CASE II. 77. When the multiplier is greater than twelve. 1. Multiply 465 by 37. SOLUTION.-We write the multiplier under the multiplicand, units under units, tens under tens, etc. Since 37 equals 7 units and 3 tens, it is evident that 37 times a number equals 7 times the number plus 3 tens times the number. Seven times 465 equals 3255; 3 times 465 equals 1395, hence 3 tens times 465 equals 1395 tens. Taking the sum of the partial products we have 17205. Hence, etc. OPERATION. 465 37 3255 1395 17205 Rule.-I. Write the multiplier under the multiplicand, placing terms of the same order in the same column, and draw a line beneath. II. Begin at the right, and multiply the multiplicand by each term of the multiplier, writing the first term of each product under the term of the multiplier which produces it. III. Add the partial products, and their sum will be the entire product. Proof. Multiply the multiplier by the multiplicand; if the work is correct this product will equal the first product. NOTES.-1. When there are ciphers between the significant terms of the multiplier, pass over them and multiply by the significant terms alone. 2. We begin at the right to multiply, so that when any product exceeds nine we may add the number expressed by the left hand figure to the next product. 2. Multiply 247 by 24; also by 204. 48. Multiply 6328 by 2552. 49. Multiply 71873 by 6036. 50. Multiply 11364 by 1629. 51. Multiply 21984 by 1021 52. Multiply 12835 by 2036. 53. Multiply 10675 by 3007. Ans. 16149056. Ans. 433825428. Ans. 26132060. MENTAL EXERCISES. 1. What will 6 yards of muslin cost at 10 cents a yard? SOLUTION.-If 1 yard of muslin costs 10 cents, 6 yards of muslin will cost 6 times 10 cents, which are 60 cents. 2. What will 8 sheep cost at 12 dollars apiece? 3. What will 12 turkeys cost at 60 cents apiece? 4. At 80 cents each, how much will 9 arithmetics cost? 5. If 5 men can do a piece of work in 6 days, how long will it take 1 man to do it? 6. If 9 men dig a trench in 14 days, how long would it take one man to do it? 7. How many trees in an orchard in which there are 12 rows with 20 trees in each row? 8. A grocer had 24 melons, sold 10 of them, and then bought 5 imes as many as he sold; how many had he then? 9. Mason earned $15 a week and paid $7 for his board; how much could he save in 8 weeks? 10. Thompson earned $50 a month and paid $5 a week for his board, and $4 for other expenses; how much could he save in a year? 11. Multiply 76 by 4. SOLUTION.-4 times 6 units are 24 units, which equals 2 tens and 4 units, times 7 tens are 28 tens, which increased by the 2 tens equals 30 tens; hence the product is 304. 12. Multiply 26 by 3; 28 by 4: 37 by 5; 46 by 6; 53 by 7; 75 by 8. 65 by 12; 88 by 11; 125 by 10. 13. Multiply 142 by 4; 325 by 3; 463 by 5; 372 by 6; 408 by 7; 1234 by 6; 2007 by 8; 1306 by 5; 508 by 11; 407 by 12. 14. If a railroad train runs 36 miles an hour, how far will it run at that rate in 6 hours? 15. If a newsboy clears 56 cents a day for 8 days, how much will he clear in all? 16. A jeweler bought 8 watches for $125 apiece, and sold them at gain of $25 each; what did he receive for them? 17. At $6 a barrel, how much are 3 loads of flour worth, each load containing 10 barrels ? 18. A man bought 5 books at 40 cents each, and 2 pairs of shoes at $1.50 a pair; what change will be left out of a $5 bill? 19. A farmer's wife took to a store 6 dozen eggs at 20 cents a dozen, and bought 8 yards of muslin at 12 cents a yard; what balance should she receive? 20. A lady went “a shopping” and bought 6 yards of silk at $3 a yard, 2 yards of velvet at $5 a yard, and 4 pairs of hose at 75 cents a pair; she handed the clerk two $20 bills; what was her change? WRITTEN EXERCISES. 1. If a steamer sails 235 miles in 1 day, how far will sbe sail in 37 days? SOLUTION.-If a steamer sails 235 miles in 1 day, in 37 days she will sail 37 times 235 miles, or 8695 miles. OPERATION. 235 37 1645 705 8695 2. How many bushels of potatoes can be raised on 56 acres of land, if each acre produces 196 bushels? Ans. 10,976. 3. How many oranges in 59 boxes, if each box contains. 275 oranges? Ans. 16,225 oranges. 4. If a clerk deposits $575 annually in a savings bank, how much will he deposit in 25 years? Ans. $14,375. 5. Mr. Gibbs bought a farm of 95 acres at $187 an acre; what was the cost of the farm? Ans. $17,765. 6. What will a hogshead of wine, containing 63 gallons, cost at the rate of $4.25 a gallon? Ans. $267.75. 7. I bought 356 sacks of Liverpool salt at $2.50 per sack; what did I pay for the whole amount? Ans. $890. 8. Sold 265 barrels of mess pork at $16.50 a barrel; what did I receive for the whole? Ans. $4372.50. 9. If a locomotive-wheel revolves 478 times in going 1 mile, how often will it revolve in 248 miles? Ans. 118,544. 10. When the market-price of butter is 18 cents a pound, what must I pay for 256 pounds? Ans. $46.08. NOTE. In this and similar problems we multiply by the smaller number, using both numbers abstractly, though in the explanation we should use the proper number as the multiplier. 11. If a barrel of flour is worth $8, how much are 596 harrels worth at the same rate? Ans. $4768. 12. A dealer bought 2875 bushels of potatoes at 37 cents a bushel; what was the cost? Ans. $1063.75. 13. A Western farmer sold 9876 bushels of wheat at 85 cents a bushel; what did he receive? Ans. $8394.60. 14. Henry earned $28 a week and paid $5 for his board; how much could he save in 52 weeks? Ans. $1196. 15. A travels 25 miles a day, and B 36 miles a day; how far will both travel in 286 days? Ans. 17,446 miles. 16. The President's cabinet consists of 7 members, who receive a salary of $8000 each; what is the amount of their salaries? Ans. $56,000. 17. A dealer shipped 2396 bushels of apples at 87 cents a bushel, and the same quantity of potatoes at 56 cents a bushel; what was the value of both? Ans. $3426.28. 18. A bought 2960 acres of prairie land at $38 an acre, and the same number of acres of woodland at $45 an acre; what did he pay for all? Ans. $245,680. 19. In a row of houses there are 46 rooms, in each room 4 windows, and in each window 12 panes of glass; how many panes in all the houses? Ans. 2208 panes. 20. If Thomas sells 48 papers a day, and Henry 72 papers how many more papers does Henry sell in 94 days than Thomas? Ans. 2256 papers. 21. In 1852, 157,548 Irish immigrants arrived in the United States; at this rate what would be the number of immigrants from the beginning of 1852 to the end of 1875? Ans. 3,781,152. |