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In dividing the quarters, pounds and 2 ounces, by the same divisor that we did the hundreds, we take the same part of the several denominations, and these denominations have not been divided before, for we only divide the remainders brought into a lower denomination, and the given numbers of each denomination added to them ; consequently, 2 cwt. 1 qr. 11 lb. 15 oz. is an eighth part of 18 cwt. 3 qr. 15 lb. 11 oz.
7. A gentleman divided 528 A. 3 R. 9 r. of land, equally between his 7 sons. How much did each re
ceive 2 Ans. 75 A. 2 R. 7 r. 8. How far must a man travel in one day, to go 351 miles in 10 days - Ans. 35 M. 32 r.
9. Wishing to divide a stick of hewn timber, containing 2 T. 28 ft. 1104 in. into 11 equal parts, how much must each part contain 7 Ans. 11 ft. 1200 in. 10. Bought 12 silver spoons, weighing 2 lb. 10 oz. 14 pwt. 12 gr. ; what was the weight of each 2 Ans. 2 oz. 17 pwt. 21 gr. 11. A silversmith is ordered to make 9 pair of sugar tongs from 8 oz. 18 pwt. 21 gr. of silver. What will be the weight of each pair? Ans. 19 pvt. 21 gr. 12. A teamster draws a pile of wood consisting of 12 C. 92 ft. at 11 loads. How much does he haul at a load 7 Ans. 1 C. 20 ft. 13. An army consisting of 10 brigades, consumes 5000 lb. 15 oz. 10 dr. of bread in one day; how much does each brigade consume? Ans. 500 lb. 1 oz. 9 dr.
When the divisor is large and a composite number, divide the dividend by one of its component parts, and that quotient by the other. -
14. If 24 yards of cotton cloth cost 1 #. 16 S. what is the price of one yard? * *
Illustration of Rule 3.—The product of the component parts of a number, is always equal to the number itself, therefore, dividing by one of the component parts, we take a part of the dividend, which is as much less than the whole dividend, as the other component part is less than the whole divisor; and dividing that part of the dividend by the other component number, must give the quotient of the dividend divided by the whole divisor. In the last question, 12 s. is a third part of the dividend, but as 8 is a third part of the whole quantity, 24 yd., the 12 s. must be the price of 8 yd. ; and dividing the price of 8 yards by 8, we obtain the price of 1 yard, in the same manner as shown before.
15. A farmer sold 56 bushels of corn for 11 f. 8s 8 d. ; what did he receive a bushel? - Ans. 4 s. 1 d. 16. If 100 acres produce 2198 bus. 1 pk. 6 qt. of rye, what does one acre produce 2 Ans. 21 bus. 3 p.k. 7 qt. 1 pt. 17. Suppose the earth to move through the space of 50’ I 59'999'999 M. 6 fur. 20 r. in 84 years; how far does it move in one year? Ans. 5971427857 M. 1 fur. 5 r.
JNote 1.--If the divisor be hundreds, divide the dividend by the number of hundreds, then proceed as directed by Rule 3,
18. If 600 pounds of copperas cost 246. 10 s. what is it per pound 7
19. 500 soldiers receive 50221. A. 3 R. 20 r. of bounty land; what is the share of each Ans. 100 A. 1 R. 31 r.
JWole 2.—If the divisor be not a composite number, we must divide the dividend by the whole divisor.
20. If a field containing 19 A. produce 17 T. S
153 o 152 1 w 4 19) 5 (0 : - 25 * . 19) 133 (? 133
Explanation.—We cannot divide 17 by 19, we therefore multiply the tons by 20, the number of cwt. in a ton, add the 3 cwt. to the product, and find 18 cwt. the first quotient. Neither can we divide the 5 qr. by 19, so that we must bring the quarters to pounds, and then divide.
21. If a planter sell 173 hhd. of tobacco for 3480 f. 18 s. 1 d. what does he receive per had 2 Ans. 2036. 2 s. 5 d. 22. If each hbd. in the last question contain 90? pounds, what does the planter receive per pound 2 Ans. 5 d. 1;# qr: 23. A stock of 12 boards measures 195 ft. 8 in. ; how much does 1 board measure ? Ans. 16 ft. 3 in. 8 s. 24. If it requires 5005 ft. of boards to cover the sides of a square building, how many feet does it take to cover one side 7 Ans. 1251 ft. 3 in. 25. What is the measure of one square stick of timber, if 13sticks of equal dimensions, measure 18 T. 24 ft. 365 in. Ans. 1 T. 21 ft. 161 in. 26. What is the 7th part of 19 C. 81 ft. of wood Ans. 2 C. 103 ft.
Questions to be performed by Subtraction and Division of compound numbers.
1. What is one-third of the difference between 6 cwt. 21 lb., and 3 cwt. 22 lb., neat Ans. 3 qr, 24 lb. 10 oz. 104 dr. 2. A man dying, left a farm of 200 A. 3 R. 1 r., of which his widow was to receive one-third, and the remainder to be divided equally between 6 children: What was the widow’s share; also, what was the share of each child 2 Ans } Widow's share, 66 A. 3 R. 27 r. & Each child’s share, 22 A. 1 R. 9r. 3. 24 men agree to construct 7 M. 1 fur. 24 r. of road in a given time. After completing one-sixth of the distance, they employ 3 men more. What distance does each man construct before and after the 8 men are employed ? Ans Each man constructs 16 r. before, and * \ 1 fur. 20 r. after the 8 men are employed.
Roduction OF COMPOUND NUMBERS,
The same quantity may be expressed by different numbers. Thus, 2 weeks or 14 days express the same space of time. It is easy to perceive that if we express the same quantity by different numbers, that each unit in the larger number must represent a less part of the quantity than an unit in the smaller number. The 14 units in the 14 days, denote as much time as the 2 units in the 2 weeks; but a single unit in the 14 days implies but 1 day, whereas a single unit in the 2 weeks denotes 7 days, and is equal to 7 units in the 14 days.
The more parts we divide any thing into, the less each part must be. Let the figure 1 stand for one apple, this figure denotes the whole; but if we divide the apple into 4 equal parts, and have 1 unit to express each part, we must have 4 units to express the same apple which was expressed by 1 unit before it was divided ; and if each quarter be divided into 2 equal parts, the whole apple will be divided into 8 equal parts, and the figure 8 will be required to express the whole apple, when each unit is to express 1 part. The figure 1, in one instance, expresses as much as 4 other units, and in the other, as much as 8 units express, for the 4 or the 8 denotes but 1 apple. From what has been said, it appears that we can fix no limit to the value of an unit, for every time we divide any thing, the parts must become smaller, and