ART. 18. From the solution of the preceding questions, the learner will perceive, that ADDITION is the process of collecting several numbers into one sum, which is called their amount. Addition is commonly represented by this character, +, which signifies plus, or added to. The expression 7+5 is read, 7 plus 5, or 7 added to 5. This character,=, is called the sign of equality, and signifies equal to. The expression 7+5=12 is read, 7 plus 5, or 7 added to 5, is equal to 12. EXERCISES FOR THE SLATE. ART. 19. The method of operation when the numbers are large, and the sum of each column is less than 10. Ex. 1. A man bought a watch for 42 dollars, a coat for 16 dollars, and a set of maps for 21 dollars; what did he pay for the whole? Ans. 79 dollars. OPERATION. 42 16 21 Having arranged the numbers so that all the units of the same order shall stand in the same column, we first add the column of units; thus, 1 and 6 are 7, and 2 are 9 (units), and write down the amount under the column of units. We then add the column of tens; thus, 2 and 1 are 3, and 4 are 7 (tens), which we write under the column of tens, and thus find the amount of the whole to be 79 dollars. Amount 79 ART. 20. 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. -This method of proof is generally used in business. NOTE. QUESTIONS. Art. 18. What is addition? What is the sign of addition, and what does it signify? What is the sign of equality, and what does it signify? Art. 19. How are numbers arranged for addition? Which col umn must first be added? Why? Where do you place its sum? Where must the sum of each column be placed? What is the whole sum called? -Art. 20. How is addition proved? What is the reason for this method of proof? Is this method in common use? Ans. 669. Ans. 698. Ans. 999. 6. What is the sum of 231, 114, and 324 ? 7. Required the sum of 235, 321, and 142. 8. What is the sum of 11, 22, 505, and 461 ? 9. Sold twelve ploughs for 104 dollars, two wagons for 214 dollars, and one chaise for 121 dollars; what was the amount of the whole ? Ans. 439 dollars. man, 432 of another, 10. A drover bought 125 sheep of one and of a third 311; how many did he buy? Ans. 868 sheep. ART. 21. Method of operation when the sum of any column is equal to or exceeds 10. Ex. 1. I have three lots of wild land; the first contains 246 acres, the second 764 acres, and the third 918 acres. I wish to know how many acres are in the three lots. Ans. 1928 acres. OPERATION. Acres. 246 764 918 Amount 1928 Having arranged the numbers as in the preceding examples, we first add the units; thus, 8 and 4 are 12, and 6 are 18 units, equal 1 ten and 8 units. We write the 8 units under the column of units, we carry or add the 1 ten to the column of tens; thus, 1 added to 1 makes 2, and 6 are 8, and 4 are 12 (tens), equal to 1 hundred and 2 tens. We write the 2 tens under the column of tens, and add the 1 hundred to the column of hundreds; thus, 1 added to 9 makes 10, and 7 are 17, and 2 are 19 (hundreds), equal to 1 thousand and 9 hundreds. We write the 9 under the column of hundreds; and there being no other column to be added, we set down the 1 thousand in thousands' place, and find the amount of the several numbers to be 1928. NOTE.A more concise way, in practice, is to omit calling the name of each figure as added, and name only results. QUESTIONS. Art. 21. are the units written? add, one for every 10? When the sum of any column exceeds ten, where What is done with the tens? Why do you carry, or How is the sum of the last column written? ART. 22. From the preceding examples and illustrations in addition, we deduce the following general RULE. -Write the numbers so that all the units 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. ART. 23. 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 divided is equal to the whole. QUESTIONS.Art 22. What is the general rule for addition?- Art. 23. What is the second method of proving addition? What is the reason of this method of proof? 23. Add 1001, 76, 10078, 15, 8761, 7, and 1678. Ans. 21616. 24. Add 49, 761, 3756, 8, 150, 761761, and 18. Ans. 766503. 25. Required the sum of 3717, 8, 7, 10001, 58, 18, and 5. Ans. 13814. 26. Add 19, 181, 5, 897156, 81, 800, and 71512. Ans. 969754. 27. What is the sum of 999, 8081, 9, 1567, 88, 91, 7, and Ans. 31622. 29. Add 51, 1, 7671, 89, 871787, 61, and 70001. Ans. 949661. 30. What is the sum of 71, 8956, 1, 785, 587, and 76178? Ans. 86578. 31. Add 9999, 8008, 8, 81, 4777, and 516785. Ans. 539658. 32. Add 5, 7, 8911, 467, 47895, and 87. Ans. 57372. 33. Add 123456, 71, 8005, 21, and 716787. Ans. 848340. 34. Add 47, 911111, 717, 81, 88767, and 56. Ans. 1000779. 35. What is the sum of 71, 8899, 4, 7111, and 678679 ? Ans. 694764. 36. Add 81, 879, 41, 76789, 42, 1, and 78967. 37. Add 917658, 75, 876789, 46, and 8222. Ans. 156800. Ans. 1802790. 38. Add 91, 76756895, 76, 14, 3, and 76378. Ans. 76833457. 39. Add 10, 100, 1000, 10000, 100000, and 1000000. Ans. 1111110. 40. What is the sum of 9, 99, 99, 1111, 8000, and 5 ? 41. Add 41, 7651, 7678956, 43, 15, and 6780. Ans. 9323. Ans. 7693486. 42. Add 1234, 7891, 3146751, 27, 9, and 5. Ans. 3155917. 43. What is the sum of 19, 91, 1, 1, 1478, 1007, and 46? Ans. 2643. 44. Add four hundred seventy-six, seventy-one, one hundred five, and three hundred eighty-seven. Ans. 1039. 45. Add fifty-six thousand seven hundred eighty-five, seven hundred five, thirty-six, one hundred seventy thousand and one, and four hundred seven. Ans. 227934. 46. Add fifty-six thousand seven hundred eleven, three thousand seventy-one, four hundred seventy-one, sixty-one, and three thousand and one. Ans. 63315. 47. What is the sum of the following numbers: seven hundred thousand seven hundred one, seventeen thousand nine, one million six hundred thousand seven hundred six, forty-seven thousand six hundred seventy-one, seven thousand forty-seven, four hundred one, and nine? Ans. 2373544. 48. Gave 73 dollars for a watch, 15 dollars for a cane, 119 dollars for a horse, 376 dollars for a carriage, and 7689 dollars for a house; how much did they all cost? Ans. 8272 dollars. |