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MISCELLANEOUS EXAMPLES.

1. The sun is 95000000 miles from the earth; the moon is 240000 miles. How much farther from us is the sun than the moon? Ans. 94760000 miles.

2. A man worth $10000 gains $1000 by one sale, and loses $500 by another. What is he then worth? Ans. $10500. 3. If the railroad from Albany to Buffalo, 326 miles in length, cost $25649 a mile, what was the whole cost?

Ans. $8361574. 4. How far will a locomotive travel in 7 days of 24 hours each, if it goes 30 miles an hour? Ans. 5040 miles.

5. A man left each of his 3 daughters 510 acres of land, and his wife 100 acres more than all his daughters together. What was the wife's portion? Ans. 1630 acres.

6. A farmer raised 1570 bushels of potatoes, and bought 730 bushels more. After selling 4 lots of 500 bushels each, how many bushels had he on hand? Ans. 300 bushels.

7. How many hours in 365 days of 24 hours? Ans. 8760. 8. The earth moves in its orbit 68000 miles an hour; how far will it move in 365 days? Ans. 595680000 miles.

9. The President's salary is $25000. If he spends $19500 a year, how much will he save during his 4 years' term? How much will he save in 1 year? How much, then, in 4 years?

Ans. $22000. 10. A has 1060 sheep; B has 849; C has 1276. How many must C buy, to have as many as A and B together? Find how many A and B have. Then find the difference between this number and C's. Ans. 633 sheep.

11. Daniel Webster was born in 1782 and died in 1852.

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How old was he?

12. At $3 a yard, what will 101 pieces of cloth cost, if each piece contains 40 yards?

Ans. $12120.

MISCELLANEOUS EXAMPLES.

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13. If a ship sails east from port 350 miles a day for 4 days, and is then driven west 289 miles, how far is she from port? Ans. 1111 miles.

14. John has 31 marbles; James has 6 times as many; Henry has as many as John and James together. How many marbles have they all? Ans. 434 marbles.

15. What cost 100 wagons, at $75 apiece?

16. Find the product of 8089 and 9007. Subtract this product increased by 377, from 100000000. Ans. 271420000.

17. Trinity Church, N. Y., is 284 feet high. St. Peter's at Rome is 166 feet higher; what is its height?

18. A man who has $1201 in the bank, draws out enough to pay for 5 lots of land at $195 a lot. How much is left in the bank? Ans. $226.

19. North America contains 8000000 square miles; South America, 7000000; Asia, 1000000 more than both Americas together. How many square miles in Asia? Ans. 16000000.

20. An army of 12100 men lost 631 in killed and wounded, and twice that number taken prisoners. How many were left? Ans. 10207 men. 21. In a school of 127 boys, four times as many study The Latin class numbers 28; Ans. 112 boys.

Arithmetic as study Latin. how many study Arithmetic?

22. What is the cost of a carriage and span of horses, if each horse cost $235, and the carriage $679? Ans. $1149.

23. A boat makes 208 trips in a season, and carries on an average 106 passengers each trip; how many does she carry in all? Ans. 22048 passengers.

24. Find the cost of 53 mules, at $100 apiece.

25. A grocer who has 15 firkins of butter, containing 56 pounds each, sells four of his customers 240 pounds. How much has he left? Ans. 600 pounds.

DIVISION.

83. If 2 apples can be bought for 1 cent, how many cents will 6 apples cost?

2 apples cost 1 cent; hence 6 apples will cost as many cents as 2 is contained times in 6. Here we are required to find how many times 2 is contained in 6. This process is called Division.

84. Division is the process of finding how many times one number is contained in another.

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83. Repeat the example. What are we here required to do? What is this process called?-84. What is Division? How many times is any number contained in 0? Recite the Table.

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85. The number to be divided, is called the Dividend; that by which we are to divide, the Divisor. The result, or number obtained by dividing, is called the Quotient. It shows how It shows how many times the divisor is contained in the dividend.

2 is contained in 6, 3 times; 2 is the divisor, 6 the dividend, 3 the quotient.

86. The divisor is not always contained an exact number of times in the dividend. It may go a certain number of times, and some over. What is left

over is called the Remainder.

5 is contained in 15 exactly 3 times. In 16 it goes 3 times, and 1 over; 3 is the quotient, 1 the remainder.

85. What is the number to be divided called? What is that by which we are to divide called? What is the result obtained by dividing called? What does the quotient show? Illustrate these definitions.-86. What is meant by the Remainder? Give an example.

87. Division is denoted by a short horizontal line between two dots ÷. This sign indicates that the number before it is to be divided by the one after it. 6÷2 is read, and denotes, six divided by two.

MENTAL EXERCISES.

How many times is 3 contained in 9? 11 in 99? 4 in 32? 9 in 81? 6 in 42? 11 in 55? 5 in 30? 12 in 96? 8 in 72?

How many times is 4 contained in 23?

10 in 40?

7 in 56?

2 in 18?

12 in 36?

7 in 0?

(Ans. 5 times, and

3 over.) 2 in 5? 6 in 27? 9 in 20? 8 in 39? 3 in 10? 4 in 29? 5 in 38? 10 in 44? 6 in 59? 12 in 75?

What is the quotient, and what the remainder, in the following? 34÷4. 31÷6. 22÷8. 108÷12. 37÷5. 13÷3. 65÷9. 0÷4. 89÷10. 8÷5. 43÷8. 72÷9. 47÷11. 72 ÷8. 24÷3. 24÷8. 64÷12. 28÷÷10. 81÷11.

1. If 64 cherries are divided into 8 equal piles, how many will there be in each pile?

MODEL.-As many cherries as 8 is contained times in 64, or 8. Answer, 8 cherries.

2. Twenty-one cents are distributed equally among 7 beggars. What is the share of each?

3. How many coats, at $5 apiece, can I buy for $20?

4. John's father gave him 18 pears, to be divided equally among his two sisters and himself. How many did each get? 5. How many bushels are there in 16 pecks, there being 4 pecks in 1 bushel?

6. Twelve make a dozen. How many dozen in 24?

7. Allowing 8 yards of calico for a dress, how many dresses can be made out of 40 yards?

87. How is division denoted? What does this sign indicate?

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