20. How many barrels of flour, at $8 a barrel, can be bought for $12736? For $7068?

21. If 9 acres of land cost $976.50, what is the cost of 1 acre ?

22. At 4 cents apiece, how many oranges will $3.72 buy? 23. At 8 cents a yard, how many yards of ribbon can be bought for $7.28?

24. How many pounds of sugar, at 9 cents a pound, can be bought for $14.67? For $27 ?

To this annex the 3 tens of the dividend, making 23 tens for the second partial dividend.

26 is not contained in 23, so write a cipher in the quotient and bring down the 7 units of the dividend, making 237 units for the third partial dividend.

26 is contained in 237 units, 9 times, with a remainder. Write the 9 units in the quotient, and multiplying and subtracting as before, there remain 3 units, which write over the divisor, and annex as a part of the quotient. Hence, the quotient is 209.

2. Find how many times 204 is contained in 1041835.

RULE.-1. Write the divisor at the left of the dividend.

2. Find how many times the divisor is contained in the least number of the left-hand orders of the dividend that will contain it, and write the result for the first figure of the quotient.

3. Multiply the divisor by this quotient figure, subtract the product from the partial dividend used, and to the remainder annex the next lower order of the dividend, for a new partial dividend, and divide as before.

4. Proceed in the same manner until all the orders of the dividend have been used.

5. If any partial dividend does not contain the divisor, write a cipher in the quotient, and annex the next lower order of the dividend, and proceed as before.

6. If the division is not exact, write the last remainder, with the divisor underneath, as a part of the quotient.

To test or prove the work, see Prin. III.

1. If the product of the divisor and quotient be greater than the partral dividend, the quotient is too large, and must be diminished.

2. If any remainder is equal to or greater than the divisor, the quotient is too small and must be increased.

In like manner, solve and prove the following:

15. Divide 35280 by 45; by 49; by 48; by 55. 16. Divide 1276704 by 36; by 33; by 39; by 42. 17. Divide 95762 by 114; by 152; by 171; by 204. 18. A planter raised 43240 pounds of cotton on 94 acres. What was the average number of pounds to the acre?

19. How many acres of land can be bought for $8370, at $18 an acre? At $25 ?

20. How many barrels of pork, at $22 a barrel, can be bought for $35354 ?

33. If 867 shares of railroad stock are valued at $84099, what is the value of each share?

34. A plantation of 736 acres was sold for $55936. What was the price of an acre?

35. The annual receipts of a company are $570685. What is the average per day, if there are 313 working days?

36. A drover received $26460 for 196 head of cattle. How much was their average value per head?

37. If 43776 pounds of cotton be packed in 96 bales, what is the average weight of the bales?

Find the second member of the following equations:

38. (630015) (372÷ 3) = ?

39. (1246010) x (475-377) = ? 40. (867 x 97) (200 × 5 × 3) = ?

41. (6070-1200) + (4680 ÷ 15)

= ?

71. When the divisor has ciphers on the right. 1. Divide 47325 by 100.

EXPLANATION.-Removing any order of units one place to the right, by cutting off or taking away the right hand figure of a number, divides the number by 10(17-III). For like reasons, cutting

1100) 473125

473....25 Rem.

473 Quotient.

off two figures divides by 100; three figures divides by 1000, etc. The remaining figures are the quotient, and the figures cut off, the remainder.

Dividing 387 by 8, the quotient is 48, and a second remainder of 3, which prefixed to the first remainder, 36, gives the true remainder, 336. Hence, the quotient is 48388.

In like manner, divide

3. 124260 by 100.

4. 304631 by 1000.

5. 71032000 by 10000.

6. 10800 by 900.

7. 47620 by 420.

8. 378000 by 1200.

RULE.-1. Cut off the ciphers from the right of the divisor, and as many figures from the right of the dividend, and divide the remaining part of the dividend by the remaining part of the divisor, for the quotient.

2. Prefix the remainder, if any, to the figures cut off, and the result will be the true remainder.

9. How many bales, each weighing 510 pounds, can be made of 76500 pounds of cotton?

10. How many horses, at $260 each, can be bought for $19500?

11. If it require $34400 to pay a regiment of 800 men, how much does each man receive?

12. At $3400 each, how many lots can be bought for $68000?

GENERAL PRINCIPLES OF DIVISION.

72. The relative values of the dividend and divisor determine the value of the quotient.

There are six cases of changing the terms by multiplication. and division, illustrated by comparing the equation 48÷8=6 with the following, thus:

Multiplying the dividend, or dividing 12 the divisor, MULTIPLIES the quotient by the same number.

I.

48 x 2
8

48

or

8÷2

A change in the DIVIDEND by multiplication or division produces a LIKE change in the quotient; but such a change in the DIVISOR produces an OPPOSITE change in the quotient.