46. When the sum of a column consists of three figures, the two left-hand figures must be carried. Thus, in Example 9, the sum of the first column is 108-set down 8, and carry 10. CHAPTER V. SUBTRACTION. 47. Five hens are on a roost. Three fly down; how many remain ? Here we are required to take 3 from 5, or to find the difference between 3 and 5. This process is called Subtraction. 48. Subtraction is the process of taking one number from another. 0 from 1 leaves 1; SUBTRACTION TABLE. from 2, 2; 0 from any number leaves that number. 47. Repeat the example. What are we here required to do?-48. What is Subraction? What does 0 from any number leave? Recite the Table. 49. The number to be subtracted, is called the Subtrahend; that from which it is to be taken, the Minuend. The result is called the Remainder, or Difference. 3 from 5 leaves 2; is the subtrahend, 5 the minuend, 2 the remainder or difference.-If the minuend is less than the subtrahend, the subtraction can not be performed; we can not take 3 from 2. 50. Subtraction is denoted by a short horizontal line called Minus, placed before the subtrahend. 5- -3 is read five minus three, and means that 3 is to be subtracted from 5. 51. Observe the following: Subtract 4 from 5. 4 from 15. 14 from 15. 4 from 24. 4 from 44. 54 from 55. 2 from 6. 2 from 66. 62 from 66. Take 3 from 5. 3 from 75. 3 from 85. 83 from 85. 1 from 9. 1 from 19. 11 from 19. 3 from 8. 3 from 38. How much is 1-1? 3-3? 23-23? 33-23? 43-33? 43-10? 53-10? 54-10? 6-3? 86-3? 86-83? 86-10? 8-4? 28-4? 28-24? 9-5? 49-5? 9-7? 69-7? Take 3 from 9. 3 from 59. 3 from 99. 2 from 10. 2 from 20. 2 from 60. 6 from 10. 6 from 50. 6 from 80. 49. What is the number to be subtracted called? What is the number from which the subtrahend is to be taken called? What is the result called? 3 from 5 leaves 2; select the minuend, subtrahend, and remainder. In what case can the subtraction not be performed?-50. How is subtraction denoted? How is 5-3 read? What does it mean?-51. How much is 3-2? What follows? How much is 7-8? 27-23? 77-73? How much is 11-10? 31-10? 51-10? Subtract 8 from 14. 8 from 64. 8 from 84. 6 from 13, 6 from 33. 7 from 14. 7 from 74. 8 from 17. 8 from 87. Take 7 from 10. 9 from 18. 6 from 15. 2 from 39. 3 from 47. 4 from 56. 25 from 29. 36 from 38. 7 from 11. Count backward by twos from 100. Thus 100, 98, 96, &c. Thus: 99, 97, 95, &c. Thus: 99, 96, 93, &c. Thus: 100, 96, 92, &c. Thus: 100, 95, 90, &c. 52. APPLICATIONS OF SUBTRACTION.-When a whole and one of its parts are given, to find the other part, subtract the given part from the whole. 53. When a whole and all its parts but one are given, to find that one, subtract the sum of the given parts from the whole. 54. When the cost and selling price are given, to find the gain, subtract the cost from the selling price. 55. When the cost and loss are given, to find the selling price, subtract the loss from the cost. 56. When the selling price and gain are given, to find the cost, subtract the gain from the selling price. 57. When a later date and the difference of years are given, to find an earlier date (A. D., or after Christ), subtract the difference of years from the later date. 1. A grocer who has 19 barrels of flour, sells 10 of them. How many has he left? Ans. 19-10, or 9, barrels. 2. Leaving home with $17, I spend $5 and give $4 away. How much have I left? (See § 53.) 52. When a whole and one of its parts are given, how do we find the other part? -53. When a whole and all its parts but one are given, how do we find that one?— 54. When the cost and selling price are given, how do we find the gain?-55. When the cost and loss are given, how do we find the selling price?-56. When the selling price and gain are given, how do we find the cost?-57. When a later date and the difference of years are given, how do we find an earlier date? 3. A colt was bought for $81, and sold for $88. What was the gain? (See § 54.) 4. A butcher lost $7 on a cow that cost $49. What did he sell her for? (See § 55.) 5. A jeweller sold a ring for $29, and thereby gained $3. What did the ring cost him? (See § 56.) President Madison was born (See § 57.) 6. La Fayette was born in 1757. six years earlier. What year was that? 7. If ten gallons of wine are drawn taining 63 gallons, how many are left? out of a hogshead con 8. I sold a watch for $57, and by so doing gained $5. How much did it cost? 9. Napoleon died in 1821. When was the battle of Waterloo fought, which took place six years before his death? 10. A farmer who has 89 sheep, sells 52 of them. How many does he retain ? MODEL.-Eighty-nine is 8 tens and 9 units; fifty-two is 5 tens and 2 units. 5 tens and 2 units from 8 tens and 9 units leave 3 tens and 7 units, or 37. Ans. 37 sheep. 11. If I buy some cloth for $95 and sell it at a loss of $32, what do I get for it? 12. A person lays out $4 for books, $2 for paper, and $1 for pens. How much change must he receive for a $20 dollar bill? 13. A boy who has 58 cents, gives 32 cents to the poor. How many cents has he left? 14. If a man buys a cow for $45 and a calf for $6, and seils both for $62, how much does he make by the operation? 58. When the numbers are too large to perform the operation mentally, write the smaller number under the greater and subtract each figure from the one above it. EXAMPLE.-A person who has $87945, gives away $6035. How much has he left? He has the difference between $6035 and $87945, which is to be found by subtraction. Set the smaller number under the greater,-units under 58. When the numbers are too large to perform the operation mentally, how do we deal with them? Go through the given example. |