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13. Suppose 47244 dollars are to be divided among 4 persons; what can eaeh receive?
Anş. $11811. 14. Five men found a purse of money containing 65465 guineas; how many guineas must each man receive for his portion?
Ans, 13093 guineas. 15. A gentleman purchased 10 acres of fine land, for which he paid $2250; what did he pay per acre ? . Ans. 225.
16. If a gentleman pays 144 shillings for eight weeks board; what does he pay per week ? Ans. 18 shillings.
17. Suppose a man's wages to be $1092 a year; what is that per calendar month, there being 12 months in a year?
Ans. $91. 18. How many barrels of pork can be bought for 1980 dollars, at 10 dollars per barrel ?
Ans. 198. 19: When flour is 5 dollars a barrel; how many barrels can be bought for 3240 dollars ?
Ans. 648, 20. If 12 yards of broadcloth cost 72 dollars; what is the cost of 1 yard? (See the following note.)
Ans, $6. Note.-It must be plain to the student, that 1 yard costs only a twelfth part as much as twelve yards; and boy dividing 72 by 12, our quotient, ($6,) is a twelfth part of 72 dollars.
Case II.— When the divisor exceeds 12. RULE.—You will place the given numbers here, as in the preceding case; remembering to place the quotient at the right of the dividend. If the left hand figure of the divisor is greater than that in the dividend, you must assume one figure more in the dividend than the figures in the divisor;'and then you can judge very near how many times the divisor is contained in the assumed part of the dividend, bý considering how many times the left hand figure of the divisor, is contained in the two left hand figures of the dividend; making an allowance for the carriage. When an equal number of figures of the dividend contains the divisor, you will consider how many times the left hand figure of the divisor, is contained in the left hand figure of the dividend, making an allowance for carriage. By,observing these rules, you will generally be able to place a proper figure in your quotient.
EXAMPLES , In this example, we find that the left hand figure of the divisor, is greater than that at the left in the dividend; we then according to our rule, assume one more figure in the dividend than we have in the divisor; and then inquire how often 4, the left hand figure of the divisor, is contained in the two left hand figures of the dividend, and we find that it is contained nine times; but considering what we shall have to carry to the product of the 4, we know that the product would exceed the assumed figures of our dividend. We then say 8
1. Divide 369463 by 46.
times, and find tha Dividend,
we have a remainder
of only 1; to which Divisor, 46 ) 369463 ( 8031 Quotient.
we bring down the 368
next figure of our divi. dend; but we find that 46, our
divisor, is not contained in 14; . 138
we then signify it, by placing a' 83
cipher in the quotient, and like46
wise to give 8, the left hand fi
gure of our quotient, its proper 37 Rem. local place; for thousands in our Proof. 369443
dividend, produced the 8; consequently it must possess the
place of thousands in the quotient. We then bring down from our dividend the next right hand figure; and inquire how often 46 is contained in 146, we suppose 3 times, and proceeding according to the rule, we find that we have 8 for a remainder; to which we bring down, -3, the next figure in our dividend; we then inquire how often 4 is contained in 8, and find it contained twice; but considering the carriage we know that the prodrict would exceed this part of our dividend; therefore we set 1 in the quotient and bring down our divisor and subtract, and we find our remainder to be 37.
2. Suppose a man's income to be 1825 dollars a year; what is that per day, there being 365 days in a year?
Ans. $5. 3. Divide 20304 by 24.
Ans. 846. 4. Divide 20304 by 846.
Ans. 24; 5. Divide 3264 by 136.
Ans. 24. 6. Divide:937387 by 54.
Ans: 17359 Rem. 1;7. Divide 2674236 by 634.
Ans. 4218 Rem. 24, 8. Divide 742364 by 462.
Ans. 1606 Rem. 392. 9. If a man spend 1008 dollars in a year; what is that per calendar month?
Ans. *84. 10. The President of the United States has a salary of 25000 dollars per year; what is that per day, allowing 365 days to the year?
Ans. $68, Rem. 180. îl. Sixteen men by contract, are to receive for a job of work, two thousand three hundred and thirty-six dollars; what is each man's part of the dividend ?
Ans. $146. 12. A man sold a farm for $5000, containing 250 acres; what did he receive per acre ?
Ans. $20. 13. The product of a certain number is 63342 and the mula tzplier 34; what is the multiplicand ?
14. The product of a number is 2336, and the multiplicand 146; what is the multiplier ?
Ans. 16. CASE III. - To divide by 10, 100, 1000, &c. RULE.-Cut off as many figures from the right hand of your dividend, as there are ciphers in the divisor. The figures so cut off at the right, will be the remainder, and the other figures of your dividend at the left, will be the quotient.
EXAMPLES. 1. Divide 36784 by 10.
Dem.—In multiplication we Quotient. | Rem.
have roved that the joining of 36.78
a cipher to the multiplicand, increases it ten times; and divi
sion being the reverse of multi10) 3 6 7 8 4 (3 6 7 8 plication, we, instead of joining 30
a figure, must cut one off, which
diminishes the dividend, so that 67
the figures in the quotient, 60
have only a tenth part of the
value which they have in the 7 8
dividend ; because the figure 70
which cxpresses tens in the divi84
dend, only expresses units in
the quotient; and it is plain, if 8.0
we should divide by 10'accord4
ing to the usual mode of divi
ding numbers, the cipher of our divisor would come under the 4, and in subtracting, leave 4 a remainder. 2. Divide 36048 by 100.
Ans. 360. Rem. 48. 3. Divide 461340 by 1000.
Ans. 461. Rem. 340. 4. Divide 634210 by 10000.
Ans. 63. Rem. 4210. NoTE.- If we cut off one figure from the right of our dividend, the left hand figures, which we call the quotient, express one tenth of the dividend, excluding the remainder; and the figure cat off at the right, shows what is left of the dividend after dividing it into ten equal parts. When we cut off two figures, the left hand figures express one hundredth part of our dividend; and when we cut off three, the left hand figures express only one thousandth part of the dividend; because the figure which before expressed thousands, after the operation, only expresses units; so that the effect may be easily discovered by the laws of notation.
CASE IV.- When the divisor is a composite number ; that 28, when it can be produced by multiplying any two figures in the table together.
RULE.--Divide the dividend first by one of the figures, and then that quotient by the other, and the last quotient will be the answer.
Note.The total remainder is found by multiplying the last reProof.
mainder by the first divisor, and to the product add tne first remainder. Or multiply the whole divisor by the last quotient; and subtract the product from the dividend; and the difference will be the true reinaiuder.
EXAMPLES 1. Divide 4.6-8 7 7 by i 2.
Three and four Dividend.
we take for the Divisor, 4 ) 46 877
of 12; because 3 Divisor, 3 ) 11719-1 Rem.
times 4 are 12; or Quotient, 3 9 0 6, 1X434+1=5 rem.
we might take 2
and 6; because 2 12
times 6 are 12.
Or according to 46872
our rule, we may 5 Add 5; the Rem. obtain 46 877
mainder by sub
tracting the produet of our quotient and divisor from the dividend thus,
4 6 8 7 7 Dividend.
5 True Rem. DEM.--The reason of this rule is plain, because it is evident, as we find in our example, that the 3d part of the 4th of any number, is the 12th of the whole. 2. Divide 146738 by 8.
Ans, 18342, Rem. 2. 3. Divide 167834 by 16.
Ans. 10489, Rem. 10. 4. Divide 56732 by 24.
Ans. 2363, Rem. 20. 5. Divide 937387 by 54.
Ans. 17359, Rem. 1. 6. Divide 634679 by 64.
Ans. 9916, Rem. 55. 7. Suppose a privateer takes a prize worth $68526, which is to be divided among 81 seamen; what is the share of each?
Ans. $846. 8. A man bought ninety-six horses for shipping, for which he gave 6720 dollars, what did they cost him on ari ave
Ans. $70. CASE V.-When there are ciphers at the right of the dis visor,
RULE.-Cut off the ciphers from the right hand of the divisor, and a like number of figures from the right of the dividend. Divide the remaining figures without regard to the figures cut off from either; and to the right hand of the remainder, annex the figures cut off from the right of the dividend, which will give the true remainder.
EXAMPLES. 1. Divide 86348634 by 67000.
NOTE.—The student, at Divisor. Dividend. Quotient.
first view, will perhaps.
look on our remainder, 67000) 863481634 ( 1288
and wonder at its being 67
so great; but his surprise
vanishes, when he takes into con193
sideration that our true divisor is 134
not 67, but 67,000. .594
Dem.-Čutting off the ciphers
from the divisor, and an equal .536
number of figures from the right ..588
of our dividend, is dividing them ..536
both by 10, 100, 1000, &c.; and
it is evident, as often as the whole 52634 Rem. divisor is contained in the whole Proof. 86348634
dividend, so often must a like por.
tion of the divisor be contained in a like portion of the dividend; so it saves the needless repetition of the ciphers as they are repeated in the common way, as the following example shows. Divisor. Dividend. Quotient.
NOTE.-This last 67000 ) 86348634 ( 1288
work shows, that 67000
the ciphers of the 193486
divisor come under 134000
the figures cut off
from the dividend, 594863
and coming at the 536000
right hand, the fig588634
ures cut off from 536000
the dividend, come 52634 Rem.
in the remainder of Proof. 86348634
course. 2. Divide 6467321 by 460. Ans. 14059, Rem. 181. 3. Divide 76173 by 320.
Ans. 238, Rem. 13. 4. Divide 4673625 by 21400. Ans. 218, Rem. 8425. 5. Divide 149596478 by 120000. Ans. 1246, Rem. 76478. 6. Divide 46646300 by 670000. Ans. 69, Rem. 416300. 7. Divide 6346211 by 20000. Ans. 317, Rem. 6211, 8. Divide 64613214 by 4000. Ans. 16153, Rem. 1214.
9. A gentleman sold 300 acres of land for 2100 dollars; at what rate did he sell it
Ans. $7. 10. A merchant sold 300 pipes of wine for $56100; at what rate did he sell it per pipe ?