onds in one day, and 365 days in a year, light moving at the ate of 192,500 miles a second? Ans. 42494760 millions.

7. A wholesale druggist bought as follows: 500 lb. opium at $7.20 per lb.; 375 lb. morphine at $4.75 per lb.; 240 lb. quinine, at $2.70 per lb.; 200 lb. camphor, at $0.29 per lb.; what was his whole bill? Ans. $6087.25.

8. A clerk's salary is $1500 a year; he pays $5 a week for his board and washing, $4 a month for car fare, and his other expenses amount to about $2 a day; how much can he save in a year? Ans. $462.

9. Mrs. Wilson bought at a furniture store an oiled walnut chamber set for $150, two cottage sets for $55 each, a dozen dining-room chairs at $3.50 each, and 3 camp chairs at $4.25 each; what was her bill? Ans. $314.75.

10. A shipping firm bought 150 lb. Manila bolt rope yarns at 16 cents per lb.; 450 lb. Manila whale lines at 17 cents a pound; 260 lb. Russia hemp tarred cordage, at 13 cents per lb.; and 850 lb. Sisal rope at 11 cents per lb.; what was the whole cost? Ans. $227.80.

11. A dry goods merchant sold to a Western customer as follows; 125 yards Cocheco fancy prints, at 7 cents a yard; 147 yards Cocheco robes, 8 cents; 156 yards Merrimac robes, 8 cents; 122 yards Merrimac checks and stripes, 7 cents; 125 yards French cashmeres, $1.15; what was the amount of the bill? Ans. $185.28.

12. James Chauncey & Co. sold to Barton Brothers, Dec. 23, 1875, the following: 450 bushels White Western oats, at 38 cents a bushel; 375 bushels New York No. 2 White oats, 43 cents; 240 bushels choice new Southern Black-eye peas, $1.45. Jan. 10, 1876, J. C. & Co. bought of Barton Brothers, 460 bushels Pennsylvania rye, 91 cents; 175 bushels No. 2 Canada barley, $1.10; 720 bushels common Winter Red Western wheat, $1.25; required the balance of the account. Ans. $830.85 favor of Barton Brothers.

INTRODUCTION TO DIVISION.

MENTAL EXERCISES.

1. At 3 cents each, how many melons can I buy for 15 cents? SOLUTION.-If 1 melon costs 3 cents, for 15 cents I can buy as many melons as 3 is contained times in 15, which are 5.

2. How many yards of ribbon, at 8 cents a yard, can be bought for 56 cents?

3. A man gave 60 dollars for sheep, at the rate of 5 dollars a head how many did he buy?

4. How many kegs, of 9 gallons each, can be filled from a hogshead containing 90 gallons of vinegar?

5. How many days must a man work, at the rate of $3 a day, to earn $45?

6. How many lemons at 6 cents apiece may be bought for 84 cents?

7. How many are 15 plus 5, divided by 5? 18 plus 6, divided by 6? 40 plus 8, divided by 8? 35 plus 7, divided by 7?

8. How many are 3 times 8 divided by 4? 5 times 9 divided by 3? 6 times 10 divided by 12? 8 times 7 divided by 4?

9. How many are 3 times 33 divided by 11? 4 times 21 divided by 7? 3 times 25 divided by 5? 3 times 24 divided by 8?

10. How many pencils, worth 5 cents each, may be bought for 4 erasers worth 15 cents each ?

11. How many barrels of flour, at $9 a barrel, can be bought for 15 barrels of apples at $3 a barrel ?

12. A woman carried to the store 6 dozen eggs at 25 cents a dozen; how many yards of calico, at 10 cents a yard, will pay her?

13. If mackerel is worth $12 a barrel, how many barrels can be bought for $6 in money and 6 barrels of pork at $15 a barrel?

14. The process of finding how often one number is contained in another is called division. The result is called the quotient.

15. The number divided is the dividend; the number we divide by is the divisor. The sign of division is ÷, and is read, "divided by.' 16. The sign() signifies that the quantities included are to b subjected to the same operation.

17. Find the result of the following:

DIVISION.

82. Division is the process of finding the quotient of two numbers.

83. The Quotient of two numbers is a number which xpresses how often one number is contained in another.

84. The Dividend is the number to be divided. 85. The Divisor is the number by which we divide. 86. The Remainder is the number which is sometimes left after dividing.

87. The Sign of Division is, and is read divided by. It denotes that the number preceding it is to be divided by the number following it.

NOTES.-1. The sign of division is a short line, in the line of writing, with one dot above and another below the middle of it.

2. The symbol was introduced by Dr. John Pell, an English mathematician, born in 1610.

3. Division is also indicated by writing the divisor beneath the dividend, with a straight line between them; or by writing the divisor at the left of the dividend, with a curved line between them; thus 27, and 9)27, mean 27 divided by 9.

PRINCIPLES.

1. The divisor and dividend are similar numbers.

2. The quotient is an abstract number; the remainder is similar to the dividend.

3. In dividing a number into equal parts, the dividend and quotient are similar, and the divisor is abstract.

METHODS OF DIVISION.

88. There are Two Methods of performing division, called Short Division and Long Division.

SHORT DIVISION.

89. Short Division is that method in which only the dividend, divisor, and quotient are written, the operation being performed mentally.

90. Short division is generally employed when the divisor does not exceed twelve, the largest multiplier in the mul. tiplication table.

1

1. How many times is 2 contained in 358?

OPERATION.

2)358

179

SOLUTION.-We write the divisor at the left of the dividend, with a curved line between them, draw a line beneath the dividend, and begin at the left to divide. 2 is contained in 3 hundreds 1 hundred times, and 1 hundred remaining; 1 hundred equals 10 tens, which with 5 tens are 15 tens: 2 is contained in 15 tens 7 tens times, with a remainder of 1 ten; 1 ten equals 10 units, which with 8 units equals 18 units: 2 is contained in 18 units 9 units times, and we have for the quotient, 179. Hence we have the following

Rule.-I. Write the divisor at the left of the dividend, with a curved line between them and a line beneath the dividend.

II. Begin at the left, divide each term of the dividend by the divisor, and write the quotient beneath.

III. If there is a remainder after any division, regard it as prefixed to the next term of the dividend, and divide as before.

IV. If any partial dividend is less than the divisor, write a cipher in the quotient and prefix the dividend to the next term.

V. When there is a final remainder, annex it, with the divisor written beneath, to the integral part of the quotient.

Proof.-Multiply the quotient by the divisor, and add the remainder, if any, to the product; if the work is correct, the result will equal the dividend.

NOTE.-In practice we need not name the denomination of the different partial dividends. Thus, in the above solution we say 2 is contained in 3, once and one remaining; 2 is contained in 15, 7 times, etc.

26. If a book cost 4 dollars, how many books, at the same rate, can you buy for 252 dollars?

SOLUTION.-If 1 book cost 4 dollars, for 252 dollars we can buy as many books as 4 dollars are contained times in 252 dollars, which are 63. Therefore, etc.

OPERATION.

4)252

63

27. There are 3 feet in one yard; how many yards in 291 feet? Ans. 97 yards. 28. There are 8 quarts in one peck; how many pecks are there in 1728 quarts? Ans. 216 pecks. 29. There are 7 days in one week; how many weeks in 364 days? Ans. 52 weeks.

30. A man gave 324 dollars to some boys, giving 6 dollars to each; how many boys were there?

Ans. 54. 31. If one sheep cost 9 dollars, how many sheep can you buy for 1935 dollars? Ans. 215 sheep.

32. If there are 12 pence in 1 shilling, how many shillings are there in 571,836 pence? Ans. 47,653 shillings. 33. If it require one sheet of paper to print 12 pages of a book, how many sheets will be required for a book of 504 pages? Ans. 42 sheets.

34. How long will it take two boys, starting at the same place, and traveling in opposite directions, to be 29,076 rods apart, if one goes 5 and the other 7 rods in a minute?

Ans. 2423 minutes.