42. To read numbers represented by figures according to the English method; Begin at the right hand, and point off the figures into periods of sit places each. Then, commencing at the left hand, read the figures of each period, giving the name of each period except that of units. EXERCISES. Read orally, or write in words, the numbers represented by the following figures, according to the English method: 1. 23457896 4. 98765421910311 2. 325487691 5. 5632411132321300012 3. 1678912161 6. 6961771889133201443345567 43. To write numbers in figures according to the English method; Begin at the left hand, and write in each successive order the figure belonging to it. If any intervening order would otherwise be vacant, fill the place by a cipher. EXERCISES. Represent by figures, and read, the following numbers, according to the English method : 1. Thirty-two million three hundred. 2. Seven billion seventeen thousand. 3. Five hundred sixty thousand one hundred two million, nine hundred twenty-nine thousand four hundred eleven. 4. One trillion, seven hundred forty-eight thousand nine hundred fifty-five billion. ADDITION. 44. ADDITION is the process of finding the sum of two or more numbers. The result obtained is called the amount. Numbers can be added together only when their units are of the same kind. When the numbers added are simple, the process is termed Addition of Simple Numbers. How many OPERATION. 45. To add simple numbers. Ex. 1. A man has three farms; the first contains 378 acres, the second 586 acres, and the third 168 acres. acres are there in the three farms. Ans. 1132. Having arranged the numbers so that all the units Acres. of the same order shall stand in the same column, 378 we first add the column of units ; thus, 8 and 6 are 5 8 6 14, and 8 are 22 units, 2 tens and 2 units. We 168 write the two units under the column of units, and carry or add the 2 tens to the column of tens; thus, Ans. 1132 2 added to 6 make 8, and 8 are 16, and 7 are 23 tens, 2 hundred and 3 tens. We write the 3 tens under the column of tens, and add the 2 hundred to the column of hundreds; thus, 2 added to one make 3, and 5 are 8, and 3 are 11 hundred, - 1 thousand and i hundred. We write the 1 hundred under the column of hundreds ; and there being no other column to be added, we set down the 1 thousand in the thousands' place, and find the amount of the several numbers to be 1132. In practice, it is better not to name each figure added, but only the results, thus, 8, 14, 22 units, 2 tens and 2 units, etc. RULE. — Write the numbers so that all the figures of the same order shall stand in the same column. Add, upward, all the figures in the column of units, and, if the amount be less than ten, write it underneath. But if the amount be ten or more, write down the unit figure only, and add in the figure denoting the ten or tens with the next column. Proceed in this way with each column, until all are added, observing to write under the last column its whole amount. 46. First Method of Proof. — Begin at the top and add the columns downward in the same manner as they were before added upward; and if the two sums agree, the work is presumed to be right. The reason of this proof is, that, by adding downward, the order of the figures is inverted ; and, therefore, any error made in the first addition would probably be detected in the second. NOTE. This method of proof is generally used in business. 47. Second Method of Proof. — Separate the numbers to be added into two parts, by drawing a horizontal line between them. Add the numbers below the line, and set down their sum. Then add this sum and the number or numbers above the line together; and if their sum is equal to the first amount, the work is presumed to be right. The reason of this proof depends on the principle, that the sum of all the parts into which any number is separated is equal to the whole. (Art. 24, Ax. 13.) EXAMPLES. 2. 3. Ans. 2 3 3 3 First am't 2 3 3 3 Ans. 1 6 2 9 First am't 1 6 2 9 2 48 37 25 8 5 9 2 1 478 2 7 2 71 2 9 39 3 381 9 6 32. What is the sum of 15 +26+ 18+ 91? Ans. 150. 33. What is the sum of 6789 + 5832 + 4671 + 8907 ? Ans. 26199. 34. Required the sum of 76 +48 +59 + 81. Ans. 264. 35. Required the sum of 123456 + 789012 + 345678 + 901234 + 567890 + 987654 + 321032 + 765437. 36. Required the sum of 876543 + 789112 + 345678 + 965887 + 445566 + 788743 + 399378 + 456789. 37. Required the sum of 789012 + 345678 + 901234 + 789037 + 891133 + 477666 + 557788 + 888878. 38. Required the sum of 987654 + 456112 + 222333 + 456789 + 987654 + 321178 + 123456 + 789561. 39. Required the sum of 678953 + 467631 + 117777 + 888888 + 444444 + 667679 + 998889 + 671236. 40. Required the sum of 783256 + 7128 + 39 + 432815 +99 +67851 + 125 + 641236 + 801 + 4328. 41. Required the sum of 12004 + 32 +1 + 7836 + 100 +46 +3 + 6176 + 32 +91876. 42. Add together 763, 4663, 37, 49763, 6178, and 671. Ans. 62075. 43. Add together 15, 7896, 1, 13, 106, 113, 156, 100, 2201. 44. A butcher sold to A 369 lbs. of beef, to B 169 lbs., to C 861 lbs., to D 901 lbs., to E 71 lbs., and to F 8716 lbs. ; what did they all receive? Ans. 11087 lbs. 45. A owes to one creditor 596 dollars, to another 3961, to another 581, to another 6116, to another 469, to another 506, to another 69281, and to another 1261. What does he owe them all ? Ans. $ 82871. 46. If a boy earn 17 cents a day, how much will he earn in 7 days? Ans. 119 cts. 47. If a man's wages be 19 dollars per month, what are they per year? Ans. $ 228. 48. If a boy receive a present every New Year's day of 1783 dollars, how much money will he possess when he is 21 years old? Ans. $ 37443. 48. Method of adding two or more columns at one operation. Ex. 1. A merchant paid for cloth 219 dollars, for flour 416 dollars, for hardware 711 dollars, and for rent 93 dollars. How much did he pay in all ? Ans. $ 1439. Beginning with the number last written down, we add the units and tens; thus, 93 and 1 = 94, 219 and 10 104, and 6 = 110, and 10 - 120, and 416 9=129, and 10 - 139. Of this amount we write 711 the 9 units and 3 tens under the columns added ; 93 and add in the 1 hundred with the column of hundreds; thus, 1 (carried) and 7 - 8, and 4 Ans. 1439 12, and 2 14 hundred, of which we write the 4 hundred under the column of hundreds and the 1 thousand in the thousands' place; and find the whole amount to be 1439. In like manner may be added more than two columns at one operation. NOTE. The examples that follow can be performed as the above, or by the common method, or by both. 2. How many were the members of Congress in 1856, there being 2 Senators from each State, and Maine sending 6 Representatives, New Hampshire 3, Massachusetts 11, Rhode Island 2, Connecticut 4, Vermont 3, New York 33, New Jersey 5, Pennsylvania 25, Delaware 1, Maryland 6, Virginia 13, North Carolina 8, South Carolina 6, Georgia 8, Alabama 7, Mississippi 5, Louisiana 4, Tennessee 10, Kentucky 10, Ohio 21, Indiana 11, Illinois 9, Wisconsin 3, Iowa 2, Missouri 7, Arkansas 2, Michigan 4, Florida 1, Texas 2, California 2. Ans. 296. OPERATION. Dollars. |