10d. and 11d. are (by uniting 1 of the 10d. with the 11d.) 12d.+ 91. 1s. 9d., and 6d. are (by uniting 3 of the 6d. with the 9d.) 18. 12d. + 3d. = 2s. 3d., and 8d. are 2s. 11d. £ 8. d. 27 18 47 19 6 86 17 11 57 13 10 Writing the 11d., and, observing that there will be £1 for every 20s., we add the 2s. with the shillings, thus: 220 9 11 2s. and 13s. are 15s., and 17s. are (by uniting 3 of the 15s. with the 17s., or else 5 of the 17s. with the 15s.) 20s. + 12s. = £1 128., 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 9s. Writing the 9s., we add the £3 to the pounds, as in simple 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. 1s., 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.+ 13s.+ 17s. + 19s. + 18s. 69s., 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 9s. 11d. 1. = £ 8. d. far. 28 16 11 3 37 18 10 2 23 19 8 3 42 13 9 3 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. £220. Hence, the required sum is 2. = 3. yd. qr. na. 24 3 2 53 1 3 48 2 3 27 0 2 *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. 27. £15 17s. 10d. 3 far. + £18 16s. 11d. 2 far. + £23 11s. 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. 14mb 83 63 29 14 gr. +7mb 103 73 19 18 gr. + 191b 93 53 19 16 gr. + 34ł 113 + 73 + 19 + 17 gr.? 30. 8 bu. 2 pk. 3 qt. 1 pt. + 5 bu. 3 pk. 7 qt. 0 pt. + 5 bu. 3 pk. 6 qt. 1 pt. +9 bu. 1 pk. 3 qt. 0 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.? = = * In adding square yards, observe that 60 sq. yd. sq. yd. 3 sq. rd.; and that 121 sq. yd. 4 sq. rd. of a sq. yd. 2 sq. ft. 36 sq. in.; of a sq. yd. 4 that of a sq. yd. 6 sq. ft. 108 sq. in. in the use of fractions. = 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.? = 2 sq. rd.; that 90 Observe, farther, that sq. ft. 72 sq. in.; and This will avoid serious difficulty 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. 0 ft. 7 in.? 35. 5 bu. 3 pk. 2 qt. 1 pt. + 8 bu. 1 pk. 7 qt. 0 pt. + 4 bu. 3 pk. 6 qt. 1 pt. 3 gi. + 5 bu. 2 pk. 5 qt. 0 pt. 2 gi. + 7 bu. 2 pk. 5 qt. 1 pt. gi. + 4 bu. 2 pk. 4 qt. 1 pt. 3 gi.? 36. £278 13s. 6d. 1 far. + £523 18s. 11d. 3 far. + £436 14s. 8d. 2 far. + £142 17s. 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. 3 = ILLUSTRATIONS.-In "3 from 7 leaves 4," or "7 minuend, 3 is the subtrahend, and 4 is the difference or remainder. 4," 7 is the |