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35. Addition of Double Columns. (a.) Accountants often add two or more columns, at one operation.
Model. - 63 plus 30 are 93, plus 8 are 101, plus 80 are 181, plus 4 are 185, plus 90 are 275, plus 7 are 282.
(b.) By adding the tens first, and then the units, as before, and omitting to name the separate numbers added, we can abbreviate the above.
Model.— 63, 93, 101, 181, 185, 275, 282.
(c.) A little practice will enable a person to abbreviate still farther ; 63 plus 38 are 101, plus 84 are 185, plus 97 are 282; or, by omitting to name the numbers added, thus, 63, 101, 185, 282.
(d.) Let the pupil now perform the preceding examples in this way, or, at least, enough of them to make the principle and process familiar.
36. Practical Problems.
1. I paid $178 for a horse, $239 for a chaise, and $43 for a harness. What did I give for all ?
2. A country trader bought cloth for $46.28, shoes for $37.93, West India goods for $98.46, and books for $86.37. What was the amount of his purchase ?
3. A merchant bought 4 bales of cloth, the first containing 527 yd., the second 497 yd., the third 534 yd., and the fourth 549 yd. How many yards did he buy, in all?
4. My garden contains 3.265 acres, my orchard contains 5.238 acres, my meadow 9.648 acres, my pasture 18.973 acres, and my wood-lot as much as my garden, orchard, meadow, and pasture together. How many acres does my wood-lot contain ? How many acres are there in all ?
5. The receipts of cotton at the city of Savannah, Ga., have been as follows, viz.: 245496 bales in 1847, 406906 bales in 1848, 340025 bales in 1849, 312294 bales in 1850, 351566 bales in 1851, and 353068 bales in 1852. How many bales were exported in all this time?
6. Four men, A, B, C, and D, form a partnership. A puts in
dollars do all put in ?
7. A merchant bought some coffee for $457.62, and some tea for $529.37: he sold the coffee at an advance of $119.87, and the tea at an advance of $186.98. How many dollars did he receive for both ?
8. In 1850, the State of Massachusetts produced 31211 bushels of wheat, 481021 bushels of rye, 2345490 bushels of Indian corn, and 1165146- bushels of oats. Ilow many bushels were produced of all these grains ?
9. In 1850, Boston had a population of 136881, Charlestown, 17216, Cambridge, 15215, and Roxbury, 18364. What was the population of the four cities ?
10. In 1850, Mississippi produced the following grains : 137990 bushels of wheat, 9606 bushels of rye, 22446552 bushels of Indian corn, and 1503288 bushels of oats. How many bushels were produced, of all these kinds ?
11. Jan. 1st, 1856, I purchased a horse for $187.50, a chaise for $225, and a harness for $48.97. During the year, it cost me $147.78 for keeping and taking care of the horse, and $28.37 for varnishing and repairing the chaise. What is the sum of the expenses thus incurred ?
12. I bought two farms, paying $3988.67 for the first, and $1867.76 more for the second than for the first. How many dollars did I pay for the second, and how many for both ?
13. A grain dealer sold 16784 bushels of corn to one man, 3251 to another, and, when he had sold 11868 to another, he bad 24785 bushels left. How many bushels had he at first ?
14. During the year ending Aug. 31st, 1854, 1603750 bales of cotton were exported to Great Britain, 374058 to France, 165172 to the north of Europe, and 176168 to other foreign ports. How many bales were exported ?
15. During the year ending Dec. 1st, 1854, the United States' mails were transported an aggregate of 15433389 miles by railroad, 20890530 miles by coach, 5795483 by steamboats, and 21267603 by other conveyances. How many miles were they transported, in all ?
16. A man invested $478.36 in real estate, $237.86 more in bank stock than in real estate, and $136.59 more in trade than in bank stock? How much did he invest in each, and how much in all ?
17. A, B, and C divided a sum of money in such a way, that A had $427.83, B had $348.59 more than A, and C had $148.26 more than A and B together. How many dollars had B? what number had C? How many dollars were divided ?
18. I own a rectangular field, 1389 feet long and 1246 feet wide. How many feet of fence will it take to enclose it?
19. My farm is worth $8794.63, my railroad stock is worth $3275.87, my bank stock is worth $7948.35, my insurance stock is worth $3298.46, and my stock of goods is worth $1985.73. What are all worth?
20. I have just paid $1273.82 on note, $4296.84 on bond and mortgage, and $1437.82 on account, and I still owe $948.62 on notes, $2578.63 on bond and mortgage, and $3258.25 on accounts. How much did I owe before paying any of those debts ?
37. Definitions and Explanations.
NOTE. - This and the other sections on Compound Numbers may be omitted till after the “Simple Rules” are mastered, if, in the opinion of the teacher, the circumstances of the class render it desirable.
(a.) COMPOUND ADDITION is the addition of Compound Numberg.
(b.) Compound Addition involves the same principles as Simple Addition.
(c.) In both, numbers of the same denomination are added together; in both, the numbers should be so written as to bring figures of the same denomination under each other; in both, the addition is commenced with the right-hand or lowest denomination; and, in both, as much as possible of the sum of each column is reduced to units of the next higher denomination. Moreover, the methods of proof are the same in both. The only difference of any kind between them is, that, in simple numbers, 10 units of any denomination equal 1 of the next higher; while, in compound numbers, there is no uniformity in this respect.
(d.) In Compound Addition, the abbreviations of the denominations should be marked over the several columns.
(e.) The application of these principles is illustrated in the following problem and solution :
1st SOLUTION.—Writing the numbers so that figures of the same denomi. nation shall fall under each other, we begin at the right, and, observing that there will be 1 shilling for every 12 pence, we add thus: