4, 3976 - 937 659 813? 10. 56125 8754 - 9326 4721 — 153727 SECTION VII. COMPOUND SUBTRACTION. 43. Definitions and Explanations. (a.) COMPOUND SUBTRACTION is the subtraction of compound numbers. (b.) It involves the same principles that simple subtraction does. (c.) Subtract 8 lb. 10 oz. 18 dwt. 21 gr., from 12 lb. 3 oz. 16 dwt. 14 gr. 16. 02. dwt. gr. SOLUTION.-Writing the numbers as opposite, 12 3 16. 14 we subtract thus: since 21 gr. cannot be sub tracted from 14 gr., we reduce 1 of the 16 dwt. 8 10 18 21 to grains. 1 dwt. 24 gr., which, added to the 3 4 17 17 14 gr., gives 38 gr., from which subtracting 21 gr. leaves 17 gr. Since 18 dwt. cannot be subtracted from the 15 dwt. (left after the reduction), we reduce 1 of the 3 oz. to pennyweights. 1 oz. = 20 dwt., which, added to the 15 dwt., gives 35 dwt., from which subtracting 18 dwt. leaves 17 dwt. Since 10 oz. cannot be subtracted from the 2 oz. (left after the reduction), we reduce 1 lb. to ounces. 1 lb. 12 oz., which, added to the 2 oz., gives 14 oz., from which subtracting the 10 oz. leaves 4 oz. 8 lb. from 11 lb. leave 3 lb. (d.) When reductions are made, the remainder can often be found most easily by subtracting from the reduced unit, and adding the remainder thus obtained to the minuend figure. ILLUSTRATION. — In the above example, by the first reduction, we have 1 dwt. 24 gr.; and 21 gr. from 24 gr. leave 3 gr. to be added to the 14 gr., giving 17 gr. By the second reduction, we have 1 oz. = 20 dwt.; and 18 dwt. from 20 dwt. leave 2 dwt., to which adding the 15 dwt. (left after the former reduction), gives 17 dwt., etc. etc. (e.) Another method, which is often found convenient, is to subtract as much of each denomination of the subtrahend as possible, from the corresponding denomination of the minuend, and then subtract the rest from the reduced unit. ILLUSTRATION. — In the above example, we can subtract 14 of the 21 gr. from the 14 gr. of the minuend, and then the remaining 7 gr. from the 1 dwt. or 24 gr. 44. Examples for Practice. 1. £27 138. 6d. 1 far. £13 16s. 3d. 1 far. 2. £54 8s. 3d, 2 far. £16 138. 8d. 3 far. 3. 16 lb. 4 oz. 14 dr. - 7 lb. 9 oz. 13 dr. 4. 5 cwt. 2 qr. 13 lb. 11 oz. 6 dr. 12 dr. 2 cwt. 3 cr. 20 lb. 13 oz. 5. 36 T. 10 cwt. 2 qr. 20 lb. 5 oz. 8 dr. 14 T. 16 cwt. 3 qr. 24 lb. 7 oz. 2 dr. 6. 38 bu. 2 pk. 3 qt. O pt. — 15 bu. 3 pk. 6 qt. 1 pt. 4 da. 18 b. 42 m. - 75 w. 37 sec. 9. 52 w. 1 da. 6 h. 26 w. 4 da. 3 h. 36 m. 15 sec. 10. 191 93 33 20 16 gr. - 316 63 13 19 5 gr. 11. 28ið 83 63 17 8 gr. - 27ib 113 73 29 19 gr. 12. 19 sq. yd. 5 sq. ft. 17 sq. in. - 4 sq. yd. 2 sq. ft. 100 sq. in. 13. 96 cd. 3 cd. ft. 12 cu. ft. 1473 cu. in. 83 cd. 2 cd. ft. 15 cu. ft. 1697 cu. in. (a.) If, in Long or Square Measure, it is necessary to reduce a rod to yards, the reduction should be made, and the 3 or 4 of a yard reduced to feet and inches, before commencing the subtraction.” 1. Subtract 14 rd. 4 yd. 2 ft. 8 in., from 28 rd. 3 yd. O ft. 4 in. 27 8 1 10 = Reduced minuend. SOLUTION. — Writing the work as rd. yd. ft. in. opposite, and observing that the sub28 3 0 4 Minuend. traction will require that l rod shall 14 4 8 Subtrahend. be reduced, we proceed thus: 1 rd. 53 yd.; adding the 5 yd. to the 13 3 2 2 = Remainder. 3 yd. gives 8 yd.; } yd. 1 ft. 6 in., which, added to the O ft. 4 in., gives 1 ft. 10 in. Now, subtracting 8 in. from 10 in. leave 2 in. Since 2 ft. cannot be subtracted from 1 ft., we reduce 1 of the 8 yd. to feet; 1 yd. - 3 ft., which, added to the 1 ft., gives 4 ft., from which subtracting 2 ft. leave 2 ft. 4 yd. from 7 yd. leave 3 yd.; 14 rd. from 27 rd. leave 13 rd. 3. 8 m. 1 fur. 36 rd. 2 yd. 1 ft. 4 in. 8 m. 1 fur. 35 rd. 5 yd. 1 ft. 5 in. 7. 37 rd. 1 ft. 2 in. 36 rd. 5 yd. 2 ft. 7 in. 18 m. 7 fur. 39 rd. 5 yd. 1 ft. 5 in. 9. 15 rd. — 8 rd. O yd. 2 ft. 11 in. 10. 137 m. 2 ft. 11. 39 sq. rd. 3 sq. yd. 2 sq. ft. 43 sq. in. 30 sq. rd. 30 sq. yd. 3 sq. ft. 78 sq. in. 12. 96 A. 2 R. 29 sq. rd. 3 sq. yd. 6 sq. ft. 107 sq. in. 14 A. 1 R. 12 sq. rd. 25 sq. yd. 1 sq. ft. 31 sq. in. 13. 538 A. 3 sq. yd. 1 sq. in. - 249 A. 1 sq. rd. 5 sq. yd. 7 sq. ft. 14. 32 sq. rd. 5 sq. yd. 1 sq. ft. 72 sq. in. 13 sq. rd. 29 sq. yd. 8 sq. ft. 140 sq. in. 15. 27 A. 1 R. 26 sq. yd. 80 sq. in. 26 A. 3 R. 39 sq. rd. 30 sq. yd. 8 sq. ft. 143 sq. in. 16. 19 A. - 5 A. 3 R. 39 sq. rd. 30 sq. yd. 2 sq. ft. 35 sq. in. 17. 48 A. - 6 sq. ft. 18. 5 A. 3 A. 1 R. 39 sq. rd. 30 sq. yd. 8 sq. ft. 137 sq. in. 19. 35 sq. rd. 6 sq. ft. 93 sq. in. - 34 sq. rd. 30 sq. yd. 8 sq. ft. in. 20. What is the difference between 24 rd. 1 ft. 3 in. and 23 rd. 5 yd. 2 ft. 11 in. ? 21. What is the difference between 28 sq. rd. 5 sq. ft. 63 sq. in. and 27 sq. rd. 30 sq. yd. 7 sq. ft. 107 sq. in. ? 129 sq. 46. Miscellaneous Problems. 1. A man bought 17 cwt. 2 qr. 13 lb. of sugar, and sold 14 cwt. 2 qr. 21 lb. How much had he left ? 2. An English' merchant bought goods for £327 14s. 6d., and sold them for £596 10s. What was his gain ? 3. My wood-lot is 32 rd. long, and 27 rd. 2 yd. 2 ft. wide. What is the difference between its length and its breadth ? 4. I bought a bar of silver weighing 7 lb., and made 5 lb. 7 oz. 5 dwt. 14 gr. of it into tea-spoons, and the rest into salt-spoons. How much did I make into salt-spoons ? 5. A farmer, carrying a load of hay to market, found that the hay and the cart together weighed 2 T. 7 cwt. 3 qr. 16 lb., and the cart alone weighed 18 cwt. 1 qr. 22 lb. What was the weight of the hay? 6. A trader purchased some sugar for $327.13, some molasses for $125.50, some flour for $520.62, some butter for $132.28, and some cheese for $86.72, giving in payment a lot of cloth worth $625.47, and the rest in money. How much money did he pay? |