§ XIII. MISCELLANEOUS EXERCISES IN ADDITION AND SUBTRACTION OF COMPOUND NUMBERS. 1. What is the amount of the following quantities of gold: 4lb. 8oz. 13dwt. 8gr., 5lb. 11oz. 19dwt. 23gr., 8lb. Ooz. 17dwt. 15gr., and 18lb. 9oz. 14dwt. 10gr. ? 2. An apothecary would mix 7 33 23 29 1 gr. of rhubarb, 2lb 103 03 19 13gr. of cantharides, and 2lb 33 73 29 17gr. of opium; what is the weight of the compound? 3. Add together 17T. 11cwt. 3qr. 11lb. 12oz., 11T. 17cwt. 1qr. 19lb. 11oz., 53T. 19cwt. 1qr. 17lb. 8oz., 27T. 19cwt. 3qr. 181b. 9oz., and 16T. 3cwt. 3qr. Olb. 13oz. 4. A merchant owes a debt in London amounting to 7671£.; what remains due after he has paid 1728£. 17s. 9d. ? 5. From 73lb. of silver there were made 261b. 11oz. 13dwt. 14gr. of plate; what quantity remained? 6. From 71tb 83 13 19 14gr. take 7lb 93 13 19 17gr. 7. From 28T. 13cwt. take 10T. 17cwt. 19lb. 14oz, 8. A merchant has 3 pieces of cloth; the first contains 37yd. 3qr. 3na., the second 18yd. 1qr. 3na., and the third 3lyd. 1qr. 2na.; what is the whole quantity ? 9. Sold 3 loads of hay; the first weighed 2T. 13cwt. 1qr. 171b., the second 3T. 271b., and the third 1T. 3qr. 11lb.; what did they all weigh? 10. What is the sum of the following distances: 16m. 7fur. 18rd. 14ft. 11in., 19m. 1fur. 13rd. 16ft. 9in., 97m. 3fur. 27rd. 13ft. 3in., and 47m. 5fur. 37rd. 13ft. 10in.? 11. From 76yd. take 18yd. 3qr. 2na. 12. From 20m. take 3m. 4fur. 18rd. 13ft. 8in. 13. From 144A. 3R. take 18A. 1R. 17p. 200ft. 100in. 14. From 18 cords take 3 cords 100ft. 1000in. 15. A gentleman has three farms; the first contains 169A. 3R. 15p. 227ft., the second 187A. IR. 15p. 165ft., and the third 217A. 2R. 28p. 165ft.; what is the whole quantity? 16. There are 3 piles of wood; the first contains 18 cords 116ft. 1000in., the second 17 cords 111ft. 1600in., and the third 21 cords 109ft. 1716in.; how much in all? 17. From 17T. take 5T. 18ft. 765in. 18. From 169gal. take 76gal. 3qt. 1pt. 19. From 17ch. 18bu. take 5ch. 20bu. 1pk. 7qt. 20. From 83y. take 47y. 10mo. 27d. 18h. 50m. 14s. 21. From 11S. 15° 36′ 15" take 5S. 18° 50′ 18′′. 22. John Thomson has 4 casks of molasses; the first contains 167gal. 3qt. 1pt., the second 186gal. 1qt. 1pt., the third 108gal. 2qt. 1pt., and the fourth 123gal. 3qt. Opt.; how much is the whole quantity? 23. Add together 17bu. 1pk. 7qt. 1pt., 18bu. 3pk. 2qt., 19bu. 1pk. 3qt. 1pt., and 51bu. 3pk. Oqt. 1pt. 24. James is 13y. 4mo. 13d. old, Samuel is 12y. 11mo. 23d., and Daniel is 18y.9mo. 29d.; what is the sum of their united ages? 25. Add together 18y. 345d. 13h. 37m. 15s., 87y. 169d. 12h. 16m. 28s., 316y. 144d. 20h. 53m. 18s., and 13y. 360d. 21h. 57m. 15s. 26. A carpenter sent two of his apprentices to ascertain the length of a certain fence. The first stated it was 17rd. 16ft. 1lin., the second said it was 18rd. 5in. The carpenter finding a discrepancy in their statements, and fearing they might both be wrong, ascertained the true length himself, which was 17rd. 5yd. 1ft. 11in.; how much did each differ from the other? 27. From a mass of silver weighing 106lb., a goldsmith made 36 spoons, weighing 5lb. 11oz. 12dwt. 15gr.; a tankard, 3lb. Ooz. 13dwt. 14gr.; a vase, 7lb. 11oz. 14dwt. 23gr.; how much unwrought silver remains? 28. From a piece of cloth, containing 17yd. 3qr., there were taken two garments, the first measuring 3yd. 3qr. 2na., the second 4yd. 1qr. 3na.; how much remained? 29. Venus is 3S. 18° 45′ 15" east of the Sun, Mars is 78. 15° 36′ 18′′ east of Venus, and Jupiter is 5S. 21° 38′ 27′′ east of Mars; how far is Jupiter east of the Sun ? 30. The longitude of a certain star is 3S. 18° 14′ 35′′, and the longitude of Jupiter is 11S. 25° 30′ 50′′; how far will Jupiter have to move in his orbit to be in the same longitude with the star? § XIV. MULTIPLICATION OF COMPOUND NUMBERS. ART. 104. MULTIPLICATION of Compound Numbers is repeating numbers of different denominations any proposed number of times. ART. 105. To multiply when the multiplier is not more than 12. Ex. 1. If an acre of land cost 14 £. 5s. 8d. 2qr., what will 9 acres cost? Ans. 128£. 11s. 4d. 2qr. OPERATION. 8. d. qr. Multiplicand 14 5 8 2 9 Product 128 11 4 2 In performing this question, we first write the multiplier under the lowest denomination of the multiplicand, and then say 9 times 2qr. are 18qr., equal to 4d. and 2qr. We set down the 2qr. under the number multiplied, reserving the 4d. to be added to the next product. We then say 9 times 8d. are 72d., and the 4d. make 76d., equal to 6s. and 4d., and set the 4d. under the column of pence, reserving the 6s. to be added to the next product. Then 9 times 5s. are 45s., and 6s. make 51s., equal to 2£. and 11s. We place the 11s. under the column of shillings, reserving the 2 £, to be added to the next product. Again, 9 times 14£. are 126£., and 2£. make 128£. This, placed under the column of pounds, gives us 128£. 11s. 4d. 2qr. for the answer. QUESTIONS. Art. 104. What is multiplication of compound numbers? -Art. 105. Explain the operation. By what do you divide the product of each denomination? What do you do with the quotient and remainders thus obtained? RULE. - Multiply each denomination of the compound number by the multiplier separately, beginning with the lowest, and carry as in addition of compound numbers. NOTE. The answers to the following questions are found in the corresponding questions in Division of Compound Numbers, p. 128. 14. What cost 7 yards of cloth at 18s. 9d. per yard? 15. If a man travel 12m. 3fur. 29rd. in one day, how far will he travel in 9 days? 16. If 1 acre produce 2 tons 13cwt. 19lb. of hay, what will 8 acres produce? * The expression åd. is equivalent to 1qr.; ¿d. to 2qr.; d. to 3qr. QUESTIONS.- What is the rule? How are farthings sometimes written? 17. If a family consume 49gal. 3qt. 1pt. of molasses in one month, what quantity will be sufficient for one year? 18. John Smith has 12 silver spoons, each weighing 3oz. 17dwt. 14gr.; what is the weight of all? 19. Samuel Johnson bought 7 loads of timber, each measuring 7 tons 37ft.; what was the whole quantity ? 20. If the moon move in her orbit 13° 11′ 35′′ in 1 day, how far will she move in 10 days? 21. If 1 dollar will purchase 2lb 83 73 19 10 gr. of ipecacuanha, what quantity would 9 dollars buy? 22. If 1 dollar will buy 2A. 3R. 15p. 30yd. 8ft. 100in. of wild land, what quantity may be purchased for 12 dollars? 23. Joseph Doe will cut 2 cords 97ft. of wood in 1 day; how much will he cut in 9 days? 24. If 1 acre of land produce 3ch. 6bu. 2pk. 7qt. 1 pt. of corn, what will 8 acres produce? ART. 106. When the multiplier is a composite number, and all its factors are within the table. Ex. 1. What cost 24 yards of broadcloth at 2£. 7s. 11d. per yard? Ans. 57£. 10s. Od. In this question, we find the number 24 equal to the product of 4 and 6; we therefore multiply the price first by 4, and then that product by 6, and the last product is the answer. Ex. 2. What cost 360 tons of iron at 17£. 16s. 1d. per ton? Ans. 6409£. 10s. Od. OPERATION. £. 8. 17 16 d. 1= price of 1 ton. 6 106 16 6= price of 6 tons. 6 640 19 In this question, we find the factors of 360 to be 6, 6, and 10. We first multiply by 6, and then that product by 6, and then 0 = price of 36 tons. again the last product by 10 6409 10 0 = price of 360 tons. 10. |