NOTE. 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 one. 51. From the preceding examples and illustrations we have the following general RULE. I. Write the less number under the greater, placing units of the same order under each other. 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 be greater than the corresponding figure above it, add 10 to that upper figure before subtracting, and then add 1 to the next left hand figure of the subtrahend. PROOF. Add the remainder to the subtrahend, and if their sum be equal to the minuend, the work is supposed to be right. What do we mean by borrowing 10? By carrying? Rule, first step? Second Third? Proof? 19. From 234100 take 9970. 31. Take 501300347 from 1030810040. 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? EXAMPLES COMBINING ADDITION AND SUBTRACTION. 52. 1. A merchant gave his note for 5200 dollars. He paid at one time 2500 dollars, and at another 175 dollars; what remained due? Ans. 2525 dollars. 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? Ans. 185 miles. 3. A man deposited in bank 8752 dollars; he drew out at one time 4234 dollars, at another 1700 dollars, at another 962 dollars, and at another 49 dollars; how much had he remaining in bank? Ans. 1807 dollars. 4. A man bought a farm for 4765 dollars, and paid 750 dollars for fencing and other improvements; he then sold it for 384 dollars less than it cost him; how much did he receive for it? Ans. 5131 dollars. 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? Ans. 768 bushels of wheat, and 509 of corn. 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. 9. Three persons bought a hotel valued at 35680 dollars. The first agreed to pay 7375 dollars, the second agreed to pay twice as much, and the third the remainder; how much was the third to pay? Ans. 13555 dollars. 10. Borrowed of my neighbor at one time 750 dollars, at another time 379 dollars, and at another 450 dollars. Having paid him 1000 dollars, how much do I still owe him? Ans. 579 dollars. 11. A man worth 6709 dollars, received a legacy of 3000 dollars. He spent 4379 dollars in traveling; how much had he left? 12. In 1850 the number of white males in the United States was 10026402, and of white females 9526666; of these, 8786968 males, and 8525565 females were native born; how many of both were foreign born? Ans. 2240535. MULTIPLICATION. MENTAL EXERCISES. 53. 1. What will 4 pounds of sugar cost, at 8 cents a pound? ANALYSIS. Four pounds will cost as much as the price, 8 cents taken 4 times; thus, 8+8+8+8=32. But instead of adding, we may say, since one pound costs 8 cents, 4 pounds will cost 4 times 8 cents, or 32 cents. 2. If a ream of paper cost 3 dollars, what will 2 reams cost? 3. At 7 cents a quart, what will 4 quarts of cherries cost? 4. At 12 dollars a ton, what will 3 tons of hay cost? 4 tons? 5 tons? 5. There are 7 days in 1 week; how many days in 6 weeks? in 8 weeks? 6. What will 9 chairs cost, at 10 shillings apiece? 7. If Henry earn 12 dollars in 1 month, how much can he earn in 5 months? in 7 months? in 9 months? 8. What will 11 dozen of eggs cost, at 9 cents a dozen? at 10 cents? at 12 cents? 9. When flour is 7 dollars a barrel, how much must be paid for 7 barrels? for 9 barrels ? for 12 barrels ? 10. At 9 dollars a week, what will 4 weeks' board cost? 7 weeks'? 9 weeks'? 11. If I deposit 12 dollars in a savings bank every month, how many dollars will I deposit in 6 months? in 8 months? in 9 months? 12. At 9 cents a foot, what will 4 feet of lead pipe cost? 7 feet? 10 feet? 13. When hay is 8 dollars a ton, how much will 3 tons cost? 4 tons? 7 tons? 9 tons? 11 tons? 14. What will be the cost of 11 barrels of apples, at 2 dollars a barrel? at 3 dollars? 15. At 10 cents a pound, what will 9 pounds of sugar cost? 11 pounds? 12 pounds? 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 taken. 56. The Multiplier is the number which shows how many times the multiplicand is to be taken. 57. The Product is the result obtained by the process of multiplication. 58. The Factors are the multiplicand and multiplier. NOTES. 1. Factors are producers, and the multiplicand and multiplier are called factors because they produce the product. 2. Multiplication is a short method of performing addition when the numbers to be added are equal. 59. The sign, X, placed between two numbers, denotes that they are to be multiplied together; thus 9 X 6 = 54, is read 9 times 6 equals 54. Define multiplication. Multiplicand. Multiplier. Product. Factors. Multiplication is a short method of what? What is the sign of multiplication? |