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10d. and 11d. are (by uniting 1 of the 10d. with the

£ 8. d. 11d.) 12d. + 91. = ls. 9d., and 6d. are (by uniting 3

27 18 8 of the 6d. with the 9d.) 18. 12d. + 3d. 2s. 3d., and

47 19 6 8d. are 28. 11d.

86 17 11 Writing the 11d., and, observing that there will be £1 57 13 10 for every 20s., we add the 2s. with the sbillings, thus: 28. and 13s. are 15s., and 178. are (by uniting 3 of the

220 9 11 15s. with the 178., or else 5 of the 178. with the 15s.) 208. + 12s. £1 12s., and 19s. are (by uniting 1 of the 12s. with the 19s.) £2 11s., and 18s. are (by uniting 2 of the 11s. with the 18s.) £3 98.

Writing the 9s., we add the £3 to the pounds, as in siinple numbers, which gives for the answer, £220 9s. 11d.

2D SOLUTION.-Writing the numbers as before, we add thus :

10d. + 11d. + 6d. + 8d. 35d., which, since 12d. = 18., must equal as many shillings as there are 12 in 35. This, found by dividing 35 by 12, gives 2s. 11d.

Writing the 11d., we add the 2s. to the column of shillings, thus :

2s. + 138. + 178. + 198. + 188. 698., which, since 20s. £1, must equal as many pounds as there are times 20 in 69. This, found by dividing 69 by 20, gives £3 9s.

Writing the 9s., we add the £3 to the column of pounds, thus :

£3 + £57 + £86 + £47 + £27 £220. Hence, the required sum is £220 9s. 11d.

Note.--We think that, as a general thing, the first solution will be found the most convenient. The teacher alone can judge of the expediency of having the class attempt to master both.

38. Examples for Practice.

1.

2.

8. d. far. 28 16 11 3 37 18 10 2 23 19 8 3 42 13 9 3

£ 8. d. far.
26 16 11 2
35 14 3 0
92 19 10.0
48 8 9 3

3.
yd. qr. na.
24 3 2
53 1 3
48 2 3
27 0 2

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A. R. sq. rd. 24 1 26 62 3 39 37 2 16 58 0 23

8q.yd. sq.ft. sq.in.

10.

16. 02. dwt. gr. 43 7 13 20 27 11 16 22 45 10 18 21 36 8 7 22 46 9 18 23

13.

Ib

3 3 gr. 13 11 5 2 18 21 8 6 1 9 32 10 7 0 13 25 7 4 2 15 32 6 7 0 18

8 6 127 3 7 100 5 5 96 2 8 138

m. fur. rd. 226 6 27 113 7 36 427 5 28 336 6 35

11.

12.

o

16. oz. dwt. gr. 16 10 11 4 21 3 18 22 15 11 17 19 14 8 17 21 42 9 14 17

14 13 46 11 45 37 10 58 49 8 17 57 3 32 25

14.

ID 3 3 gr. 21 11 7 2 19 35 10 6 1 18 27 9 5 0 17 18 10 6 1 18 94 11 7 2 19

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* In adding yards, the reductions can generally best be made by regarding every 11 yards as 2 rods. It should be also borne in mind that } yard equals 1 ft. 6 in., and that if, in any case, there are 5 yd. and 1 ft. 6 in. besides, the value can best be expressed as 1 rod.

23.* 8.rd.8.yd. s.ft.s.in.

5 29 8 140 9 28 3 26 7 30 6 100 8 27 7 136 6 30 8 142

24. A. R.8.rd.s.yd.8.ft. s.in. 46 3 25 15 8 128 39 2 17 17 6 135 28 0 36 26 0 36 59 2 28 30 7 72 47 3 35 28 8 130

25. C.cd.ft.cu.ft.cu.in. 58 3 14 1720 96 6 13 896 37 7 15 1725 54 5 10 597

26. C.cd.ft.cu.ft.cu.in. 47 7 14 1650 83 0 8 1722 58 6 9 1528 49 7 13 1628

27. £15 178. 10d. 3 far. + £18 16s. 11d. 2 far. + £23 118. 8d. 3 far. + £34 19s. 6d. 1 far.?

28. 85 lb. 10 oz. 19 dwt. 22 gr. + 43 lb. 6 oz. 17 dwt. 21 gr. + 49 lb. 8 oz. 14 dwt. 13 gr. + 87 lb. 7 oz. 18 dwt. 23 gr.?

29. 14ib 83 63 29 14 gr. + 7ið 103 73 19 18 gr. + 19ib 93 53 17 16 gr. + 34ib 113 + 73 + 10 + 17 gr.?

30. 8 bu. 2 pk. 3 qt. 1 pt. + 5 bu. 3 pk. 7 qt. O pt. + 5 bu. 3 pk. 6 qt. 1 pt. + 9 bu. 1 pk. 3 qt. O pt. + 3 bu. 2 pk. 7 qt. 1 pt. ?

31. 6 T. 13 cwt. 2 qr. 24 lb. 5 oz. 13 dr. + 8 T. 18 cwt. 3 qr. 20 lb. 15 oz. 15 dr. + 9 T. 13 cwt. 1 qr. 22 lb. 8 oz. 9 dr. + 2 T. 11 cwt. 1 qr. 15 lb. 7 oz. 14 dr. + 4 T. 19 cwt. 2 qr. 21 lb. 14 oz. 11 dr.?

32. 23 C. 6 cd. ft. 14 cu. ft. 1379 cu. in. + 87 C. 4 cd. ft. 11 cu. ft. 1600 cu. in. + 68 C. 7 cd. ft. 9 cu. ft. 1425 cu. in. ?

33. 9 wk. 6 da. 13 h. 50 min. 35 sec. + 12 wk. 4 da. 21 h. 48 min. 37 sec. + 5 wk. 4 da. 22 h. 53 min. 25 sec. + 2 wk. 5 da. 17 h. 38 min. 49 sec. + 9 wk. 4 da. 13 h. 22 min. 13 sec.?

* In adding square yards, observe that 604 sq. yd. 2 sq. rd.; that 903 8q. yd.

3 sq. rd.; and that 121 sq. yd. 4 sq. rd. Observe, farther, that of a sq. yd. = 2 sq. ft. 36 sq. in.; } of a sq. yd. 4 sq. ft. 72 sq. in.; and that of a sq. yd. 6 sq. ft. 108 sq. in. This will avoid serious difficulty in the use of fractions.

34. 18 m. 5 fur. 26 rd. 4 yd. 2 ft. 7 in. + 23 m. 7 fur. 37 rd. 5 yd. 1 ft. 2 in. + 31 m. 5 fur. 32 rd. 4 yd. 2 ft. 10 in. + 17 m. 4 fur. 31 rd. 3 yd. 2 ft. 11 in. + 3 m. 4 fur. 39 rd. O ft. 7 in.?

35. 5 bu. 3 pk. 2 qt. 1 pt. + 8 bu. 1 pk. 7 qt. O pt. + 4 bu. 3 pk. 6 qt. 1 pt. 3 gi. + 5 bu. 2 pk. 5 qt. O pt. 2 gi. + 7 bu. 2 pk. 5 qt. 1 pt. 1 gi. + 4 bu. 2 pk. 4 qt. 1 pt. 3 gi. ?

36. £278 138. 6d. 1 far. + £523 188. 11d. 3 far. + £436 14s. 8d. 2 far. + £142 178. 10d. 3 far. + £203 10s. 8d. 1 far. + £850 158. 7d. 3 far. + £312 18s. 11d. 2 far.?

37. I have 3 bars of silver: the first weighs 6 lb. 3 oz. 5 dwt. 17 gr.; the second weighs 5 lb. 10 oz. 13 dwt. 17 gr.; and the third weighs 5 lb. 11 oz. 18 dwt. 22 gr. What is the weight of the whole ?

38. After paying £17 13s. 6d. to one man, £12 16s. 3d. 1 far. to another, £21 19s. 11d. 3 far. to another, and £10 14s. 9d. 3 far. to another, I had £58 10s. 7d. 1 far. left. How much had I at first?

SECTION VI.

SUBTRACTION.

39. Definitions and Explanations.

(a.) SUBTRACTION is a process by which we find how many units there are in the difference of two numbers, or in the excess of one number over another.

(b.) The larger given number, or the one from which we sub. tract, is called the MINUEND; the smaller number, or the number subtracted, is called the SUBTRAHEND; and the result is called the DIFFERENCE or REMAINDER.

ILLUSTRATIONS. - In “3 from 7 leaves 4,” or 7 - 3 4," 7 is the minuend, 3 is the subtrahend, and 4 is the difference or remainder.

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