58. Suppose the product of 649 × 4587 is required. The multiplier 649 is 600+40+9, and the product is found by multiplying by 9, then by 40, and then by 600, and adding the partial products. Thus, 4587 9 times the multiplicand 40 times the multiplicand: 183480 600 times the multiplicand = 2752200 products. 649 times the multiplicand 2976963 59. The zeros at the right of the partial products do not affect the result of the addition, and may be omitted if care is taken to put the right-hand digit of each partial product directly under the multiplier used. Thus, 4587 649 41283 18348 27522 2976963 60. If the multiplier contains zeros, the products that correspond to them will be zero, and need not be written. Find the product of 2007 x 4587. 61. To test the accuracy of the work in multiplication, interchange the multiplicand and the multiplier. If the numerical result is the same in both cases, as in the last example, the work may be assumed to be correct. Ex. 42. 1. What will 29 acres of land cost, at $475 an acre? 2. What will 89 passenger-cars cost, at $3785 each? 3. An orchard contains 25 rows of 24 apple trees each; if these trees average 16 bushels of apples apiece, how many bushels will the orchard yield? 4. A gentleman's investments yield him $75 per day. What income will he receive in two years, allowing 365 days for a year? 5. A square mile contains 640 acres How many acres in a county containing 26 townships of 36 square miles each? 6. A cotton factory has 240 looms; if each loom makes 39 yards of cloth daily, how much cloth will the factory make in 60 days? How 7. A merchant living 25 miles out from New York City goes to his business and returns every day. many miles does he travel in 6 weeks? 8. The cost of building a certain road was, on an average, $1789 to the mile. What was the cost of 327 miles of this road? 9. A line of telegraph is 585 miles in length; the wire necessary for one mile weighs 378 pounds. What will be the weight of the wire for the whole line? 10. There are 4 fields, each containing 585 hills of potatoes, and every hill averages 12 potatoes. How many potatoes in the 4 fields? 11. If a saw-mill turns out 5708 feet of boards in a day, how many feet will it turn out in 49 weeks of 6 days each? 12. If ninety-five men can do a piece of work in three thousand four hundred seventy-nine days, in how many days will one man, laboring at the same rate, perform the work? 13. 640 acres make one square mile. How many acres in 3481 square miles? 14. If a railroad train runs 38 miles in an hour, how many miles will it run in 84 trips of 3 hours each? 15. Two towns, two hundred ninety-four miles apart, are to be connected by a railroad, at a cost of twentyfour thousand six hundred forty-five dollars per mile. What will be the cost of the road? 16. A house requires 7865 shingles on each side of the roof. How many shingles would be necessary for three hundred forty-eight houses of the same size? 17. If 125 tons of steel rails are required for one mile of railroad, how many tons will be necessary for 389 miles? 18. A mile contains 5280 feet. How many feet in 542 miles? 19. At the rate of 1275 words in an hour, how many words will be sent over a telegraph line in a week, allowing six days for the week, and eighteen workinghours each day? 20. The garrison of a fort consume 785 pounds of bread per day. How many pounds will they consume in three years of 365 days each? In all the examples containing dollars and cents, the pupil will remember that two places on the right are used for cents, and that dollars and cents are always separated by the decimal point. (1) Required the cost of fifteen yards of cloth, at $1.25 per yard. (2) Required the cost of nineteen yards of linen, at 60 Find the amount of the following bills: 21. Mrs. Anne Brown bought of P. Marsh 6 pairs of shoes, at $3.25; 8 yards of silk, at $2.48; 3 pairs of gloves, at $1.73; 9 collars, at $0.25. OPERATION. 6 pairs of shoes, @ $3.25, cost $19.50 Ans. $46.78 22. Mr. Henry Carey bought of John Rouse 52 pounds of butter, at $0.45; 16 yards of cassimere, at $2.25 ; 23 pairs of boots, at $3.88; 19 lamps, at $2.37; 28 pounds of sugar, at $0.16. 23. Mrs. Jane Wilcox bought of G. Ferrey 12 rolls of paper, at $0.85; 32 yards of carpet, at $2.32; 15 curtain fixtures, at $0.75; 14 yards of drugget, at $0.87 ; 18 yards of Nottingham lace, at $1.45; 14 yards of oil-cloth, at $1.85. 24. Mr. H. Humphrey bought of D. Thomson 6 bureaus, at $8.75; 3 easy-chairs, at $15.32; 12 dining-room chairs, at $4.67; 15 spring mattresses, at $3.75; 2 extension tables, at $17.85; 4 mirrors, at $9.79. |