12. At 30 dollars for 3 plows, what is the cost of each

plow?

13. Mr. Rollins bought 9 barrels of flour for 72 dollars; what did he pay per barrel?

14. How many times is 8 contained in 96?

SOLUTION.

96 is 9 tens 6 units; 8 in 9 tens, 1 ten time, and 1 ten remaining; 1 ten remaining equals 10 units; 10 units and 6 units are 16 units; and 8 in 16 units 2 units times. Therefore, 8 is contained in 96, 1 ten and 2 units times, or 12 times.

15. How many times is 5 contained in 65?

16. Divide 99 by 3. 88 by 4.

77 by 7.

17. How many times 5 in 125?

18. How many times 6 in 132?

In 175?

In 108?

19. If 9 writing-books cost 108 cents, what is the cost of each?

20. At 104 dollars for 8 tons of coal, what is the cost per ton?

21. At 7 cents a pound, what will 11 pounds of rice cost?

PRINCIPLES OF DIVISION.

62. 1. Division is the reverse of multiplication.

For the dividend answers to the product, and the divisor and quotient to the factors. Hence,

2. The product of the quotient and divisor is equal to the dividend.

Of what is Division the reverse? What does prefixed mean? Ans. Placed before.

63.

SHORT DIVISION.

Division is called Short Division when the work

of the solution is not written, except the answer. 1. Divide 1701 by 4.

64.

OPERATION.

Divisor, 41701 Dividend.

425 Quotient.

For convenience we write the divisor at the left of the dividend, and begin at the left to divide.

4 is contained in 17 hundreds 4 hundreds times and 1 hundred

remaining. We write the 4 hundreds in the quotient.

The 1 hundred we consider prefixed to the 0 tens, making 10 tens. 4 in 10 tens, 2 tens times, and 2 tens remaining. We write the 2 tens in the quotient.

The remaining 2 tens we consider prefixed to the 1 unit, making 21 units. 4 in 21 units, 5 units times, and 1 unit remaining. We write the 5 units in the quotient.

We then indicate the division of the remainder, 1 unit by the divisor 4, and annex to the integral part of the quotient; and have for the complete quotient 4254.

Therefore, the quotient of 1701 divided by 4 is 4251.

2. Divide 763 by 7.

OPERATION.

Divisor, 7763 Dividend.

109 Quotient.

For convenience we write the divisor and begin to divide as in the preceding operation.

7 in 7 hundreds, 1 hundreds time, which we write in the quotient.

7 in 6 tens, 0 tens time, which we write in the quotient.

We prefix the undivided 6 tens to the 3 units, making 63 units. 7 in 63 units, 9 times, which we write in the quotient.

Therefore, the quotient of 763 divided by 7 is 109.

In practice we may say, 7 in 7, 1, which we write; 7 in 6, 0, which we write; prefix the 6 to the figure 3; 7 in 63, 9, which we write; answer, 109.

When is the division called Short Division?

Rule. Write the divisor at the left of the dividend.

Begin at the left; divide the number expressed by the fewest figures of the dividend that will contain the divisor, and write the result beneath.

If there be a remainder, regard it as prefixed to the figure of the next lower order; divide as before, and so continue till all the figures of the dividend have been used.

If any partial dividend be less than the divisor, write a cipher in the quotient, and prefix the partial dividend to the figure of the next lower order, if any, for a new dividend.

If there be a final remainder, write it, with the divisor beneath, after the integral part of the quotient.

PROOF. Multiply the integer of the quotient by the divisor, and to the product add the remainder, if any; and the result will equal the dividend, if the work is right.

How do you write the divisor? Where do you begin to divide? How do you proceed if there is a remainder? When any partial dividend is less than the divisor? When there is a remainder after dividing the last figure? What is the Rule? The Proof?

65. When the divisor is 10, 100, 1000, etc., the quotient is obtained, at once, by cutting off at the right of the dividend as many figures as there are ciphers in the divisor.

For, since figures are multiplied by 10 by annexing one cipher, by 100 by annexing two ciphers, etc., (Art. 54,) and as division is the reverse of multiplication, cutting off one figure at the right of the dividend divides it by 10, cutting off two figures divides it by 100, etc.

The Decimal Point (Art. 24), by being removed as many places to the left as there are ciphers in the divisor, may be used to denote where the cutting off is made, and the remainder will be the part on the right of the point. Thus,

132610 132.6 = 1321%, and is read, one hundred thirty-two units and six tenths; 132610013.26130, and is read, thirteen units and twenty-six hundredths; 1326

1000

1000 1.326 = 1,82%, and is read, one unit and three hundred twenty-six thousandths, etc. That is,

When the divisor is 10, 100, 1000, etc., how can the quotient be obtained at once? How do you denote where the cutting-off is made? Why is the decimal point so called? Ans. From decem, the Latin for ten.

The first order at the right of the decimal point expresses tenths; the second, hundredths; the third, thousandths, etc.

31. At 6 dollars each, how many sheep can be purchased for 1806 dollars?

Ans. 301.

32. At 10 dollars a barrel, how many barrels of flour can be purchased for 1440 dollars?

Ans. 144.

33. 7 men working together earned 1547 dollars; what is each man's share of it? Ans. 221 dollars.

34. A gentleman dying left 24560 dollars, to be divided equally between his wife and three sons. What will be the share of each? Ans. 6140 dollars.

35. John Stevens sold melons at 9 cents each, to the amount of 2943 cents. How many did he sell?

36. How many watches, at 100 dollars each, can be bought for 978000 dollars?

37. If a man can do a piece of work in 365 days, how many days will it take 5 men to do the same? Ans. 73.

38. If a prize amounting to 95163 dollars be divided between 8 men, how much will each receive?

Ans. 11895 dollars.

39. At 6 dollars a ton, how much coal can be bought

for 19201 dollars?

Ans. 3200 tons.

What does the first order at the right of the decimal point express? The second order? The third?