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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 ?
6. What is the product of 625 X 947 X 16 ?
7. What is the product of 91 x 9.X 132 X 8?
8. What is the product of 86 X 1663 X 154 X 78?
9. What is the product of 371 x 15 x 64 x 275 ?
10. What is the product of 63 X 374 X 663 X 443 ?
11. What is the product of 55 x 1376 X 65 X 35 ?
12. What is the product of 871-X 104 x 4796 ?

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.
13 times $8.64 =$112.32 = 6 13 cwt.

£ of $8.64 = 4.32
of $4.32

.54

16 17 lb. $117.18

“ 13 cwt. 2 qr. 7 lb.

66 2 qr.

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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.
of $174.25 43.562

- 1 R.
1 of $43.562 21.781 “ 20 sq. rd.
of $21.781

5.445

66 5
sq.

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
bushel. How much did it cost him ?

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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.
4 of 857£ 428£, 10s. = cost at 10s. per yd.
of 857£ 285£, 13s. 4d. = cost at 6s. 8d. 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.

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