ADDITION OF SIMPLE NUMBERS. Art. 10. ADDITION is the method of finding the amount or sum of two or more numbers. The amount or sum of two or more numbers is a number that contains the number one as many times as it is contained in all the numbers whose amount or sum is to be found. ILLUSTRATION. William has 6 cents, and James has 4 cents. We can find the number of cents which both of them have, by adding 4 cents to 6 cents; 4 cents and 6 cents are 10 cents, the number of cents that they both have. 10 cents is the amount or sum of 4 cents and 6 cents. 9. There are 10 houses on one side of a street, and 11 on the other; how many are there on the two sides? 11. How many are 10 and 11? 13. George purchased 12 apples at one time, and 10 at another; what number of apples did he purchase? 2. John gave 7 cents for a pencil, and 8 cents for a book; how many cents did he give for both? 4. How many are 7 and 8? 6. There are 9 girls in the first class, and 10 in the second; how many girls are there in the two classes? 8. What is the sum of 9 and 10? 10. William has performed 11 questions in arithmetic, and Henry 12; how many have both of them performed? 12. How many are 11 and 12? 14. Julia has recited 11 lessons her teacher, and Harriet 10; how many lessons have both of them recited? to 16. What is the sum of 11 and 15. What is the amount of 12 and 10? 10? 17. A little girl is 7 years old; how old will she be, if living, at the end of 10 years from the present time? 19. What is the sum of 7 and FO? 21. There are 11 boys in one sleigh, and 9 in another; how many boys are there in the two sleighs? 23. How many are 11 and 9? 25. What is the sum of 3, 5, 7, 9, and 11? 27. What is the sum of 1, 2, 3, 4, 5, and 6? 18. William was 12 years old when he came to Boston, and has resided in the city 8 years; how old is William ? 20. What is the amount of 12 and 8? 22. John purchased 12 peaches of one man, and 9 of another; how many peaches did he purchase? 24. How many are 12 and 9? 26. What is the amount of 2, 4, 6, 8, 10, and 12? 28. What is the amount of 7, 8, 9, 10, 11, and 12? Art. 11. Besides figures, we use several signs in arithmetic indicating equality, or that some operation is to be performed. Two parallel horizontal lines indicate equality; thus, 1 dollar = 100 cents, which is read 1 dollar is equal to 100 cents. A cross, one line being horizontal, and the other perpendicular, indicates addition; thus, 5+7=12, which is read 5 added to 7 is equal to 12, or 5 plus 7 is equal to 12. There are other signs, which will be explained when we have occasion to use them. 29. How many are 13+2? 14 30. How many are 13+3? 14 +2? 15+2? 16+2? 17+2?+3? 15+3? 16+3? 17+3? 18+2? 19+2? 183? 193? 31. How many are 13+4? 14 32. How many are 13+5? 14 +4 15+4? 16+4? 17+4?+5? 15+5? 16+5? 17+5? 18+4? 19+4? 1852 195? 33. What is the sum of 13+ 6? 14+6? 15+6 16+6? 17 +6 18+6? 19+6? 35. What is the amount of 13 +8? 14+8? 15+8? 16+8? 17+8? 18+8? 19+8? 37. William paid 20 cents for a knife, and 10 cents for a writingbook; how many cents did he pay for both of them? 39. How many are 30+10? 41. A man paid 50 dollars for a gold watch, and 20 dollars for a silver one; how many dollars did the two watches cost him? 43. What is the sum of 60+ 30? 45. A merchant borrowed 30 dollars of A., 20 dollars of B., and 10 dollars of C; what was the whole number of dollars that he borrowed? 47. What is the amount of 40 +30+20? 49. A trader paid 70 dollars for a horse, 60 dollars for a yoke of oxen, and 20 dollars for a cow; how many dollars did he pay for all of them? 51. What is the sum of 80+ 60-+-40? 34. What is the sum of 13+ 7? 14+7? 15+7? 16+7? 17 +7? 18+7? 19+7? 36. What is the amount of 13 +9 14+9? 15+9? 16+9? 179? 18+9? 19+9? 38. A man lived in the country until he was 30 years old, and has lived in the city 20 years; what is his age? 40. How many are 40+20? 42. In a certain school, there are 50 boys, and 30 girls; what is the whole number of pupils in the school? 44. What is the sum of 60+ 40? 46. A trader purchased three pieces of cloth; the first measured 50 yards, the second, 40 yards, and the third, 30 yards; how many yards did he purchase? 48. What is the amount of 60 +50+40? 50. A farmer purchased three pieces of land; the first contained 80 acres, the second, 70 acres, the third, 60 acres; how many acres did he purchase? 52. What is the sum of 90+ 80+70? 54. A trader borrowed 45 dollars of C., and 35 dollars of D; what number of dollars did he borrow? 56. What is the amount of 55 +45? 58. A stage driver purchased four horses. He paid 120 dollars for the first, 110 dollars for the second, 90 dollars for the third, and 80 dollars for the fourth. What number of dollars did they cost him? 60. What is the sum of 150+ 140+130+120 ? 62. What is the sum of 550 dollars+460 dollars+370 dollars +230 dollars? Art. 12. A man has three carriages. 950 dollars. 764 dollars. worth? hunds. tens. units. 950 875 Ans. 2589 dols. No. 1 is worth No. 3 is worth three carriages These numbers being large, it is not convenient to add them mentally. We first write them in order, placing units under units, tens under tens, hundreds under hundreds, and then draw a line under them. We begin at the bottom of the column of units, and say, 4 units and 5 units are 9 units, the sum of the units being less than 10, we write the 9 units under the column. We then proceed to the column of tens, and say, 6 tens and 7 tens are 13 tens, and 5 tens are 18 tens, or 1 hundred and 8 tens; we write the 8 tens under the column of tens, and add the 1 hundred with the figures in the column of hundreds. We then say, 1 hundred and 7 hundred are 8 hundred, and 8 hundred are 16 hundred, and 9 hundred are 25 hundred, or 2 thousand and 5 hundred; we write the 5 hundred under the column of hundreds, and the 2 thousand at the left of the 5 hundred; and the whole amount is 2589 dollars. From the preceding illustration, we obtain the following rule for the addition of simple numbers: RULE. Write the numbers, placing units under units, tens under tens, hundreds under hundreds, and draw a line under them. Begin at the bottom of the column of units, and add all the figures in that column, in succession; if the amount does not exceed nine, write it under the column; if the amount exceeds nine, write the right hand figure of it under the column, and add the left hand figure, or figures, which are units of the next higher order, with the figures in the next column. Add the figures in each succeeding column in the same manner, and write down the whole amount of the last column. METHODS OF PROOF. Begin at the top of each column, and add the figures downwards in the same manner that they were added upwards; if both operations have been performed correctly, this amount will be equal to the first amount. Or separate the numbers into two or more divisions, find the amount of each of these divisions, then find the sum of these amounts; if the several operations have been performed correctly, the sum of these separate amounts will be equal to the first amount. 63. What is the sum of 1, 2, 3, 4, 5, 6, 7, 8, and 9? Ans. 45. 64. What is the amount of 10, 11, 12, 13, 14, 15, 16, 17, 18, and 19? Ans. 145. 65. What is the sum of 20, 25, 30, 35, 40, 45, 50, 55, and 60? Ans. 360. 66. What is the amount of 65, 70, 75, 80, 85, 90, 95, and 100? 84 Ans. 660. 1706, and was 67. Dr. Benjamin Franklin was born in Ans. 1790. 68. The creation of the world was 4004 years before the Christian era; how many years since the creation to the present time, 1847? Ans. 5851 years. 69. In January there are 31 days, February 28, March 31, April 30, May 31, June 30, July 31, August 31, September 30, October 31, November 30, December 31. How many days are there in the twelve months, or one year? Ans. 365 days. 70. A provision dealer purchased eight hogs, weighing as follows: 275 pounds, 286 pounds, 305 pounds, 315 pounds, 334 pounds, 345 pounds, 350 pounds, and 375 pounds. What was their whole weight? Ans. 2585 pounds. 71. A butcher killed five fat oxen. The weight of the first was 1124 pounds; the second, 1235 pounds; the third, 1300 |