10. A jeweller buys the following quantities of silver: 8 lb. 6 pwt.; 10 oz. 4 pwt. 21 gr.; 8 oz. 20 gr.; 3 lb. 6 oz. 8 pwt. 7 gr. How much does he buy in all? 290. If a fraction occurs in the answer, what must be done? 16. What are the contents of four hogsheads, the first of which contains 63 gal. 2 qt. 13 pt.; the second, 60 gal. 3 qt. 1.75 pt.; the third, 62 gal. 1 pt. 3 gi.; the fourth, 61 gal. 2 qt. 2 gi.? Ans. 248 gal. 1 qt. 1 pt. 2 gi. 17. How much wood in three piles, the first of which contains 10 Cd. 6 cd. ft. 4 cu. ft.; the second, 12 Cd. 12 cu. ft.; the third, 17 Cd. 1 cd. ft.? 18. A surveyor measures four distances; the first he finds to be 40 ch. 59 1. 3 in., the second 28 ch. 43 1. 5 in., the third 16.27 ch., the fourth 12 ch. 7 in. What is the whole distance measured, expressed first in chains, &c., then in the denominations of linear measure? Ans. 97 ch. 301. 7.08 in.: 1 mi. 1 fur. 29 rd. 1 yd. 10.68 in. 19. How many yards in 3 pieces of cloth, containing respectively 24 Ells French 3 qr. 1 in., 28 Ells English 3 qr. 2 nails, 40 Ells Flemish 1 qr. 1 nail 1 in. ? 2 inches make 1 nail; 4 nails, 1 qr. of a yd.; 3 qr., 1 Ell Flemish; 5 qr., 1 Ell English, 6 qr., 1 Ell French. Reduce the ells to the common denomination, quarters; add the whole, and reduce the quarters to yards. Ans. 103 yd. 20. Find the sum total in pounds, &c., of the following items: £20 10s., £1 6s. 8d., 5 guineas 10s. 6d., 15 guineas, and £1 15s. 31d. Ans. £45 2s. 51d. 21. A person owning a section of land (§ 251) buys three additional tracts, containing 347 A. 2 R. 27 sq. rd., 201 A. 19 sq. rd., and 417 A. 3 R. 14 sq. rd. How much does he then own in all? Ans. 2 sq. mi. 326 A. 2 R. 20 sq. rd. 22. How much coke in three carts, the first of which contains 1 chal. 5 bu. 2 pk., the second 1 chal. 5 bu., and the third 35 bu. 3 pk.? 23. How much beer in four hogsheads, containing respectively 53 gal. 2 qt., 54 gal. 1 qt. 1 pt., 52 gal. 3 qt. 1 pt., and 51 gal. 3 qt. 1 pt.? 24. Add together 6 da. 37 min., 43 da. 5 h. 29 sec., 94 da. 19h. 18 sec., 126 da. 7 h. 9 min. 8 sec., and 94 da. 16 h. 13 min. 5 sec. How many years in the sum? 25. How many yards in four pieces of cloth, containing respectively 30 yd. 1 qr., 20 Ells Fr. 1 na., 24 Ells En. 14 in., 32 Ells Fl. 2 qr. 2 na. in. Ans. 115 yd. CHAPTER XV. COMPOUND SUBTRACTION. 292. Compound Subtraction is the process of finding the difference between two numbers, when one or both are compound. EXAMPLE 1.-From 20 lb. 5 oz. 3 dr. take 18 lb. 7 oz. 1 dr. Write the subtrahend under the minuend, pounds under pounds, &c., marking the denominations above. Begin to subtract at the right. 1 dr. from 3 dr. leaves 2 dr., which we write in the column of drams. Ib. Oz. dr. 20 5 3 18 7 1 7 oz. can not be taken from 5 oz. We therefore take one of the next higher denomination Ans. 1 14 2 (1 lb.), reduce it to ounces, and add it to the 5 oz.; 16 + 5 = 21. Then subtracting 7 from 21, we get 14, which we write under the ounces.-To balance the 16 oz. added to the minuend, we now 292. What is Compound Subtraction? Go through the given example explaining the steps. add 1 lb. to the subtrahend, or carry 1 to the next column; 19 lb. from 20 lb., 1 lb. Ans. 1 lb. 14 oz. 2 dr. This process involves the same principle as carrying in Simple Subtraction. In the latter, as the orders uniformly increase in value tenfold, we add 10 to the figure of the minuend when it is necessary, and to balance it carry 1 to the figure of the next higher order in the subtrahend. 293. RULE.-1. Write the subtrahenā under the minwend, placing numbers of the same denomination in the same column. Beginning at the right, subtract as in simple numbers. 2. If, in any denomination, the subtrahend exceeds the minuend, add to the latter as many as make one of · the next higher denomination. Subtract, and carry 1 to the subtrahend in the next higher denomination. 3. Prove by adding remainder and subtrahend. EXAMPLE 2. mi. fur. rd. yd. From 1 0 0 4 7 39 52 We may have to carry several times in succession.-If fractions occur, proceed as in subtraction of fractions. Thus, in Example 2, 5 yd. can not be taken from 4 yd. Add, therefore, to the minuend 5 yd., which equal 1 rd. 4+ 59. Subtracting 53 from the sum, we get 35 yd., and carrying 1 successively to the columns of rods, furlongs, and miles, we find the remainder to be 0 in each case. Ans. 3 yd. If a fraction occurs in any denomination of the remainder, except the lowest, it should be reduced and added, as in Addition, § 290. Take Rem. 0 0 0 35 294. To find the interval between different dates since the Christian era, Write the earlier date under the later, representing the month in each by its number (January, 1; February, 2, &c.). Subtract, allowing 30 days to the month and 12 months to the year. EXAMPLE 3.-Washington was born Feb. 22, 1732. How old was he July 4, 1776 ? Represent July, the seventh month, by 7— and February, the second month, by 2. Thirty days being allowed to the month, we subtract 22 from 30 + 4, and carry 1. yr. mo. da. 1776 7 4 1732 2 22 Ans. 44 4 12 Show how the same principle is involved in carrying in Simple Subtraction.293. Recite the rule. If fractions occur, how are we to proceed? Illustrate this with the given example.-294. Give the rule for finding the interval between different dates since the Christian era. Apply this rule to Example 3. மப்புடன். 5 26 1 8 1 6=+yd. 5 1 32 73 2 36=sq.yd. 0 2 Ans. 5 1 32 1 6 109 Ans. 2 5 38 41 2 5 38 5 Find the value of the following. Prove each example. 9. 25° 15′ 31′′ - 18° 52′ 49′′. 14. 200 da. 13 h. 15 sec. · 195 da. 21 h. 49 min. 15. 9 lb. 3 oz. 1 sc. 19 gr. — 8 lb. 2 dr. 2 sc. 6 gr. 16. 2 T. 9cwt. 3 lb. 4 dr. — 3 qr. 24 lb. 15 oz. 13 dr. 20. 11 cu. yd. 111 cu. in. — 8 cu. yd. 20 cu. ft. 1000 cu. in. *Wine Measure. Carrying 1, we get 32 gal., which can not be taken from one barrel reduced to gallons (81 gal.). Hence we take two barrels, reduce to gallons, subtract, and carry two. 31 × 2 = 63. 63 - 32 = 31. Remember, in such a case, to carry 2. |