EXAMPLES IN THE PRECEDING RULES. 1. George Washington was born in 1732, and lived 67 years; in what year did he die? Ans. in 1799. 2. How many dollars a day must a man spend, to use an income of 1095 dollars a year? Ans. 3 dollars. 3. If I give 141 dollars for a piece of cloth containing 47 yirds, for how much must I sell it in order to gain one dollar yard? Ans. 188 dollars. 4. A speculator who owned 500 acres, 17 acres, 98 acres, and 121 acres of land, sold 325 acres; how many acres had he left? Ans. 411 acres. 5. A dealer sold a cargo of salt for 2300 dollars, and gained 625 dollars; what did the cargo cost him? Ans. 1675 dollars. 6. If a man earn 60 dollars a month, and spend 45 dol lars in the same time, how long will it take him to save 900 dollars from his earnings? 7. If 9 persons use a barrel of flour in 87 days, how many days will a barrel last 1 person at the same rate? Ans. 783 days. 8. The first of three numbers is 4, the second is 8 times the first, and the third is 9 times the second; what is their sum? Ans. 324. 9. If 2, 2, and 7 are three factors of 364, what is the other factor? Ans. 13. 10. A man has 3 farms; the first contains 78 acres, the second 104 acres, and the third as many acres as both the others; how many acres in the 3 farms? 11. If the expenses of a boy at school are 90 dollars for board, 30 dollars for clothes, 12 dollars for tuition, 5 dollars for books, and 7 dollars for pocket money, what would be the expenses of 27 boys at the same rate? Ans. 3888 dollars. 12. Four children inherited 2250 dollars each; but one dying, the remaining three inherited the whole; what was the share of each? Ans. 3000 dollars. 13. Two men travel in opposite directions, one at the rate of 35 miles a day, and the other at the rate of 40 miles a day; how far apart are they at the end of 6 days? 14. Two men travel in the same direction, one at the rate of 35 miles a day, and the other at the rate of 40 miles a day; how far apart are they at the end of 6 days? 15. A man was 45 years old, and he had been married 19 years; how old was he when married? Ans. 26 years. 16. Upon how many acres of ground can the entire population of the globe stand, supposing that 25000 persons can stand upon one acre, and that the population is 1000000000? Ans. 40000 acres. 17. Add 384, 1562, 25, and 946; subtract 2723 from the sum; divide the remainder by 97; and multiply the quotient by 142; what is the result? Ans. 284. 18. How many steps of 3 feet each would a man take in walking a mile, or 5280 feet? Ans. 1760 steps. 19. A man purchased a house for 2375 dollars, and ex、 pended 340 dollars in repairs; he then sold it for railroad stock worth 867 dollars, and 235 acres of western land valued at 8 dollars an acre; how much did he gain by the trade? Ans. 32 dollars. 20. The salary of a clergyman is 800 dollars a year, and his yearly expenses are 450 dollars; if he be worth 1350 dollars now, in how many years will he be worth 4500 dollars? Ans. 9 years. 21. How many bushels of oats at 40 cents a bushel, must be given for 1600 bushels of wheat at 75 cents a bushel? Ars. 3000 bushels. 22. Bought 325 loads of wheat, each load containing 50 bushels, at 2 dollars a bushel; what did the wheat cost? 23. If you deposit 225 cents each week in a savings bank, and take out 75 cents a week, how many cents will you have left at the end of the year? Ans. 7800 cents. 24. The product of two numbers is 31383450, and one of the numbers is 4050; what is the other number? 25. The Illinois Central Railroad is 700 miles long, and cost 31647000 dollars; what did it cost per mile? Ans. 4510 dollars. 20. What number is that, which being divided by 7, the quotient multiplied by 3, the product divided by 5, and this quotient increased by 40, the sum will be 100? Ans. 700. 27. How many cows at 27 dollars apiece, must be given for 54 tons of bay at 17 dollars & on? 28. A mechanic receives 5 dollars for 26 days' work, and spends 2 dollars a day for the whole time; how many dollars has he left? Ans. 4 dollars. 29. If 7 men can build a house in 98 days, how long would it take one man to build it? Ans. 686 days. 30. The number of school houses in the State of New York, in 1855, was 11,137; suppose their cash value to have been 5,301,212 dollars, what would be the average value? Ans. 476 dollars. 31. A cistern whose capacity is 840 gallons has two pipes; through one pipe 60 gallons run into it in an hour, and through the other 39 gallons run out in the same time; in how many hours will the cistern be filled? Ans. 40 hours. 32. The average beat of the pulse of a man at middle age is about 4500 times in an hour; how many times does it beat in 24 hours? Ans. 108000 times. 33. How many years from the discovery of America, in 1492, to the year 1900? 34. According to the census, Maine has 31766 square miles; New Hampshire, 9280: Vermont, 10212; Massachusetts, 7800; Rhode Island, 1306; Connecticut, 4674; and New York, 47000; how many more square miles has all New England than New York? 35. What is the remainder after dividing 62530000 by 87900? Ans. 33100. 36. A pound of cotton has been spun into a thread 8 miles in length; allowing 235 pounds for waste, how many pounds will it take to spin a thread to reach round the earth, supposing the distance to be 25000 miles? Ans. 3360 pounds. 37. John has 8546 dollars, which is 342 dollars less than 4 times as much as Charles has; how many dollars has Charles? Ans. 2222 dollars. 38. The quotient of one number divided by another is 37, the divisor 245, and the remainder 230; what is the dividend? Ans. 9295. 39. What number multiplied by 72084 will produce 5190048 ? Ans. 72. 40. There are two numbers, the greater of which is 73 times 109, and their difference is 17 times 28; what is the less number? Ans. 7481. 41. The sum of two numbers is 360, and the less is 114; what is the product of the two numbers? Ans. 28044. 42. What number added to 2473248 makes 2568754? Ans. 95506. 43. A farmer sold 35 bushels of wheat at 2 dollars a bushel, and 18 cords of wood at 3 dollars a cord; he received 9 yards of cloth at 4 dollars a yard, and the balance in money; Ans. 88 dollars. how dollars did he receive? many 44. A farmer receives 684 dollars a year for produce from his farm, and his expenses are 375 dollars a year; many dollars will he save in five years! ? how 45. The salt manufacturer at Syracuse pays 58 cents for wood to boil one barrel of salt, 10 cents for boiling, 5 cents to the state for the brine, 28 cents for the packing barrel, and 3 cents for packing and weighing, and receives 125 cents from the purchaser; how many cents does he make on a barrel? Ans. 21 cents. 46. A company of 15 persons purchase a township of western land for 286000 dollars, of which sum one man pays 6000 dollars, and the others the remainder, in equal amounts; how much does each of the others pay? Ans. 20000 dollars. 47. If 256 be multiplied by 25, the product diminished by 625, and the remainder divided by 35, what will be the quoAns. 165. tient? 48. Two men start from different places, distant 189 miles, and travel toward each other; one goes 4 miles, and the other 5 miles an hour; in how many hours will they meet? GENERAL PRINCIPLES OF DIVISION. 86. The quotient in Division depends upon the relative values of the dividend and divisor. Hence any change in the value of either dividend or divisor must produce a change in the value of the quotient. But some changes may be produced upon both dividend and divisor, at the same time, that will not affect the quotient. The laws which govern these changes are called General Principles of Division, which we will now examine. I. 5496. If we multiply the dividend by 3, we have. ? 54 X 39162918, and 18 equals the quotient, 6, multiplied by 3. Hence, Multiplying the dividend by any number, multiplies the quotient by the same number. II. Using the same example, 5496. 591892, and 2 the quotient, 6, divided by 3. Hence, Dividing the dividend by any number, divides the quotient by the same number. III. If we multiply the divisor by 3, we have 549X354272, and 2 the quotient, 6, divided by 3. Hence, Multiplying the divisor by any number, divides the quotient by the same number. IV. If we divide the divisor by 3, we have Upon what does the value of the quotient depend? What is the first general principle of division? Second? Third Fourth? |