NOTE 2. A fraction occurring in the amount may sometimes be reduced to whole numbers of other denominations; thus, in Ex. 15, the half yard equals 1ft. and 6in.; the 6in. put with the 4in. make 10in. and the lft. put with the 2ft. make 3ft. or lyd. Oft., and, finally, the lyd. put with the lyd. in the original amount gives 2yd. The answer, when reduced, may contain a denomination higher or lower than any in the given example; higher, as in Ex. 16; lower, as in Ex. 17. 199. What may be done with a fraction in the amount? Explain Ex. 15. Ex. 16. Ex. 17. May the answer contain a higher or lower denomination than the example? How? 21. Bought 4 pieces of cloth, measuring 6yd. 3qr. 1na. 2in., Syd. 2qr. 3na. lin., 25yd. 1qr. 2na. 2in., and 14yd. 3qr. 2na. lin.; how much cloth did I buy? 22. A farmer raised in one field 21bush. 3pk. 7qt. 1pt. of wheat; in another, 48bush. 2pk. 1pt.; in another, 28bush 6qt.; and in another, 75bush. 1pk. 5qt. 1pt.; how much wheat did he raise in the 4 fields? 23. A planter sold cotton at various times, as follows: 2t. 18cwt. 2qr. 12 lb., 6t. 1cwt. 1qr. 64lb., 3t. 19cwt. 3qr. 183lb., 16t. 6cwt. 3qr. 124lb., and 16t. 3qr. 18lb.; what did he sell in all? 24. What is the sum of 14a. 2r. 30rd. 25yd. 3ft. 72in., 37a. 3r. 39rd. 30yd. 6ft. 36in., 50a. 1r. 18rd. 25yd. 2ft. 108in., and 25a. 2r. 25rd. 25yd. 3ft. 72in.? 25. Add 3circ. 9s. 29° 59′ 59′′, 2circ. 11s. 25° 20′ 30′′, 5circ. 4s. 8° 25′ 55′′, and 6circ. 10s. 10° 10′ 10′′ together. 26. A horse traveled 35m. 6fur. 18rd. 5yd. in one day, 42m. 3fur. 25rd. 2yd. the next day, 37m. 5fur. 32rd. 4yd. the next, and 45m. 7fur. 24rd. 3yd. the next; how far did he travel in the 4 days? 27. A blacksmith bought 4t. 18cwt. 3qr. 20lb. of iron at one time, 6t. 15cwt. 3qr. 12lb. at another time, 3t. 6cwt. 1qr. 181b. at another, and 8t. 3cwt. 2qr. 10 lb. at another; how much did he buy in all? SUBTRACTION. 200. The principle is like that of subtraction of simple numbers. Hence, To subtract compound numbers, RULE. 1. Write the less quantity under the greater, arranging the denominations as in addition. 2. Beginning at the right, take each denomination of the subtrahend from the number above it, and set the remainder beneath. 3. If any number of the subtrahend is greater than the number above it, add to the upper number as many as it takes of that denomination to make one of the next higher, and take the subtrahend from the SUM; set down the remainder, and, considering the number in the next denomination in the minuend ONE LESS, or that in the subtrahend ONE GREATER, proceed as before. 201. PROOF. As in subtraction of simple numbers (Art. 53). Ex. 1. From 8£ 6s. 9d. 3qr. take 2£ 4s, 5d. 1qr. 2. From 9£ 6s. 10d. 1qr. take 2£ 17s. 2d. 3qr. OPERATION. £ S. d. qr. 1 As 3qr. cannot be taken from 1qr., borrow one of the 10d., reduce it to farthings and add it to the 1qr., giving 5qr.; then say 3qr. from 5qr. leave 2qr. Now, as one of the 10d. has been employed, say 2d. from 9d., or, what is practically the same, 3d. from 10d. leave 7d., and so proceed through the example. 200. Rule for subtracting compound numbers? Explain Ex. 1. Ex. 2. Principle? 201. Proof? SUBTRACTION. The form of the minuend may be changed and the work performed as follows (Art. 53, Ex. 28): Min., 9 £ S. d. qr. (8 26. 9 5 = 2 17 2 3 202. Sometimes, as in the following examples, it is necessary to borrow two of the higher denomination of the minuend instead of one; but in all such cases we must carry two to the next term of the subtrahend; i. e. we must PAY as much as we BORROW. 203. To find the time between two dates. 17. What is the difference of time between July 15, 1857, and Apr. 25, 1862? Ans. 4yr. 9m. 10d. SECOND OPERATION. yr. m. d. (1861 3 24 1856 6 14 202. What is said of borrowing two? Explain Ex. 13. 203. How many modes of finding the time between two dates? What are they? |