in the product is tens; hence the first figure of the product is written under tens, and the rest in their proper order.

In multiplying by hundreds, the lowest order of units in the product is hundreds; hence the first figure of the product is written under hundreds, and the rest in their proper order.

Write the multiplier under the multiplicand, with units under units, tens under tens, etc.

Multiply each figure of the multiplicand by each significant figure of the multiplier successively, beginning with units. Place the right-hand figure of each product under the figure of the multiplier used to obtain it, and add the partial products.

PROOF. Review the work, or multiply the multiplier by the multiplicand. If the results agree, the work is probably

correct.

When there is a cipher in the multiplier, multiply by the significant figures only, taking care to place the first figure in the product under the figure of the multiplier used to obtain it.