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33. Sold a farm containing 367 acres, what was the
amount at 97 dollars per acre ? Ans. 35599 dollars. 34. An army of 17006 men receive each 109 dollars as their annual pay; what is the amount paid the whole
Ans. 1853654 dollars, 35. Íf a mechanic deposit annually in the Savings Bank, 407 dollars, what will be the sum deposited in 27 years ?
Ans. 10989 dollars. 36. If a man travel 37 miles in one day, how far will he travel in 365 days?
Ans. 13505 miles. 37. If there be 24 hours in one day, how many hours in 365 days ?
Ans. 8760 hours. 38. How many gallons are in 87 hogsheads, there being
63 gallons in each hogshead ? Ans. 5481 gallons. 39. If the expenses of the Massachusetts Legislature be 1839 dollars per day, what will be the amount in a session of 109 days?
Ans. 200451 dollars. 40. If a hogshead of sugar contains 368 pounds, how many pounds in 187 hogsheads ? Ans. 68816 pounds.
MENTAL EXERCISES. 1. A gentleman divided 6 apples between 2 boys ; how many did each receive ? 2. A' farmer received 8 dollars for 2 sheep ; what was
the price of each ? 3. A' man gave 15 dollars for 3 barrels of flour ; what
was the cost of each barrel ? 4. A lady divided 20 oranges among her 5 daughters ; how many did each receive ? 5. If 4 casks of lime cost 12 dollars, what is the value
of 1 barrel ? 6. A laborer earned 48 shillings in 6 days; what did he
receive per day? 7. A man can perform a certain piece of labor in 30 days ; how long will it take 5 men to do the same ?
8. When 72 dollars are paid for 8 acres of land ; what
cost 1 acre ? What cost 3 acres ? 9. If 21 pounds of flour can be obtained for 3 dollars, how much can be obtained for 1 dollar ? How much for 8 dollars ? How much for 9 dollars ? 10. Gave 56 cents for 8 pounds of raisins ; what cost
1 pound? What 7 pounds? 11. If a man walk 24 miles in 6 hours, how far will be
walk in 1 hour ? How far in 10 hours ? 12. Paid 56 dollars for 7 hundred weight of sugar; what
cost 1 hundred weight ? What cost 10 hundred weight ? 13. If 5 horses will eat a load of hay in one week, how
long would it last one horse ? 14. In 20, how many times 2 ? How many times 4 ? How many times 5? How
times 10 ? 15. In 24 how many times 3 ? How many times 4?
How many times 6 ? How many times 8?
In 14 ? In 63 ? In 77 ? In 70?/ In 84 ?,
Division is a short or compendious way of performing Subtraction.
Its object is to find how often one number is contained in another: It consists of four parts, the divide d, or number to be divided ; the divisor, the number we divide by ; the quotient, which shows how many times the divisor is contained in the dividend ; and the remainder, which is always less than the divisor, and of the same name of the dividend.
I. When the divisor is less than 13, the question should be performed by
SHORT DIVISION. 1. Divide 7554 dollars equally among 6 men. Dividend.
In performing this question, inDivisor 6 ) 7554
quire how many times 6, the divi
sor, is contained in 7, which is 1 Quotient 1259
time, and 1 remaining ; write the
1 under the 7, and suppose 1, the remainder, to be placed before the next figure of the dividend, 5 ; and the number would be 15. Then inquire how many times 6, the divisor, is contained in 15. It is found to be 2 times, and 3 remaining. Write the 2 under the 5, and suppose the remainder, 3, to be placed before the next figure of the dividend, 5; and the number would be 35. Inquire again how many times 35 will contain the divisor, 6. "It is found to be 5 times, and 5 remaining. Write the 5 under the 5 in the dividend, and suppose the remainder, 5, to be placed before the last figure of the dividend, 4; and the number would be 54. Lastly, inquire how many times 54 will contain the divisor, 6. It is found to be 9 times, which we place under the 4 in the dividend. Thus we find, that each man will receive 1259 dollars.
From the above illustration we deduce the following
See how many times the divisor may be contained in the first figure or figures of the dividend, and place the result immediately under that figure; and what remains suppose to be placed directly before the next figure of the dividend ; and then inquire how many times these two figures will contain the divisor, and place the result as before; and so proceed until the question is finished.
16. Divide 944,580 dollars equally among 12 men, and
what will be the share of each ? Ans. 78,715 dollars. 17. Divide 154,503 acres of land equally among 9 per
Ans. 17,167 acres. 18. A plantation in Cuba was sold for 7,011,608 dollars, and the amount was divided among
persons. What was paid to each person ? Ans. 876,451 dollars.
Quotients. Rem. 19. Divide 5678956 by 5.
1. 20. Divide 1135791 by 7.
6. 21. Divide 1622550 by 8.
6. 22. Divide 2028180 by 9.
3. 23. Divide 2253530 by 12.
2. 24. Divide 1877940 by 11.
9. Sum of the quotients, 2084732. 25. A prize, valued at 178,656 dollars, is to be equally divided among 12 men ; what is the share of each
Ans. 14,888 dollars. 26. Among 7 men, 67,123 bushels of wheat are to be distributed ; how
Ans. 9,589 bushels. 27. If 9 square feet make 1 square yard, how many
yards in 895,347 square feet ? Ans. 99,483 yards. 28. A township of 876, 136 acres is to be divided among 8 persons ; how many acres will be the portion of each?
Ans. 109,517 acres. 29. Bought a farm for 5670 dollars, and sold it for 7896 dollars, and I divide the net gain among 6 persons ; what does each receive ?
Ans. 371 dollars. 30. If 6 shillings make a dollar, how many dollars in 7890 shillings?
II. When the divisor exceeds 12, the operation should be performed by
LONG DIVISION, as in the following question. 31. A gentleman divided equally among his 19 sons, 4712 dollars ; what is the share of each ?
The object of this Dividend.
question is to find Divisor. 19)4712( 248 Quotient. how many times
4712 will contain 19, 91 2232
or how many times 76 248
19 must be subtract152 4712 Proof.
ed from 4712, un
til nothing remains. 152
We first inquire 000 Remainder.
how many times 19 may be contained in 47 (thousand). Having found it to be 2 (hundred) times, we write 2 in the quotient and multiply it by the divisor, 19, and place their product under 47, from which we subtract it, and find the remainder to be 9, to which we annex the next figure in the dividend, 1. And having found that 91 (tens) will contain the divisor, 19, 4 (tens) times, we write 4 in the quotient, multiply it by 19, and place the product 76 under 91, from which we subtract it, and, to the remainder, 15 (tens), we annex the last figure of the dividend, 2, and inquire how many times 152 will contain 19, and we find it to be 8 times ; and having placed the product of 8 times 19, that is, 152, under the 152, we find there is no remainder, and that the number 4712 will contain 19, the divisor, 248 times ; that is, each man will receive 248 dollars.
To prove our operation is correct, we reason thus. If one man receive 248 dollars, 19 men will receive 19 times as much, and 19 times 248 are 4712, the same as the dividend ; and this operation is effected by multiplying the divisor by the quotient, and adding in the remainder if there be one. The student will now see the propriety of the following
Place the divisor before the dividend, and inquire how many times it is contained in a competent number of figures in the dividend, and place the result in the quotient ; multiply the figure in the quotient by the divisor, and place the product under those figures in the dividend, in which it was inquired, how many times the divisor was contained ; subtract this product from the dividend, and to the remainder