From the preceding illustrations we derive the following rule: RULE.-I. Write the less number under the greater, placing units of the same order in the same column. II. Begin at the right hand, and take each figure of the subtrahend from the figure above it, and write the result underneath. III. If any figure in the subtrahend is greater than the corresponding figure in the minuend, add 10 to that figure in the minuend before subtracting, and then add 1 to the next left-hand figure of the subtrahend; or add 10 to that figure in the minuend and take 1 from the next left-hand figure of the minuend. PROOF. Add the remainder to the subtrahend, and if their sum is equal to the minuend, the work may be presumed to be right. 52. The process of adding 10 to the minuend is sometimes called borrowing 10, and that of adding 1 to the next figure of the subtrahend, carrying 1. 14. 479-382 : = ? 15. 6593-1807 = ? Ans. 97. 16. 17380 - 3417 = ? 17. 80014-43190 = ? 19. From 234100 take 9970. 31. Take 501300347 from 1030810040. Ans. 4786. Ans. 13963. Ans. 36824. Ans. 191975. Ans. 4111107. Ans. 3968579. Ans. 50000001. Ans. 3819851. Ans. 800924. Ans. 7623024. 32. Subtract nineteen thousand nineteen from twenty thousand ten. Ans. 991. 33. From one million nine thousand six take twenty thousand four hundred. Ans. 988606. 34. What is the difference between two million seven thousand eighteen, and one hundred five thousand seventeen? 35. Take 67092 from 91307. 39. What is the difference between 19553068 and 3204313? 40. The population of Great Britain in 1891 was 37888153, and that of England alone, 27482104. What was the difference? EXAMPLES COMBINING ADDITION AND SUBTRACTION. 1. A merchant gave his note for $5200. one time $2500, and at another $175. What remained due? He paid at Ans. $2525. 2. A traveler who was 1300 miles from home, traveled homeward 235 miles in one week, in the next 275 miles, in the next 325 miles, and in the next 280 miles; how far had he still to go before he would reach home? How 3. A man deposited in a bank $8752; he drew out at various times $4234, $1700, $962, and $49. much had he remaining in the bank? 4. A man bought a farm for $4765, and paid $750 for fencing and other improvements; he then sold it for $384 less than it cost him. What did he receive for it? 5. A forwarding merchant had in his warehouse 7520 barrels of flour; he shipped at one time 1224 barrels, at another time 1500 barrels, and at another time 1805 barrels. How many barrels remained? 6. A had 450 sheep, B had 175 more than A, and C had as many as A and B together minus 114. How many sheep had C? Ans. 961 sheep. 7. A farmer raised 1575 bushels of wheat, and 900 bushels of corn. He sold 807 bushels of wheat, and 391 bushels of corn to A, and the remainder to B. How much of each did he sell to B? 8. A man traveled 6784 miles; 2324 miles by railroad, 1570 miles in a stage coach, 450 miles on horseback, 175 miles on foot, and the remainder by steamboat. How many miles did he travel by steamboat? Ans. 2265 miles. Having paid 9. I borrowed of my neighbor at one time $750, at another time $379, and at another $450. him $1000, how much do I still owe him? Ans. $579. MULTIPLICATION. ORAL EXERCISES. 53. 1. What will 4 pounds of sugar cost, at 8 cents a pound? SOLUTION. Four pounds will cost 4 times 8 cents, or 32 cents. 2. If a ream of paper costs 3 dollars, what will 2 reams cost? 3. At 7 cents a quart, what will 4 quarts of cherries cost? 4. At $12 a ton, what will 3 tons of hay cost? 4 tons? 5 tons ? 5. There are 7 days in one week. How many days are there in 6 weeks? In 8 weeks? 6. What will 9 quarts of berries cost, at 10 cents a quart? 7. If Henry earns 12 dollars in one month, how much can he earn in 5 months? In 7 months? In 9 months? 8. What will 11 dozen eggs cost, at 9 cents a dozen? At 10 cents? At 12 cents? 9. When flour is $7 a barrel, what must be paid for 7 barrels ? For 9 barrels ? For 12 barrels ? 10. At $9 a week, what will 4 weeks' board cost? 7 weeks' board? 9 weeks' board? 11. At 9 cents a foot, what will 4 feet of lead pipe cost? 7 feet? 10 feet? 12. If I deposit $12 in a savings bank every month, how many dollars will I deposit in 6 months? 13. When hay is $8 a ton, how much will 3 tons cost? 4 tons? 7 tons? 9 tons? 14. What will be the cost of 11 $2 a barrel? At $3? 11 tons? barrels of apples at 15. At 5 cents a pound, what will 9 pounds of sugar cost? 11 pounds? 12 pounds? 16. John is 12 years old and his father is 5 times as old. How old is his father? 54. Multiplication is the process of taking one of two given numbers as many times as there are units in the other. 55. The Multiplicand is the number to be multiplied. 56. The Multiplier is the number by which to multiply, and shows how many times the multiplicand is to be taken. 57. The Product is the result obtained by the process of multiplication. 1. Factors are producers, and the multiplicand and multiplier are factors of the product because they produce it. 2. Multiplication is a short method of performing addition when the numbers to be added are equal. 58. The sign x, placed between two numbers, denotes that one is to be multiplied by the other. Thus 9 × 6 = 54, is read 9 times 6 equal 54, or 6 multiplied by 9 equals 54. 59. The multiplier is always regarded as an abstract number. Either factor of a product may be used abstractly, even though it be concrete, hence either factor may be used as a multiplier. |