22. A manufacturer sold 328 self-binding reapers at $469 each. How much did he receive for them?

23. If 1 barrel of flour weighs 200 pounds, what will 760 barrels weigh?

24. What will 894 bushels of wheat weigh if 1 bushel weighs 60 pounds?

25. A farmer bought 207 acres of land at $80 per acre. What was the cost?

26. In 1 hogshead there are 63 gallons. How many gallons are there in 3267 hogsheads?

27. How many cubic inches are there in 2362 gallons, if 1 gallon contains 231 cubic inches?

28. If in 1 bushel of apples there are 56 pounds, how many pounds are there in 942 bushels?

29. Find the cost of 2450 bushels of wheat at 85 cents per bushel.

30. If a man takes 30300 steps each day for 260 days, how many steps does he take?

31. If a boy writes 1605 words an hour, how many words will he write in 40 days by working 12 hours each day?

32. A man bought 420 loads of corn, 36 bushels in each load. How many pounds did he buy if each bushel weighs 56 pounds?

33. I sold 18 carloads of hogs, 35 hogs in each car, at 10 cents per pound. The hogs averaged 320 pounds. How much did I receive for the whole lot?

SPECIAL CASES IN MULTIPLICATION

a. To multiply by 10, 100 or 1 with any number of ciphers following.

b. To multiply when the multiplier has ciphers at the right. c. To multiply when there are ciphers at the right of cach

term.

one.

d. To multiply when the unit figure of the multiplier is one. e. To multiply when the left-hand figure of the multiplier is

f. To multiply by 11, 22, etc.

g. Cross multiplication.

910.

a. 32 × 100

=

Illustration

32 and the addition of two ciphers, or 3200. EXAMPLES.-49 X 100; 53 X 10; 645 X 10; 327 × 100.

b. 24 X 909 X 24 and the addition of one cipher, or 2160. EXAMPLES.-25 × 80; 84 × 600; 36 × 200; 71 × 800.

c. 90 × 809 X 8 and the addition of two ciphers, or 7200. EXAMPLES. 240 X 30; 3600 X 900; 2500 X 2500; 90 X

EXAMPLES. 294 X 31; 846 X 51; 327 X 601; 426 X 701. e. 374 X 16

=

374 X 16

2304

6044

EXAMPLES.-427 X 17; 375 X 104; 724 X 19; 562 X 109. f. 3452 X 11

= 37972.

Write 2 as the first figure, (5+ 2) as the second, (5+ 4) as the third, (34) as the fourth and 3 as the fifth. Carry when necessary.

To multiply by 33, multiply each addition by 3, then add the carrying number.

EXAMPLES. 3463 X 11; 4234 X 22; 3714 X 33; 4637 X 55; 9876 X 11; 7964 X 66.

g. 64 × 76 =4864.

=

(6 X 14) units. Write the 4 and carry the 2. 2 + (6 × 6) + (4 X 7) = tens' place. Write the 6 and carry the 6+ (6 × 7) = hundreds' place; 4864 the desired result.

PROBLEMS IN ADDITION, SUBTRACTION AND

MULTIPLICATION

50. 1. Bought 230 bushels of corn at 40 cents a bushel and 365 bushels of wheat at 80 cents a bushel. What did both cost?

2. A teacher receives a salary of $1300 a year and pays $360 for board, $200 for clothing, $100 for books and $45 for other expenses. What does he save in the year?

3. A merchant bought 288 barrels of flour for $1960 and sold it at $8 a barrel. How much did he gain?

4. A farmer bought 34 head of cattle at $18 a head and sold them at $21 a head. How much did he gain by the operation?

5. A lawyer has an income of $4325 a year, and his daily expenses are $4. What will he save in a year of 365 days? 6. A sold a farm of 360 acres at $45 an acre; B sold one of 280 acres at $60 an acre. Which received the greater sum, and how much?

7. A farmer sold 263 bushels of wheat at $1 a bushel. He received in payment 23 yards of cloth at $4 a yard, and the balance in groceries. What did, the groceries cost him?

8. I sold 17 cows at $36 apiece and for them received 65 tons of hay at $9 a ton and the remainder in money. How much money did I receive?

9. A man bought a house for $2867. He expended in repairing it $16 for plumbing, $73 for carpenter work, $48 for painting. He then sold the house for $3265. What did he gain?

10. Two persons start from the same point and travel in opposite directions, one at the rate of 45 miles a day and the other 36 miles a day. How far apart will they be in 16 days?

11. A dealer bought 535 barrels of pork at $8 a barrel. He sold 245 barrels of it at $10 a barrel and the remainder at $7 a barrel. What did he gain or lose?

12. Mr. Brown has an income of $12650 a year. He spends $1650 for house rent and twice as much for other expenses. How much does he save in a year?

13. A sold 3 houses. For the first he received $2875, for the second $230 more than the first, and for the third as much as the first two. How much did he receive for all?

14. Mr. C bought 14 cows at $23 each, 7 horses at $96 each, 34 oxen at $57 each, and 300 sheep at $2 each. He sold the whole for $3842. What did he gain?

15. A merchant having $7632 deposited in his bank, drew out for the purchase of dry-goods, $1867; groceries, $362; boots and shoes, $218; hardware, $160. What amount had he left in the bank?

DIVISION

51. Division is finding how many times one number is contained in another.

52. The Dividend is the number to be divided.

53. The Divisor is the number by which to divide.

54. The Sign of division is a short horizontal line with a dot above and one below it. The divisor follows the dividend as $62 or $6 $2. It may be written $6, 2)$6, or $6 (2.

2

55. The Quotient is the number obtained by dividing, and shows how many times the divisor is contained in the dividend.

1. When the dividend does not contain the divisor an exact number of times, the part of the dividend left is called the remainder, and it must be less than the divisor.

2. As the remainder is always a part of the dividend, it is always of the same name and kind.

3. When there is no remainder, the division is said to be exact.

4. When the process of dividing is performed mentally, and the results only are written, the operation is termed Short Division.

5. When the whole process of division is written, the operation is termed Long Division.