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10. Divide 54yd. 2qr. 3na. equally among persons. 11. Divide 123tun 3hhd. 36gal. 3qt. by 7. 12. Divide 209hhd. 55gal. 3qt. Opt. lgi. by 7. 13. What is the value of 118bu. 1pk. 5qt. • 6? 14. What is the value of 110y. 343d. 3h. 41m. 12s. • 8? 15. Divide 149deg. 9m. 5fur. 13rd. 3yd. 1ft. by 9.
16. A man divides his farm of 214A. 3R. 12p. equally among his 9 sons; how much does each receive ?
17. If one man perform a certain piece of labor in 3d. 16h. 54m., how long would it take 12 men to perform the same work?
18. A farmer has 29 bushels of oats which he wishes to put in 8 sacks; how much must each sack contain ?
151. When the divisor is a composite number, and none of its factors exceed 12.
Ex. 1. If 35 loads of coal weigh 72T. 14cwt. 2qr. 10lb., what will i load weigh?
We find the fac
tors of 35 to be 5 5) 72 14 2 10 weight of 35 loads. and 7. We there
fore divide 7) 14 10 3
the 17 weight of 7 loads.
weight of 35 loads 2 1 2 6= weight of 1 load. by 5, and obtain
the weight of 7 loads; and the weight of 7 loads we divide by 7, and thus find the weight of 1 load. Hence, when the divisor is a composite number,
Divide by its factors in succession.
2. If 90 hogsheads of sugar weigh 56T. 14cwt. 3qr. 15lb., what is the weight of 1 hogshead?
3. What will be the price of 1 sheep, if 18 cost 5£. 4s. 3d. ?
4. If 21 yards of cloth cost 10£. 8s. 3d., what is the price of 1 yard?
5. What is the value of 1 hat, when 22 cost 12£. 13s. Od. ?
6. When 96 shares of a certain stock are valued at 1290£. 4s. Od., what would be the cost of 1 share ?
7. If 120 spoons weigh 321b. 9oz. 15pwt., what does 1 weigh?
8. If a man in 1 month travels 746m. 5fur., how far does he go in 1 day?
9. If the earth revolves 15° on its axis in 1 hour, how far does it revolve in 1 minute ?
10. Divide 1275A. 2R. 16p. 22yd. 8ft. 32in. equally among
11. If a man walk round the earth in 2y. 68d. 19h. 54m., how long would it take him to walk 1 degree, allowing 365) days to a year?
152. When the divisor is not a composite number, and exceeds 12, or when a composite number one of whose factors exceeds 12, the whole operation can be written, as in the following example.
Ex. 1. Divide 360£. 8s. 4d. by 173. Ans. 2£. 13. 8d.
OPERATION. £. S.
17 3 ) 3 6 0 8 4 ( 2£.
173) 2 8 8 (1s.
We divide the pounds by 173, and obtain 2£. for the quotient, and 14£. remaining, which we reduce to shillings, and add the 8s., and again divide by 173, and obtain 1s. for the quotient. The remainder, 115s., we reduce to pence, and add the 4d., and again divide by 173, and obtain 8d. for the quotient. Thus, the method is the same as by general rule (Art. 150). By uniting the several quotients, we obtain 2£. 1s. 8d. for the answer.
17 3)1 3 8 4 ( 8d.
2. Divide 89hhd. 52 gal 3qt. 1pt. by 39.
5. If 57 gallons of wine cost 23£. 11s. 54d., what cost 1 gallon ?
6. Divide 3419 A. 2R. 23p. by 29.
7. If 89 pieces of cloth contain 3375yd. 3qr. Ina. 0fin., how much does 1 piece contain ?
8. If 59 casks contain 44hhd. 52gal. 2qt. 1pt. of wine, what are the contents of 1 cask ?
9. If a man travel in 1 year (365 days) 6357m. 5fur. 14rd. 11}ft., how far is that per day ?
10. When 175gal. 2qt. of beer are drunk in 52 weeks, how much is consumed in 1 week ?
11. When 17 sticks of timber measure 15T. 38ft. 1074in., how many feet does 1 contain ?
12. Divide 132 cords 2ft. by 17.
Ans. 4T. 15cwt. 2qr. 1014 lb. 14. Divide 916m. 3fur. 30rd. 10ft. 6in. by 47.
Ans. 19m. 3fur. 39rd. 13ft. 24in. 15. Divide 718A. 3R. 37p. by 29.
Ans. 24A. 3R. 63 3p. 16. Divide 815A. 1 R. 17p. 200ft. by 87.
Ans. 9 A. 1 R. 19p. 1393 ft. 17. Divide 144A. 3R. 18p. 3yd. 1ft. 36in. by 11.
Ans. 13A. OR. 27p. 3yd. Oft. 45 i in.
PRINCIPLES AND APPLICATIONS.
DIFFERENCE BETWEEN DATES.
153. To find the time between two different dates.
Ex. 1. What is the difference of time between May 16, 1819, and March 4, 1857 ?
Ans. 37y. Imo. 18d. Commencing with January,
the first month in the year, and d.
counting the months and days in Min. 18 5 7 2 4
the later date up to March 4th, Sub. 18 19 4 16 we find that 2mo. and 4d. have
elapsed. We therefore write the Rem. 37 9 18 numbers for subtraction as in the
The same result, however, Min. 18 5 7
4 could be obtained, as some preSub. 1819 5 16 fer, by reckoning, the number
of the given months instead of Rem. 37 9 18 the number of months that have
elapsed since the beginning of the year, which would require the numbers to be written as in the second operation. Written either way, the earlier date, being placed under the later, is subtracted from it.
NOTE. — In finding the difference between two dates, and in computing interest for less than a month, 30 days are considered a month. In legal transactions, however, a month is reckoned from any day in one month to the corresponding day of the following month, if it has a corresponding day, otherwise to its end. The above process, which is that ordinarily used by business men, does not give always the exact time between two different dates. The result obtained by it may deviate sometimes a day, and, less often, two days, from the exact difference. But for practical purposes it is generally regarded as sufficiently accurate.
2. What is the time from June 30, 1854, to April 19th, 1857?
3. A note was given October 26th, 1856, and paid June 12th, 1857; how long was it on interest ?
4. The Pilgrims landed at Plymouth December 22d, 1020, N. S., and the Declaration of Independence was made July 4th, 1776; what is the difference of time between these events ?
5. General Washington was born February 22d, 1732, and died December 14th, 1799; how long did he live?
Ans. 67y. Imo. 22d. 154. To find the exact number of days between two different dates.
Ex. 1. How many days from January 28 to July 30, common year?
Ans. 183 days. January to July 6mo.
6 x 31
18 6 days. For Feb. 3d., April 1d., June 1d., 3+1+1= 5
181 For difference between 30 and 28, 30 - 28
Ans. 1 8 3 days. The difference between January and July we find to be 6mo., which, multiplied by 31, the greatest number of days in any month in the year, gives 186 days. But since in the interval of time included between the given dates several months end that do not con
tain 31 days, we make deductions for these, which, in all, amount to 5 days, and have left 181 days; and as the difference between the given dates is the difference between 30 and 28 more than exactly Emo., we add 2 to the 281 days, thus obtaining 183 days, the difference of time required. Hence, to find the number of days between two different dates,
Find the number of months ending between the given dates, and multiply that number by 31, and from the product make the necessary deduction for the months counted that do not contain 31 days, if any Should the later date end later in the month than the earlier, add the difference of days; but should it end earlier, subtract the same.
NOTE. — The exact difference in days between two different dates can also be obtained by use of the table in Note 2, Art. 142.
EXAMPLES. 2. How many days has a note to run dated November 15, 1856, and made payable February 13, 1857 ? Ans. 90 days.
3. How many days from June 18, 1855, to May 1, 1856?
4. How many days from March 4 to May 3 of the same year?
5. From November 4, 1856, to April 4, 1857, how many days?
Ans. 151 days. 6. In a leap year, how many days are there from the 7th of January to the 11th of December?
Ans. 339 days. 155. To find the day of the week corresponding to any given day of the month, when the day of the week of some other date is given.
Ex. 1. If the 16th day of May be on Saturday, what day of the week will the next 25th of December be?
From May 16 to December 25
. Having found the difference of time in days between the given dates, we bring the days to weeks by dividing by 7, and obtain 31 weeks and 6 days. The 25th of December, therefore, must come 6 days after Saturday, or on Friday. Hence, we
Reduce the days between the given dates to weeks. Should there be no remainder, the day given will be the same as that sought, but should there be a remainder, it will indicate the number of days that the day sought is after the day given.