EXAMPLES. 1. What is the product of 462, multiplied by 4 ? Multiplicand 462 462 multiplicand. X3 one less than (4) the multiplier. +-462 multiplicand added. 1848 Proof, by the 2d method given. In the first place, we ought to write down the multiplicand; then we write the multiplier under the unit figure of the multiplicand, and draw a line underneath. We then say 4 times 2 are 8; as the product does not exceed 9 we write it under the multiplier, we then say 4 times 6 are 24, we write down the right hand figure, (the four units,) and reserve the left hand figure 2 to be added to the product of the next figure; we then say 4 times 4 are 16 and the 2 tenths we reserved are 18, this being the last figure, we write down the whole product 18, and find the product to be 1848. 2. A farmer bought 125 acres of land, at 35 dollars an acrewhat did the land cost the farmer? Multiplicand 125 Proof. 35 multiplier and 125 multiplicand inverted. 5 x 125=625 175=5 times 35, or 175 30 x 125=375 420=120 times 35, or 4200 125 X 35=4375 ans. 4375 all the same pro. 4375 Having set the sum down ready for work, we say 5 times 5 are 25, (two tens and five units,) we set down the 5 and carry the 2, and say 5 times 2 are 10, and 2 (we carried) are 12, we set down the 2 and carry the 1, and say 5 ones are 5, and 1 we carried are 6, we set it down, which finishes the first line. We then say 3 fives are 15, we set down the 5 directly in line under the 3 which we are multiplying with, and carry the 1, we then say 3 times 2 are 6, and I we carried are 7, which we set down, and say 3 times 1 are 3, we set it down, and add up the two products, and find the total product to be 4375 dollars, the answer required. See proof. 3. What will 245 barrels of flour cost, at 4 dollars a barrel ? 4. Suppose 6521 to be a multiplicand, and 23 the multiplierhow much will be the product ? 5. What is the product of 82602 multiplied by 61 ? 20 MULTIPLICATION. Questions to be put to the Learner. 1. What is Multiplication ? 2. What is the number to be multiplied called ? 3. What is the number to multiply by called ? 4. What number is written down first? 5. How must the multiplier be set under the multiplicand ? 6. What is the result or answer called ? 7. How many times larger is the product than the multiplicand ? 8. Where do you begin to multiply? 9. Why do you begin to multiply at the right hand figure ? 10. Why do you carry one for every ten ? 11. How do you place the first product figure of each line ? 12. What rule does multiplication shorten ? 13. How many numbers are given in multiplication ? 14. How many numbers are required in multiplication ? Days. Miles. Dollars. Yards. 11. 57319 12. 60271 13. 43186 14. 24681 3 5 7 9 18. There are 320 rods in a mile-how many are there in 12 miles ? Ans. 3840 rods. 19. What is the product of 19603 multiplied by 402? Ans. 7880406. 20. A prize was divided among 325 men, and each man received 25 dollars—how much was the prize ? Ans. 8125 dollars. 21. A man travelled 365 days, travelling 35 miles a day-how far did he travel in the whole time? Ans. 12775 miles. 22. A merchant sold 365 tons of iron, at 125 dollars per tonwhat was the price of the whole ? Ans. 45625 dollars. 23. A merchant bought 42 mules, for shipping, at 42 dollars per head—what did the whole cost? Ans. 1764 dollars. 24. How many are 225 times 625 ? Ans. 140625 25. Multiply 675 by 45, and tell the product. Ans. 30375. 26. Suppose 70316 to be a multiplicand, and 224 the multiplier; how much will be the product ? Ans. 15750784. 27. What will 10 horses cost, at 75 dollars apiece ? Ans. 750 dollars. Mr. T. Webster Bought of S. Adams, 28. 6 slates, at 24 cents apiece, 4 books, at 32 cents apiece, 1 arithmetic, at 25 cents, Ans. 329 cts. 29. What sum of money must be divided among 38 men, so that each man shall receive 525 dollars ? Ans, 19950 dolls. NOTE 1.-When the multiplier is 10, 100, 1000, &c., merely place the ciphers on the right hand of the multiplicand, for the product required. Thus, 10 times 75 are 750 ; for the 5, which was units before, is now made tens, and the 7, which was tens before, is now made hundreds. "If any. figure be removed two places toward the left hand, its value is increased 100 larger 30. What is the product of 325 multiplied by 10? Ans. 3250. 31. In 1 dollar there are 100 cents; how many cents are there in 25 dollars ? Ans. 2500 cents. 32. What is the product of 111 multiplied by 1000 ? Ans. 111000. NOTE 2.-Ciphers on the right hand of the multiplier and multiplicand both, may all be omitted, or disregarded in multiplying, and finally placed on the right hand of the product. 33. What is the product of 4600 multiplied by 220 ? Thus 46 or, 4600 22 220 Ans. 1012000 1012000 product required. 34. How many are 80 times 34100 ? Ans. 2728000. NOTE 3.-When the multiplier is a number that can be produced by mul. tiplying two smaller numbers together, multiply the multiplicand first by one of the smaller numbers, and the product thence arising by the other. 35. A merchant bought 212 hogsheads of molasses, at 24 dol. lars a hogshead_what did the whole cost ? 212 4X6=24 6 1272 price of 6 hogsheads. 4 Ans. 5088 dols. price of 4 times 6 hogsheads, or 24 hhds. 22 MULTIPLICATION. 36. An army of 3500 men having plundered a city, took so much money that, when it was shared among them, each man received 250 dollars—what was the sum of money taken? Ans. 875000 dollars. 37. A farmer sold 38 pounds of pork, at 6 cents a pound, and 15 pounds of cheese, at 7 cents a pound-how many cents must he receive in pay? Ans. 333 cents. 38. What sum of money must be divided between 86 men, so that each man may receive 50 dollars ? Ans. 4300 dollars. 39. If 28 men can do a piece of work in 9 days, how many men will it require to do it in 1 day? Ans. 252 men. 40. Supposing the number of houses in a certain town to be 316, each house on an average containing 2 families, and each family 5 members, what would be the number of inhabitants in that town? Ans. 3160. 41. If the multiplicand be twice 25, and the multiplier twice 5 and 20, what is the product? Ans. 1500. 42. What is the product of 1236 multiplied by thirty-five units? Ans. 43260. 43. If sound flies 68520 feet in a minute; how far will it fly in 60 minutes, or an hour ? Ans. 4111200 feet. 44. A lady bought 8 yards of cambric, at 36 cents a yard, and 6 yards of lace, at 85 cents a yard—how many cents did she pay for the whole ? Ans. 798 cents. 45. If a ship sail at the rate of 216 miles a day, how many miles will she sail in 12 days? Ans. 2592 miles. 46. If 1 man can dig 35 bushels of potatoes in a day, how many bushels can 11 men dig? Ans. 385 bushels. 47. How many are 2001 times 4002? Ans. 8008002. 48. What is the product of 576 multiplied by 21 ? Ans. 12096. Questions. 1. To multiply by 10, 100, &c., what suffice ? 2. When there are ciphers on the right hand of the multiplicand, or multiplier, or on the right of both, how may we proceed? 3. How do you proceed with a composite number, that is, when the multiplier can be produced by multiplying two smaller numbers together? DIVISION. DIVISION teaches how often one number contains another, of the same kind; that is, it shows how many times a less number may be taken from a larger. It is a short way of doing Subtraction. NOTE, To Teachers. Before the learners are required to answer any questions, either mentally or by the use of the slate, they should thoroughly learn the following DIVISION TABLE. 66 2 66 1 in 1 once. 1 2 twice. 2 66 2 once. 2 " 3 once and 1 over. 2 “ 4 twice. 5 twice and 1 over. 2 " 6 3 times. 2 6 ng 3 times and l over. 8 4 times. 2 16 9 4 times and 1 over. 2 6 10 5 times. 2 “ 11 5 times and 1 over. 2 66 12 6 times. 2 66 13 6 times and 1 over. 2 6 14 7 times. 2 6 15 7 times and 1 over. 2 6 16 8 times. 26 17 8 times and 1 over. 2 6 18 9 times. 2 66 19 9 times and 1 over. 2 ".20 10 times. 2 66 21 10 times and 1 over. 2 66 22 11 times. 2 66 23 11 times and 1 over. 2 4 24 12 times. 3 66 3 once. 3.6 4 once and 1 over. 3 « 5 once and 2 over. 3 6 twice. 3 « 7 twice and 1 over. 3 66 8 twice and 2 over. 3 9 3 times. 3 .66.10 3 times and 1 over. 3 6 11 3 times and 2 over. 3 12 4 times. 4 4 4 once. 4 " 5 once and 1 over. 46 6 once and 2 over. 4 in 7 once and 3 over. 4 66 8 twice. 4 66 9 twice and 1 over. 4 6 10 twice and 2 over. 4 " 11 twice and 3 over. 4 6 12 3 times. 5 5 once. 5 6 10 twice. 5 6 15 3 times. 5 " 20 4 times. 5 66 25 5 times. 5 6 30 6 times. 5 6 35 7 times. 56 40 8 times. 5 66 45 9 times. 56 50 10 times. 5 66 55 11 times. 5 " 60 12 times. 6 " 6 once. 6 66 12 twice. 6 “ 18 3 times. 6 6 24 4 times. 6. " 30 5 times. 6 66 36 6 times. 6 66 42 7 times. 6 66 48 8 times. 6 46 54 9 times. 6 " 60 10 times. 6 6 66 11 times. 6 66 72 12 times. 7 66 7 once. 7 “ 14 twice. 7 “ 21 3 times. 7" 28 4 times. 7 6 35 5 times. ng 66 42 6 times. 7 66 49 7 times. ng 6 56 8 times. |