Now, each column, by itself, is a sum in simple addition; and, as here are three columns, we have three sums in addition. But when we make the reduced sum of one column run into the next column we unite or compound the additions. We must commence with the lowest column, (the pence column); its sum is 20 pence, which, reduced to shillings, give 1 shilling, and 8 pence over. The 8 pence must, of course, be put down in the pence column. The 1 shilling, added in with the other shillings, all make 40 shillings; which, reduced, make 2 pounds and O shillings over. The 2 pounds, added into the column of pounds, make the whole number of pounds 55; and the several sums of money make the total sum of £55 0s. 8d. If the pupil retains the principle, that compound addition is simple addition and reduction combined, no rule for addition will be required; but for the sake of conciseness, we give the following RULE. 1. Place the numbers so, that those of the same denomination will stand directly under each other, and in distinct and separate columns. 2. Add up the figures in the lowest denomination, and find, by reduction, how many units or ones of the next higher denomination are contained in their sum. 3. Set down the remainder below its proper column, and carry those units or ones to the next denomination, which add up in the same manner as before. 4. Proceed thus through all the denominations, to the highest, whose sum, together with the several remainders, will give the answer sought. N. B. The method of proof, rather a test, is to vary the order of addition that is, break the sum into several sums, and then take the partial sums for the sum total; and if two methods give the same sum total, that sum may be regarded as correct. N. B. In practical astronomy, when the object is to find the position of a body in a circle, we reject every 360 degrees in addition. APPLICATION. 1. A merchant bought 4 barrels of sugar; the first weighed 2 hundred weight 3 quarters 20 pounds, the second 1 hundred weight 2 quarters and 15 pounds, the third 2 hundred weight 1 quarter 27 pounds, and the fourth 2 hundred weight 3 quarters and 10 pounds; what was the entire weight of the whole? Ans. 9 cwt. 3 qrs. 16 lbs. 2. A merchant shipped 3 boxes of freight to New Orleans; the first weighed 7 hundred weight 56 pounds, the second 4 hundred weight 80 pounds, and the third 5 hundred weight and 20 pounds; what was the weight of the whole? This is done like simple addition; modern reform is happily doing away with denominate numbers in many cases. 3. There are 4 fields; the first contains 12 acres 2 roods and 38 perches, the second 4 acres 1 rood 26 perches, the third 85 acres 0 roods 19 perches, and the fourth 57 acres 1 rood 2 perches; how many acres in the four fields? Ans. 159a. 2r. 5p. 4. In 4 piles of wood, the first containing 32 feet 149 inches, the second 121 feet 1436 inches, the third 97 feet 498 inches, the fourth 115 feet 1356 inches; how much did the whole amount to? Ans. 2 C. 110 ft. 1711 in. 5. In 6 boat-loads of wood, the first containing 22 cords 114 feet 987 inches, the second 18 cords 121 feet 1436 inches, the third 21 cords 109 feet 1629 inches, the fourth 15 cords 82 feet 1321 inches, the fifth 16 cords 98 feet 1111 inches, the sixth 24 cords 89 feet 987 inches; how much did they all contain? Ans. 120 C. 105 ft. 559 in. 6. A tailor requires 1 yard 3 quarters 3 nails of cloth for a father's coat, and 1 yard 1 quarter and 2 nails for each of 2 sons; how much in all? Ans. 4 yds. 2 qrs. 3 na. 7. How much land is in a farm which consists of 50 acres 2 roods 33 rods of wood-land, 25 acres 14 rods meadow-land, 30 acres tillage, 20 acres rough pasture land, 12 acres 1 rood covered with water, and 10 acres 25 rods swamp? Ans. 148 a. 32 r. 8. A farmer sowed 3 fields of wheat; the first yielded 45 bushels 3 pecks, the second 36 bushels 1 peck 7 quarts, and the third 30 bushels 2 pecks 1 quart; how much wheat did he raise? Ans. 112 bu. 3 pks. COMPOUND SUBTRACTION. (ART. 29.) SUBTRACTION of compound or denominate numbers is essentially the same as in simple numbers, except the care that must be taken to borrow or reduce from the tables, in place of borrowing or reducing from 10. For instance, we cannot take 9 pence from 7 pence: we must first add, or conceive to be added, 12 pence more, (1 shilling,) to 7 pence, borrowing or taking a shilling from the next superior column, &c. From such necessary operations, we deduce the following RULE. Place the numbers as in compound addition. Begin with the lowest denomination in the subtrahend, and take it from the number above it; but, if that above be the least, add as many to it as make one of the next higher denomination; then subtract, and carry one to the next denomination in the subtrahend. The method of proof is the same as in simple subtraction. A person residing in latitude 27° 32′ 45′′ north, wishes to visit a place 52° 24′ 18′′ north; how many degrees, minutes, and seconds northward must he travel? Ans. 24° 51′ 33′′. From 900 years take 111 years and 6 months. Ans. 788 yrs. 6 m. If I take 1 year 1 month from 6 years, what space of time will still remain ? Ans. 4 yrs. 11 m. |