SECTION III. SUBTRACTION. MENTAL EXERCISES. ART. 30. Ex. 1. Henry having 7 peaches, gave 4 to his sister how many had he left? OBS. To solve this question, think what number added to 4 makes 7. Now, from addition we know that 4 and 3 make 7; that is, 7 is composed of the numbers 4 and 3. It is evident, therefore, one of these numbers be taken from 7, the other number will be left. Hence 4 peaches from 7 peaches leave 3 peaches. Ans. 3 peaches. 2. James had 7 cents and spent three of them: how many had he left? 3. Jack has 6 marbles: how many more must he get to make 10? 4. A farmer having 9 cows, sold 5 of them: how many had he left? 5. A pound of raisins costs 11 cents and a pound of sugar 8 cents: what is the difference in their prices? 6. In a stage coach there were 10 passengers, 6 of them got out at a hotel: how many remained in the coach? 7. Dick bought a knife for 12 cents, and having but 7 cents in his pocket, agreed to pay the rest to-morrow: how much does he owe for it? 8. John gathered 8 quarts of chestnuts: how many more must he gather to make 14 quarts? 9. The cost of a cap is 13 shillings, and the cost of a comforter is 3 shillings; what is the difference in their cost? 10. Susan is 15 years old, and Harriet is only 9: what is the difference in their ages? OBS. This Table is the reverse of Addition Table. Hence if the pupil has thoroughly learned that, it will cost him but little time or trouble to learn this. (See observations under Addition Table, p. 20.) 11. 4 from 7 leaves how many? 4 from 9? 4 from 12? 4 from 8? 4 from 11? 4 from 13? 12. 6 from 8 leaves how many? 6 from 10? 6 from 13? 6 from 11? 6 from 15? 6 from 12? 6 from 16? 13. 7 from 9 leaves how many? 7 from 11? 7 from 14? 7 from 15? 7 from 16? 7 from 13? 7 from 15? 7 from 17? 14. 8 from 11? 8 from 13? 8 from 16? 8 from 12? 8 from 15? 8 from 17? 8 from 14? 8 from 18? 15. 9 from 12? 9 from 14? 9 from 11? 9 from 13? 9 from 17? 9 from 15? 9 from 18? 9 from 19? 16. 2 from 4 leaves how many? 2 from 14? 2 from 24? 2 from 34? 2 from 44? 2 from 54? 2 from 64 ? 2 from 74? 2 from 84? 2 from 94 ? 17. 3 from 6? 3 from 16? 3 from 26? 3 from 36? 3 from 46 3 from 56? 3 from 66? 3 from 76? 3 from 86? 3 from 96 ? 18. 4 from 9? 4 from 29? 4 from 39? 4 from 49? 4 from 59? 4 from 69? 4 from 79? 4 from 89? 4 from 99? 19. 6 from 15? 6 from 25? 6 from 35? 6 from 45? 6 from 55? 6 from 65? 6 from 75? 6 from 95? 20. 8 from 14? 8 from 24? 8 from 34? 8 from 44? 8 from 54 8 from 64? 8 from 74? 8 from 84? 8 from 94? 21. A gentleman bought a coat for 15 dollars and a hat for 6 dollars: how much more did his coat cost than his hat? 22. A farmer having sold 6 cords of wood for 18 dollars, took a barrel of flour at 6 dollars towards his pay and the rest in cash: how much money did he receive? 23. A lady bought a shawl for 15 dollars and handed the shop keeper a 20 dollar bill: how much change ought she to receive back? 24. A man having 25 watermelons in his garden, some wicked boys stole 9 of them: how many had he left? 25. James is 14 years old and his sister is 19: what is the difference in their ages? 26. A merchant had a piece of calico which contained 33 yards; on measuring the remnant he finds he has but 7 yards left: how many yards has he sold? 27. A hogshead of cider contains 63 gallons; after drawing out 9 gallons, how many will be left? 28. Henry had 48 silver dollars and gave 8 to the orphan asylum: how many dollars did he have left? 29. A man bought a piece of cloth containing 39 yards, and sold 6 yards of it: how many yards had he left? 30. George gave 75 cents for a pair of skates, and sold them for 9 cents less than he gave: how much did he get for his skates ? 31. William had 67 cents; he spent 5 for chestnuts and 2 for apples: how many cents has he left? 32. A man sold a load of wood for 18 shillings; he laid out 4 shillings for tea and 6 for sugar: how many shillings had he to carry home? 33. Sarah having 85 cents, gave 10 cents to the Sabbath School Society, 8 to the Bible Society, and spent 6 for candy how many cents had she left? 34. If I pay 27 dollars for a cow and sell it for 18, how much do I lose by the bargain? 35. Richard had 45 marbles; he lost 7 and gave away 5: how many had he left? 36. A man having 56 dollars in his pocket, bought a hat for 5 dollars, a coat for 10, and a pair of boots for 4: how much money had he left? 37. If I owe a merchant 50 dollars and pay him 20 dollars, how many dollars shall I then owe him? Ans. 30 dollars. Suggestion. It is advisable for beginners to analyze the numbers in this question, as in Art. 16, Ex. 31, and take 2 tens from 5 tens. 38. A farmer having 80 sheep, sold all but 30: how many did he sell? 39. A man having 90 acres of land, gave 50 acres to his son how many acres has he left? 40. George had 70 cents and spent 30: how many had he left? 41. In a certain orchard there are 100 trees, 60 of them are apple-trees and the rest are peach-trees: how many peach-trees are there? 42. A grocer bought 150 eggs and afterwards found that 20 of them were rotten: how many sound ones were there? 43. In the Centre School there are 150 scholars, 60 of whom are girls how many boys are there? 44. A man bought a horse for 90 dollars and sold it immediately for 130 dollars: how much did he make by his bargain? 45. A man owing me 200 dollars turned me out a horse worth 80 dollars, and is to pay the balance in cash : how much money must he pay me? 46. A boy going to market with 80 cents, bought 20 cents worth of cheese and 30 cents worth of butter: how much change had he left? ? 47. 35 from 42 leaves how many? 63 from 75? 48. 26 from 40 leaves how many? 35 from 45? 49. 65 from 85, how many? 82 from 94, how many 50. 8 from 17, how many? 13 from 26, how many? 6 from 25, how many? 8 from 94, how many? 5 from 68, how many? 17 from 34, how many? 7 from 43, how many? 6 from 72, how many? 9 from 75, how many? 7 from 86, how many ? 31. It will be observed that all the preceding examples of this section, though expressed in a variety of ways, involve the same principle; that the object aimed at in each of them, is to find the difference between two numbers; consequently, they are all performed in the same manner. The operation consists in taking a less number from a greater, and is called subtraction. Hence, 32. SUBTRACTION is the process of finding the difference between two numbers. The difference or answer to the question is called the remainder. OBS. 1. The number to be subtracted is sometimes called the subtrahend, and the number from which it is subtracted, the minuend. 2. Subtraction, it will be perceived, is the reverse of addition. Addition unites two or more numbers into one single number; subtraction, on the other hand, separates a number into two parts. 3. When the given numbers are of the same denomination, the operation is called Simple Subtraction. (Art. 18. Obs.) 33. Subtraction is often represented by a short horizontal line, which is called minus. When placed between two numbers, this sign shows that the number after it is to be subtracted from the one before it. Thus the expression 8-5, signifies that 5 is to be subtracted from 8; and is read, 8 minus 5," or "8 less 5." 66 OBS. The term minus is a Latin word signifying less. EXERCISES FOR THE SLATE. 34. When we wish to find the difference between two small numbers, it is the most convenient way to perform the subtraction in the mind. But when the numbers are large, it is difficult to retain them in the mind, and carry on the operation at the same time. By setting them down upon a slate or black-board, however, the process of subtracting large numbers is rendered short and simple. (Art. 21.) QUEST.-31. What is the object aimed at in the preceding examples? In what does the operation consist? What is it called? 32. What then is subtraction? What is the difference or answer called? Obs. What is the number to be subtracted sometimes called? That from which it is subtracted? Of what is subtraction the reverse? When the given numbers are of the same denomination, what is the operation called? 33. What is the sign of subtraction called? Of what does it consist? What does it show? How is the expression 9 4 read? Obs. What is the meaning of the term minus? 34. What is the most convenient way of finding the difference between two small numbers? What between two large ones? |