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we ascertain how many thousand parts of 8 each there are in the 29 thousands. As 8 is contained in 29 thousands 3 thousand times, with a remainder of 5 thousands, we write 3 in the thousands' place of the quotient, and reduce the 5 thousands to hundreds, adding to them the 5 hundreds in the hundreds' place of the dividend. This gives 55 hundreds.
As 8 is contained in 55 hundreds 6 hundred times, with a remainder of 7 hundreds, we write 6 in the hundreds' place of the quotient, and reduce the 7 hundreds to tens, adding to them the 7 tens written in the tens' place of the dividend. This gives 77 tens.
As 8 is contained in 77 tens 9 tens times, with a remainder of 5 tens, we write 9 in the tens' place of the quotient, and reduce the 5 tens to units, adding them to the 6 units written in the units' place. This gives 56 units.
As 8 is contained in 56 units 7 times, with no remainder, we write 7 in the units' place of the quotient.
We thus find that the quotient is 3697, which represents the number of parts of $8 each there are in the dividend, and since each such part is the price of 1 barrel, the number of barrels that can be bought must equal the number of these parts.
To test the correctness of the previous work, we have only to ascertain whether 3697 times 8 dollars will equal 29576 dollars. For, since 1 barrel costs $8, 3697 barrels must cost 3697 times $8, which ought to be $29576.
1. How many yards of German broadcloth at $6 per yard can be bought for $174564?
2. How many sheep at $7 apiece can be bought for $7833 ?
3. If 8 melons cost $1, how many dollars will 3744 melons cost ?
4. How many weeks are equal ta 87638 days? 5. How many feet are equal to 69847 inches? 6. How many ounces are equal to 98764 3? 7. How many square yards are equal to 5987536 sq. ft. ? 8. How many yards and quarters are equal to 97875 qr. ? 9. How many bu., pk. and qt. are equal to 87637 qt. ? 10. How many gal., qt., pt. and gi. are equal to 798953 gills ? 11. How many lb, 3, 3, and are equal to 793527 = ? 12. How many £, s., d. and qr. are equal to 587537qr. ?
13. How many sq. yd. in a surface 984 ft. long and 876 ft. wide ?
many bushels ?
14. In a cornfield there are 488 rows and 928 hills in a row, each hill producing a half pint of corn. How many half pints are there in the field ? How many quarts ? How many pecks? How
15. A man bought some land, paying for it at the rate of $1 for every
7 square rods. The field he bought was 1673 rods long, and 985 rods wide. How much did it cost him ? He paid for it in half-eagles. How many did it take?
16. Reduce 9784 35 to ones. 17. Reduce 86379 to ones. 18. Reduce 583793 to ones. 19. Reduce 74 53 9 5 to ones. 20. Reduce 894,7 32 to ones.
C. 1. If 8 acres of land cost $9707, what will 1 acre cost?
By the usual reasoning process we determine that 1 acre will cost as many dollars as there will be in each part obtained by dividing $9707 into 8 equal parts, that is, each acre will cost of $9707. Divisor. 8 ) $9707, Dividend = cost of 8 acres.
12133, Quotient = cost of 1 acre. We divide thus: of 9 thousands = 1 thousand, with a remainder of 1 thousand. 1 thousand 10 hundreds, and 7 hundreds added = 17 hundreds. $ of 17 hundreds 2 hun. dreds, with a remainder of 1 hundred. 1 hundred = 10 tens, and there are no tens to add. of 10 tens = 1 ten, with a remainder of 2 tens. 2 tens 20 units, and 7 units added = 27 units. f of 27 units 3 units, with a remainder of 3 units.
of 3 units g of a unit. Therefore, šof $9707 $1213}, and hence 1 acre will cost $1213} when 8 acres cost $9707.
To prove this work we can ascertain if 8 times $12133 are equal to $9707. For, if 1 acre costs $1213}, 8 acres will cost 8 times $1213}, which ought to be $9707.
We might have obtained the answer in another form, by reducing the 3 units, remaining from the division of the units, to lower denominations, thus: 3 units 30 tenths, and f of 30 tenths 3 tenths, with a remainder of 6 tenths. 6 tenths 60 hundredths, and of 60 hundredths 7 hundredths, with a remainder of 4 hundredths. 4 hundredths 40 thousandths,
and } of 40 thousandths 5 thousandths. The answer now appears in the form, $1213.375, which may be proved to be correct in the same way that the first form was proved.
The second form of answer might have been obtained from the first by reducing the f of a dollar to a decimal fraction.
2. If 7 cases of cloth cost $6545, how many dollars will i case cost ? 3. If 18579 lb. of hay are obtained from 9
many pounds are obtained from 1 acre ?
4. If 7 horses can draw 16786 lb., how many pounds can 1 horse draw?
5. If it cost $173549 to build 9 miles of rail-road, how much will it cost to build 1 mile?
6. A father divided his estate, valued at $879643, equally among his 5 children. What was the share of each ?
7. What is 4 of 975646 ? 8. What is of 3954.7 bushels ? 9. What is şof 7354.278 tons ? 10. What is & of 12456.78 miles ? 11. If 6 piano fortes cost $1837.44, how much will 7 cost ?
12. The ship Surprise is valued at $25427. Joseph Ward owns of her, and Samuel Lowe owns the remainder. What is the value of Mr. Ward's share ? of Mr Lowe's ?
13. A father, dying, left to his son an estate valued at $87646.44. The first year after the son came into possession of the property he spent of it in dissipation, the second year he spent of the remainder, and at the end of the third year he was penniless. How much did he spend in the first year? How much in the second year? How much in the third ? 14. Statistics show that the whole number of
relieved or supported as paupers in Massachusetts during the year 1849, was 24892, and that 141 less than of this number were state paupers, and the remainder were town paupers. How many were state paupers? How many were town paupers ? 3091 less than of the state paupers were foreigners. the number of foreigners ? 804 more than 1 of the whole were made paupers by intemperance in themselves or others. What was the number of these ?
15. A benevolent society divided 10 cwt. 3 qr. 23 lb. of flour equally among 6 poor persons. What was each person's share?
Solution. If 6 persons had 10 cwt. 3 qr. 23 lb. of flour, 1 person would have of 10 cwt. 3 qr. 23 lb.
6) 10, 3, 23.
share of 6
of 19 qr.
1, 3, 8, 8. = share of 1 person. Explanation of process. $ of 10 cwt is 1 cwt. with a remainder of 4 cwt. 4 cwt. = 16
with a remainder of 1 qr. 1 qr. : 28 lb., and 23 lb. added 51 lb. of 51 lb. 8 lb, with a remainder of 3 lb. 3 lb. = 48 oz. $ of 48 oz. =
The quotient is, therefore, 1 cwt. 3 qr. 8 lb. 8 oz.
16. 10 men bought a stack of hay weighing 4 T. 15 cwt. 3 qr. 26 lb. 14 oz. 6 dr. What ought each man's share to weigh?
17. A farmer had 9 equal hins filled with grain. They all contained 2047 cu. ft. 1436 cu. in. How many feet and inches did each bin contain ?
18. The brig Maria sailed from Philadelphia to Boston, with 207 T. 13 cwt. 2 qr. 19 lb. of coal, $ of which was landed at one wharf, and the remainder at another. What was the weight of that landed at the first wharf ? at the second ?
19. If John walks & as fast as George, how far will John walk while George is walking 97 m. 6 fur. 37 rd. 2 yd. ?
20. A company of 9 California gold-diggers found in 1 month 37 lb. 4 oz. 16 dwt. 17 gr. of gold, which they divided equally. What was the share of each ?
21. An English ship, valued at 8743£, carries a cargo which is worth s as much as the ship. How many £, s. and d. is the cargo worth? In a storm the sailors were obliged to throw 1 of the cargo overboard. What was the value of what they threw overboard ?
22. A merchant bought 17 T. 14 cwt. 2 qr. 23 lb. 10 oz. of sugar. He sold of it to one man, if of the remainder to another, and what there was left to another. What was the weight of that which he sold to the first man ? to the second ? to the third ?
D. The following illustrates the method of dividing, when, in the first class of questions, there are decimal fractions in the divisor.
1. How many baskets, each containing .8 of a bushel, can be filled from 347.54 bushels of peaches ?
347.54 number of bushels of peaches.
347.54 number of baskets bolding 1 bushel each. 10 times 347.54 = 3475.4
= number of baskets holding .1 of a bu. each. $ of 3475.4 434.425 = number of baskets holding .8 of a bu. each. Explanation. If each basket held 1 bushel, there would be as many baskets required as there are bushels, or 347.54 baskets. If each basket held .1 of a bushel, it would take 10 baskets to hold i bushel, and hence, there would be 10 times as many baskets as there are bushels, or 3475.4 baskets. But, when each basket holds .8 of a bushel, it will take ţ as many as when each basket holds .1 of a bushel, or $ of 3475.4 baskets, which, found by the methods already explained, is 434.425 baskets.
2. How many vest patterns, each containing .9 of a yard in a piece of cloth containing 34.758 yds. ?
3. How many lots, each containing . 7 of an acre, can be made from a field containing 94.381 acres ?
4. How many pounds of nails, at $.09 per lb., can be bought for $94.734 ?
5. How many pounds of cheese, at $.08 per lb., can be bought for $7.50 ?
6. How many yards of sheeting, at $.08 per yd., can be bought for $273 ?
7. If .04 of a yard of broadcloth is worth 1 yd. of calico, how many yards of calico are 85.4784 yd. of broadcloth worth ? 8. If .008 of a yard of silk is worth 1 yard of tape,
many yards of tape are 375 yd. of silk worth?
The following example and explanation illustrate the method of dividing when in the second class of questions the divisor contains decimal fractions.
9. If .06 of a lot of land cost $1847.52, how much will the whole lot cost?
$1847.52 = cost of .06 of the lot. # of $1847.52 $307.92 = cost of .01 of the lot. 100 times $307.92 $30792. = cost of the lot.
Explanation. If .06 of the lot cost $1847.52, .01 of the lot will cost of $1847.52, which, found by the method before ex