8. If 8 men can do a piece of work in 15 days, how long will it take 12 men to do it?

9. If a quantity of provisions will supply a ship's crew of 20 men 15 weeks, how large a crew will it supply 25 weeks?

10. If a man can do a piece of work in 40 days, by working 8 hours a day, how long would it take him if he should work 10 hours a day?

11. A man earns $16 while a boy earns $9: how many dollars will the man earn while the boy is earning $72?

12. The fore wheels of a carriage are each 9 feet in circumference, and the hind wheels are each 12 feet: if the fore wheels each rotate 400 times in going a certain distance, how many rotations will each hind wheel make?

13. Five times Harry's age plus 4 times his age, minus 6 times his age, plus 7 times his age, minus 5 times his age, equals 60 years: how old is Harry?

14. A number multiplied by 6, divided by 3, multiplied by 8, and divided by 4, equals 96: what is the number?

WRITTEN PROBLEMS.

15. Divide 486 by 6; by 8; by 9.
16. Divide 8408 by 12; by 24; by 36.
17. Divide 84600 by 900; by 12000.

18. Divide 412304 by 3600; by 303000.

19. The dividend is 1059984 and the divisor is 306: what is the quotient?

20. The dividend is 2185750 and the quotient is 250: what is the divisor?

21. The product is 1123482 and the multiplier is 246: what is the multiplicand?

22. How many passenger cars, costing $2450 each, can be bought for $100450?

23. There are 5280 feet in a mile, and the height of Mount Everest, in Asia, is 29100 feet: what is its height in miles?

24. There are 3600 seconds in an hour: how

in 738000 seconds?

DEFINITIONS AND PRINCIPLES.

many hours

41. Division is the process of finding how many times one number is contained in another; or, it is the process of finding one of the equal parts of a number.

The Dividend is the number divided.

The Divisor is the number by which the dividend is divided.

The Quotient is the number of times the divisor is contained in the dividend; or it is one of the equal parts of the dividend.

The Remainder is the part of the dividend which is left undivided.

42. The Sign of Division is a short horizontal line between two dots, thus: . It is read divided by. Thus, 16 4 is read 16 divided by 4.

Division is also expressed by writing the dividend above and the divisor below a short horizontal line. Thus, 1 is read 18 divided by 3.

18

3

43. There are two methods of division, called Short Di vision and Long Division.

In Short Division, the partial products and partial dividends are not written, but are formed mentally.

In Long Division, the partial products and partial dividends are written.

44.-1. One number is contained in another as many times as it must be taken to produce it. Hence, Division is the reverse of multiplication.

2. One number is contained in another as many times as it can be taken from it. Hence, Division is a brief method of finding how many times one number can be subtracted from another.

45. PRINCIPLES.-1. The divisor and quotient are factors of the dividend.

2. When division finds how many times one number is contained in another, the divisor and dividend are LIKE NUMBERS, and the quotient is an abstract number.

3. When division finds one of the equal parts of a number, the divisor is an abstract number, and the dividend and quotient are LIKE NUMBERS.

4. The multiplying of both divisor and dividend by the same number does not change the value of the quotient.

5. The dividing of both dividend and divisor by the same number does not change the value of the quotient.

ABBREVIATED PROCESSES.

Case I.

The Divisor 10, 100, 1000, etc.

1. There are 10 cents in a dime: how many dimes in 80 cents? 120 cents? 240 cents?

2. There are 10 dimes in a dollar: how many dollars in 70 dimes? 250 dimes? 2500 dimes?

3. There are 100 cents in a dollar: how many dollars in 800 cents? 2400 cents? 7500 cents?

4. At $10 a barrel, how many barrels of flour can be bought for $90? For $150?

5. At $100 apiece, how many horses can be bought for $1200? For $2500? For $45000?

The explanation of these processes is obvious. The cutting off of the right-hand figure removes all the other figures one place to the right, and thus decreases their value ten times. The cutting off of two figures removes the other figures two places to the right, and de

creases their value one hundred times. The figures cut off denote the remainder.

8. Divide 356000 by 100; by 1000.

9. Divide 46035 by 100; by 1000.

10. Divide 384602; by 1000; by 10000.

11. Divide 95000000 by 10000; by 1000000.

46. PRINCIPLE.-The removal of a figure one order to the right decreases its value tenfold.

47. RULE. To divide by 10, 100, 1000, etc., Cut off as many figures from the right of the dividend as there are ciphers in the divisor. The figures cut off denote the remainder.

Case II.

The Divisor ending with one or more Ciphers. 12. There are 20 quires of paper in a ream: how many reams in 80 quires? 160 quires?

13. There are fifty cents in a half-dollar: how many halfdollars in 150 cents? 350 cents?

14. There are 60 minutes in an hour: how many hours in 240 minutes? 720 minutes?

15. A barrel of beef contains 200 pounds: how many barrels will 1200 pounds make? 3600 pounds?

PROCESS.

4500) 588.64 ( 13

45

138

135

3

Remainder, 364

First divide both dividend and divisor by 100, which, in the case of the dividend, leaves a remainder of 64. Next divide 588 by 45, leaving a remainder of 3, which is 3 hundreds since the dividend (588) is hundreds. The first remainder is 64 units which, annexed to the 3 hundreds, give 364, the true remainder.

18. Divide 63200 by 7900; by 7000.
19. Divide 116000 by 2500; by 4800.
20. Divide 172800 by 14400; by 18000.
21. Divide 129600 by 4800; by 64000.

48. PRINCIPLE.-The dividing of both divisor and dividend by the same number does not change the value of the quotient.

49. RULE.-To divide by a number ending in one or more ciphers, 1. Cut off the ciphers from the right of the divisor, and an equal number of figures from the right of the dividend. 2. Divide the new dividend thus formed by the new divisor, and the result will be the quotient.

3. Annex the figures cut off from the dividend to the remainder, if there be one, and the result will be the true remainder.

Case III.

The Divisor a convenient part of 10, 100, etc.

22. At 3 cents apiece, how many lemons can be bought for 90 cents? For 240 cents?

SUGGESTION. Since 10 is 3 times 3}, multiply the dividend by 3 and divide the product by 10.

23. At 12 cents a yard, how many yards of cloth can be bought for 75 cents? For 225 cents?

24. At 163 cents a bushel, how many bushels of coal can be bought for 150 cents? For 550 cents?

25. At $33 a head, how many cows can be bought for $200? For $1200?