X 5 X 47=(13 x 11 x 7) X (4 X 5 X 5) X (3 x 47)= 1001 X 100 X 141 = 14114100. Explanation. Observing that 39 = 3 X 13, that 55 = 5 x 11, that 28 = 4 X 7, we select from these the factors 13, 11, and 7, the product of which is 1001. From the remaining factors, since 235 = 5 x 47, we may select the factors 5, 5, and 4, the product of which is 100. The remaining factors being 3 and 47, the product of which is 141, we have for the complete product 141 X 100 X 1001 = 14114100. Note. The pupil should perform and explain most, if not all, of the questions in this and the next letter, without writing any figures. 5. What is the product of 24 x 47 x 334 X 125 ? N. The principles illustrated below can frequently be applied to advantage. 1. 6 X 84 + 7 x 43 + 47 X 84 + 17 X 84 + 18 x 43 = (6 + 47+17) X 84 +17+ 18) X 43 = 70 X 84 + 25 X 43 = 5880 + 1075 = 6955. 2. 47 x 28 +36 x 62 +28 X 23-29 X 62 - 66 x 28 – 62 X 2= (47 + 23 - 66) 28 + (36 — 29 - 2) X 62=4 X 28 +5 X 62=112 + 310 = 422. 3. What is the value of 7 x 64 + 9 X 75 — 3 X 64 5 X 75 + 8 X 64 + 4 X 75 ? 4. What is the value of 9 x 93 + 27 X 6 + 88 X 93 + 17 x 27 ? 5. What is the value of 84 X 17+ 36 x 4 + 36 X 84 + 12 X 36 - 3 X 84? 6. What is the value of 9 x 13 + 16 x 9 +8 X 31+ 9 X 23 + 23 X 8+ 21 x 7 + 43 x 9? 7. What is the value of 25 X 19 + 124 x 9 + 25 X 21 + 29 X 121 ? 8. What is the value of 8 X 163 + 17 X 334 + 14 X 61 +9 X 121? Suggestions. 8 X 163=4 X 2 X 164=4 X 33. 14 X 61=7 X 2 X 61 =7 X 124. Therefore, the value of the above expression = (4 + 17) X 334 + (7 +9) X 124 = 700 + 200 900. 9. What is the value of 18 X 121 + 7 x 25 + 28 X 75? Suggestions. 18 x 12 = 9 X 25. 28 x 75 = 28 X 3 x 25 = 84 x 25. 10. What is the value of 46 X 12 + 19 X 24 + 27 X 48 + 16 X 96 + 19 X 72 + 83 X 24? 11. I bought 17 lb. of raisins at $.09 per lb., 28 lb. of flour at $.04 per lb., 4 lb. of butter at $.23 per Ib., 37 lb. of cheese at $.09 per lb., and 9 lb. of tea at $.43 per lb. What was the amount of my purchase ? 12. Mr. Elijah Wheelock, Jr., bought of Mr. Elbridge Clapp, 7 bags of corn at $1.50 per bag, 9 bushels of oats at $.374 per bu., 121 lb. of rice at $.05 per lb., 150 lb. of sugar at $.09 per lb., and 25 yd. of sheeting at $.08 per yd. What was the value of the goods he purchased ? 13. Miss Lucy Smith bought of Jones & Brown, 9 yd. of black silk at $.871 per yd., 6 yd. of muslin at $.42 per yd., 8 skeins of sewing silk at $.06 per skein, and 3 pair of kid shoes at $.871 per pair. What was the amount of her purchase ? 0. 1. How much will 13 cwt. 2 qr. 7 lb. of sugar cost at $8.64 per cwt. ? Direction. First get the cost of 13 cwt.; then of 2 qr. or 1 of a cwt.; and then of 7 lb. or of 2 qr. The work may be written as below: $8.64 = cost of 1 cwt. £ of $8.64 = 4.32 .54 16 17 lb. $117.18 “ 13 cwt. 2 qr. 7 lb. 66 2 qr. 2. How much will 26 A. 1 R. 25 sq. rd. of land cost, at $174.25 per acre ? $174.25 = cost of 1 A. 26 times $174.25 $4530.50 66 26 A. - 1 R. 5.445 66 5 rd. $4601.288= “ 26 A. 1 R. 25 sq. rd. Note. In dividing, in examples like the above, it is unnecessary to carry out the work further than to mills. 3. How much will 16 cwt. 3 qr. 21 lb. of tea cost, at $47.83 per cwt. ? Suggestion. Since 16 cwt. 3 qr. 21 lb. lacks but 7 lb. of being 17 cwt., its cost must equal the cost of 17 cwt. minus the cost of 7 lb. We have, therefore, the following written work: $47.83 = cost of 1 cwt. 17 times $47.83 = $813.11 = 17 cwt. To of $47.83 = 2.989 = 6 7 lb. to be subtracted. $810.121 = “ 16 cwt. 3 qr. 21 lb. 4. How much will it cost to build a road 37 m. 5 fur. 25 rd. in length, at the rate of $2173.75 per mile ? 5. How much will 47 yd. 2 qr. 3 na. of broadcloth cost, at $3.125 per yd.? 6. How much will 22 hhd. 21 gal. 3 qt. 1 pt. of wine cost, at $47.875 per hhd., if each hogshead contains 63 gallons ? 7. How much will 24 bu. 1 pk. 6 qt. of wheat cost, at $1.375 per bushel ? 8. How much will 37 bu. 3 pk. 4 qt. of wheat cost, at $1.625 per bushel ? 9. How much will 14 cwt. 2 qr. 15 lb. of coffee cost, at $12.625 per cwt., the cwt. being reckoned at 100, and the qr. at 25 lb. ? 10. A man bought a farm, containing 137 A.3 R. 30 sq. rd., at $46.94 per acre. How much did it cost him? 11. A trader bought 184 bu. 2 pk. 6 gt. of Indian corn, at $.875 per = 1£ 12. An English merchant purchased 1728 yd. of cloth, at 1s. 8d. per yd. What was the cost of the whole ? Suggestion. ls. 8d. = of 1£. 13. What will 857 yd. of broadcloth cost, at 16s. 8d. per yd. ? Suggestions. 16s. 8d. 3s. 4d. = 1£ $£. Again : 16s. 8d. = 10s. + 6s. 8d. = 4£ + 4£. Adopting the first of the above suggestions, the work would be written thus : 857£ = cost at 1£ per yd. # of 857£= 142£, 16s. 8d. = cost at 3s. 4d. per yd. By subtraction, 714£, 3s. 4d. = cost at 16s. 8d. per yd. Adopting the second of the above suggestions, the work would be written thus : 857£ =cost at 1£ per yd. 714£, 3s. 4d. = cost at 16s. 8d. per yd. 14. What will 1478 reams of paper cost, at 13s. 4d. per ream ? Suggestion. 13s. 4d. 6s. 8d. = 1£ £. 15. What will 737 yd. of black silk cost, at 17s. 6d. per yd. ? Suggestion. 2s. 60. = of 1£. 16. If 14 yd. 1 qr. 2 na. 1 in. of cloth cost 12£, 13s. 8d., what will 28 yd. 3 gr. 2 in. cost ? Suggestion. 28 yd. 3 qr. 2 in. =twice 14 yd. 1 nr. 2 na. 1 in. 17. If 7 lb. 3 oz. 4 dr. of sugar cost 2s. 9d. 1 qr., what will 21 lb. 9 oz. 12 dr. cost ? 18. If 17 A. 3 R. 7 rd. of land cost 19£, 14s. 9d., what will 88 A. 3 R. 35 rd. cost ? 19. If 2 lb. 10 oz. 18 dwt. 22 gr. of gold can be bought for $667.75, for how much can 1 lb. 5 oz. 9 dwt. 11 gr. be bought? 20. If 23 lb. 13 oz. 8 dr. of potash can be bought for $2.12, how much can be bought for $16.96 ? = l£ A LIST OF BOOKS PUBLISHED BY BENJAMIN B. MUSSEY AND COMPANY, NO. 29, CORNHILL, AND 36, BRATTLE STREET, BOSTON. MUSIC BOOKS. THE MODERN HARP, Or, BOSTON SACRED MELODIST.--A Collection of Church Music, comprising, in addition to many of the most Popular Tunes in common use, a great variety of new and original Tunes, Sentences, Chants, Motets, and Anthems, adapted to Social and Religious Worship, Societies, Singing Schools, &c. By EDWARD L. WHITE and JOAN E. GOULD. This Book, in the short space of twelve months, has passed through no less than sixteen editions, and is now used in all the best Choirs and Societies in New England, and is universally considered as one of the best books of Church Music now in use. “So far as we have been able to examine this work, we should judge it to be superior to any modern work that we have seen.” - Skowhegan Democrat. “In bringing this work before the public, no time or pains have been spared to render it not only a popular, but a useful Collection. More than the usual number of new Tunes occupy a space in it, and most of this new Music is of a high character, and possesses the true attributes of Church Music. There is also to be found an unusual number of Sentences, Select Pieces, Chants, &c., suitable for the opening and closing of divine worship, among which the entire service of the Protestant Episcopal Church is given in the order of performance. "" The whole Collection is judiciously arranged, and will undoubtedly ake a rank second to none of the numerous publications of Church alusic now in usc.' -- Atlas. |