36. Add 413, 6471, 3142, 718, 6437, 27, 5792. 49. Add 46 thousand, 2 hundred; 72 thousand, 3 hundred 27; 65 thousand, 7 hundred 50; 87 thousand, 4 hundred 84; 25 thousand, 4 hundred 60. 50. Add 324 thousand, 6 hundred 85; 237 thousand, 4 hundred 18; 2 million, 46 thousand, 7 hundred 36; 14 million, 305 thousand, 4 hundred 90; 5 million, 6 thousand, 7 hundred 39. PRACTICAL PROBLEMS. How many 42. 1. A farmer produced 75 bushels of rye, 250 bushels of wheat, 185 bushels of oats, and 360 bushels of corn. bushels of grain did he produce? 75 SOLUTION.—If he raised 75 bushels of rye, 250 bushels of wheat, 250 185 bushels of oats, and 360 bushels of corn, he raised in all the 185 sum of 75 bushels, 250 bushels, 185 bushels, and 360 bushels, or 870 360 bushels. 870 2. A merchant bought beef for $560, pork for $275, and fish for $138. What was the entire cost ? 3. In a certain book there are 330 pages, in another 360, and in another as many pages as in the other two. How many pages in the three books? 4. A man bought a horse for $250, a buggy for $175, and 8 cows for as much as he paid for the horse and buggy. What was the cost of all? 5. A farm that cost $4350, was sold for $850 more than it cost. How much was received for it? 6. A merchant paid his bookkeeper $1200 a year, two salesmen $650 each, and a boy $250. What amount of salaries did he pay? 7. A town lot was bought for $785. A house was built upon it which cost $2,350. For how much must the property be sold to gain $500 ? 8. In 1890, the population in Brooklyn was 806343. The population of New York City was 708958 more than that of Brooklyn. What was the population of both cities ? 9. If Europe contains 3807195 square miles, Asia 17805146, Africa 11647428, America 14850400, and Oceanica 334780, how many square miles of land surface do these grand divisions comprise? 10. A grain dealer bought wheat for $7500, corn for $12080, and oats for $2000. He sold the wheat at a profit of $1500, the corn at a gain of $2020, and the oats at cost. What did he receive for the whole ? 11. The area of New York is 49170 square miles, New Jersey 7815, Pennsylvania 45215, Delaware 2050, Maryland 12210, Vir ginia 42450, and West Virginia 24780 square miles. What is the total area of these states ? 12. A man sold a house for $2780 and a lot for $875. He lost $510 on the house and $125 on the lot. What did he pay for both? 13. A, B, and C formed a partnership. A invested $2750, B invested $2875, and C invested as much as A and B together. How much did they all invest in the business? 14. A firm's resources are cash $1285, dry-goods $3769, personal accounts due the firm $1621, office furniture $205, and real estate $4760. What are the total resources of the firm? 15. A lady bought a stove for $23.50, a side-board for $18, a table for $9.50, dishes for $25, a bed-room suit for $40, a carpet for $13.75, a set of chairs for $9, a lamp for $2.65, and an organ for $85. What was the entire bill? 16. A dealer in live stock paid $3478 for horses, $2831.85 for cattle, and $1217.90 for sheep. He gained $850 on the sale of the horses, $760.90 on the cattle, and $215 on the sheep. How much did he receive for all? 17. Mr. M. deposited in the First National Bank of Philadelphia, on June 1, 1902, $375.50; on June 4, $680.75; on June 11, $700; on June 15, $225.65. He also deposited in the Globe National Bank, New York City, on June 18, $3167; on June 24, $1859. How much did he deposit in both banks? SHORT METHODS IN ADDITION. 43. The process of addition may be much shortened by observing the following suggestions: 1. In adding name merely the results. 2. When two or more numbers of a column can be easily grouped together, add their sum instead of adding each figure separately. 3. When a number is repeated consecutively in a column, multiply it by the number of times it is repeated, and add the result. 4536 1ST METHOD.-Say, 3, 10, 16, 20, 22, 28; write the 8 and carry 3822 the 2; 2, 5, 10, 15, 20, 22, 25; write the 5 and carry the 2; etc. 7854 2D METHOD.-We may say 10, 20, 28, in which we group 3 and 1256 7, 6 and 4, and 2 and 6. In the second column, we may say 5, 15, 5657 22, 25, grouping 2 and 3, 5 and 5, 5 and 2; etc. 3633 26758 grouping, five 5's are readily seen; in the third column, four 8's and 5; in the last column, two 6's, 10 and 4; thus, 12, 22, 26. 3D METHOD.-In the second column with the 2 carried and 322 ADDING BY TENS. 44. The method of adding by tens is helpful in the adding of long columns. 1. What is the sum of 897, 645, 257, 461, 798, 529, 397, and 489 ? 897 64 5 4 6 1 798 5 29 397 48 9 EXPLANATION.—In adding by 10's, the beginner should place a dash at the upper right corner of each figure where the sum equals or exceeds 10, thus keeping account of the number of 10's and adding only the units which exceed each 10 of the column. Thus, in the first column, 9 and 7 are 16, or 10 and 6. We place a dash at the 7 to mark the 10, and consider only the 6; 6 and 9 are 10 and 5; mark for the 10 and consider only the 5, etc. Thus, in adding the first column, we say, 9, 6, 5, 3, 4, 1, 6, 3.' We write the 3 and carry to the next column 5, the number of dashes. Adding the second column, we say, 5 (carried), 3, 2, 4, 3, 9, 4, 8, 7. We write the 7, count the dashes and carry to the next column. Adding, we say, 5, 9, 2, 7, 4, 8, 0, 6, 4. We write the 4, and counting the dashes, write the number to the left, since it is the last column. 44 7 3 1. In adding, never fail to mark each 10 as you drop it, either by a dash or some other easily made mark. 2. The advantage in this method is that you can not only acquire the ability by a little practice, to add rapidly and accurately, but you may be interrupted at any point without inconvenience, if the unit figure is just placed to the right or above the last added figure; for the dashes marked while adding the column show the 10's of the column already added, so that there is really nothing to remember. 3. This method is recommended chiefly for beginners, who may find it difficult to carry in mind both the unit figure and the precise number of 10's accumulated. In all practice the student should at empt to keep clearly in mind the exact amount computed to any point, and a little effort of attention will, with experience, ensure this result. It is unnecessary to remark that the use of dashes is, like counting on the fingers, unworthy of the expert. 45. The method of adding by hundreds is adapted to adding long columns of figures. By this method a dash is placed at the upper right hand of the figure at which each hundred is obtained. 1. Find the sum of the following: 7 4 5 867 976 789 967 8 38 694 749 9 54 879 786 878 996 *8 58 . EXPLANATION.-In adding the first column, we begin at the bottom and say, 7, 13, 19, 27, 33, 41, 47, 56, 63, 67, 73, 80, 88, 97, 1 (dash), 7, 15, 22, 31, 37, 44, 49. Glancing at the column we see 1 dash. Hence, the sum of the column is 149. We write the 9 and carry 14 to the next column. Adding the second column we say, 14 (carried), 22, 29, 38, 43, 52, 59, 67, 74, 78, 83, 90, 94, 99, 3 (dash), 12, 19, 22, 28, 36, 43, 49, 53. Glancing at the column we see 1 dash. Hence the sum of the column is 153. We write the 3, and carry 15 to the next column. Adding the third column we say, 15 (carried) 24, 32, 39, 47, 56, 64, 71, 79, 85, 94, 1 (dash), 9, 18, 25, 31, 40, 48, 57, 64, 73, 81, 88. Glancing at the column we see 1 dash. Hence the sum of the column is 188, all of which is written since it is the last column. Hence the sum is 18839. 1. The advantage of this method over the method of 796 adding by tens is that scarcely any time is consumed by making dashes, and hence the additions may be more quickly performed. 876 9 8 7 8839 2. For practice, the student should add by hundreds examples 45, 46, 47, and 48, under article 40, and make other exercises of loag columns for himself. |