SUPPLEMENT TO DIVISION. QUESTIONS. 1. What is division? 2. In what does the process of division consist? 3. Division is the reverse of what? 4. What is the number to be divided called, and to what does it answer in multiplication? 5. What is the number to divide by called, and to what does it answer, &c.? 6. What is the result or answer called, &c.? 7. What is the sign of division, and what does it show? 8. What is the other way of expressing division? 9. What is short division, and how is it performed? 10. How is division proved? 11. How is multiplication proved? 12. What are integers, or whole numbers? 13. What are fractions, or broken numbers? 14. What is a mixed number? 15. When there is any thing left after division, what is it called, and how is it to be written? 16. How are fractions written? 17. What is the upper number called? 18. the lower number? 19. How do you multiply a fraction? 20. To what do the numerator and the denominator of a fraction answer in division? 21. What is long division? 22. Rule? 23. When the divisor is a composite number, how may we proceed? 24. When the divisor is 10, 100, 1000, &c., how may the operation be contracted? 25. When there are ciphers at the right hand of the divisor, how may we proceed? EXERCISES. 1. An army of 1500 men, having plundered a city, took 2625000 dollars; what was each man's share? 2. A certain number of men were concerned in the payment of 18950 dollars, and each man paid 25 dollars; what was the number of men? 3. If 7412 eggs be packed in 34 baskets, how many in a basket? 4. What number must I multiply by 135, that the product may be 505710? 5. Light moves with such amazing rapidity as to pass from the sun to the earth in about the space of 8 minutes. Admitting the distance, as usually computed, to be 95,000,000 miles, at what rate per minute does it travel? 6. If the product of two numbers be 704, and the multiplier be 11, what is the multiplicand? Ans. 64. 7. If the product be 704, and the multiplicand 64, what is the multiplier? Ans. 11. 8. The divisor is 18, and the dividend 144; what is the quotient? 9. The quotient of two numbers is 8, and the dividend 144; what is the divisor? 10. A man wishes to travel 585 miles in 13 days; how far must he travel each day? 11. If a man travels 45 miles a day, in how many days will he travel 585 miles? 12. A man sold 35 cows for 560 dollars; how much was that for each cow? 13. A man, selling his cows for 16 dollars each, received for all 560 dollars; how many did he sell? 14. If 12 inches make a foot, how many feet are there in 364812 inches ? 15. If 364812 inches are 30101 feet, how many inches make one foot? 16. If you would divide 48750 dollars among 50 men, how many dollars would you give to each one? 17. If you distribute 48750 dollars among a number of men in such a manner as to give to each one 975 dollars, how many men receive a share? 18. A man has 17484 pounds of tea in 186 chests; how many pounds in each chest? 19. A man would put up 17484 pounds of tea into chests containing 94 pounds each; how many chests must he have? 20. In a certain town there are 1740 inhabitants, and 12 persons in each house; how many houses are there? are 2 families; how many persons in each family? in each house 21. If 2760 men can dig a certain canal in one day, how many days would it take 46 men to do the same? How many men would it take to do the work in 15 days? in 5 days? in 120 days? days? in 40 days? in 20 22. If a carriage wheel turns round 32370 times in running from New York to Philadelphia, a distance of 95 miles, how many times does it turn in running 1 mile? Ans. 346. 23. Sixty seconds make one minute; how many minutes in 3600 seconds? in 86400 seconds? in 604800 seconds? in 2419200 seconds? 24. Sixty minutes make one hour; how many hours in 1440 minutes.? in 10080 minutes? -in 40320 minutes? 525960 minutes? in 25. Twenty-four hours make a day; how many days in 168 hours? in 8766 hours? in 672 hours? 26. How many times can I subtract forty-eight from four hundred and eighty? 27. How many times 3478 is equal to 47854 ? 28. A bushel of grain is 32 quarts; how many quarts must I dip out of a chest of grain to make one half (4) of a bushel? one fourth (4) of a bushel? 29. How many of 20? for for one eighth (4) of a bushel? Ans. to the last, 4 quarts. of 48? of 204030648? of 247 ? Ans. to the last, 102015324. one third part () of 3 walnuts? of 12? of 30? of 3456320? Ans. to the last, 11521063. 4 of 320 ? of 478? of 20? Ans. to the last, 19604. MISCELLANEOUS QUESTIONS, Involving the principles of the preceding Rules. Note. The preceding rules, viz. Numeration, Addition, Subtraction, Multiplication and Division, are called the Fundamental Rules of Arithmetic, because they are the foundation of all other rules. 1. A man bought a chaise for 218 dollars, and a horse for 142 do lars; what did they both cost? 2. If a horse and chaise cost 360 dollars, and the chaise cost 213 dollars, what is the cost of the horse? If the horse cost 142 dollars what is the cost of the chaise ? 3. If the sum of 2 numbers, be 487, and the greater number be 348 what is the less number? If the less number be 139, what is the greater number? 4. If the minuend be 7842, and the subtrahend 3481, what is the remainder ? If the remainder be 4631, and the minuend be 7842, what is the subtrahend? ¶ 23. When the minuend and the subtrahend are given, how do you find the remainder? When the minuend and remainder are given, how do you find the subtrahend? When the subtrahend and the remainder are given, how do you find the minuend? When you have the sum of two numbers, and one of them given, how do you find the other? When you have the greater of two numbers, and their difference given, how do you find the less number? When you have the less of two numbers, and their difference given, how do you find the greater number? 5. The sum of two numbers is 48, and one of the numbers is 19; what is the other? 6. The greater of two numbers is 29, and their difference 10; what is the less number? 7. The less of two numbers is 19, and their difference is 10; what is the greater? 8. A man bought 5 pieces of cloth, at 44 dollars a piece; 974 pairs of shoes, at 3 dollars a pair; 600 pieces of calico, at 6 dollars a piece; what is the amount? 9. A man sold six cows, worth 15 dollars each, and a yoke of oxen for 67 dollars; in pay, he received a chaise, worth 124 dollars, and the rest in money; how much money did he receive? 10. What will be the cost of 15 pounds of butter, at 13 cents per pound? 11. How many bushels of wheat can you buy for 487 dollars, at 2 dollars per bushel? T24. When the price of one pound, one bushel, &c. of any commodity is given, how do you find the cost of any number of pounds or bushels, &c. of that commodity? If the price of the 1 pound, &c. be in cents, in what will the whole cost be? If in dol lars, what? if in pence? &c. When the cost of any given number of pounds, or bushels, &c., is given, how do you find the price of one pound, or bushel, &c. ? ́In what kind of money will the answer be if in shillings? When the cost of a number of pounds, &c., is given, and also the price of one pound, &c., how do you find the number of pounds, &c.? 12. When rye is 84 cents per bushel, what will be me cost of 948 bushels? how many dollars will it be? 13. If 648 pounds of tea cost 284 dollars, (that is, 28400 cents,) what is the price of one pound? When the factors are given, how do you find the product? When the product and one factor are given, how do you find the other factor? When the divisor and quotient are given, how do you find the dividend? When the dividend and quotient are given, how do you find the divisor? 14. What is the product of 754 and 25? 15. What number, multiplied by 25, will produce 18850? 16. What number, multiplied by 754, will produce 18850? 17. If a man save six cents a day, how many cents would he save in a year, (365 days,)? how many in 45 years? how many dollars would it be? how many cows could he buy with the money, at 12 dollars each? Ans. to the last, 82 cows, and 1 dollar 50 cents remainder. 18. A boy bought a number of apples; he gave away ten of them to his companions, and afterwards bought thirty-four more, and divided one half of what he then had among four companions, who received 8 apples each; how many apples did the boy first buy? Let the pupil take the last number of apples, 8, and reverse the Ans. 40 apples. 19. There is a certain number, to which, if 4 be added, and 7 he subtracted, and the difference be multiplied by 8, and the product divided by 3, the quotient will be 64; what is that number? process. Ans. 27. 20. A chess board has 8 rows of 8 squares each; how many squares on the board? 25. 21. There is a spot of ground 5 rods long, and 3 rods wide; how many square rods does it contain? D A C B Note. A square rod is a square (like one of those in the annexed figure) measuring a rod on each side. By an inspection of the figure, it will be seen that there are as many squares in a row as rods on one side, and that the number of rows is equal to the number of rods on the other side; therefore, 5 X315, the number of squares. Ans. 15 square rods. A figure like A, B, C, D, having its opposite sides equal and parallel, is called a parallelogram or oblong." 22. There is an oblong field, 40 rods long, and 24 rods wide; many square rods does it contain? how 23. How many square inches in a board 12 inches long and 12 inches broad? Ans. 144. 24. How many square feet in a board 14 feet long and 2 feet wide? 25. A certain township is six miles square; how many square miles does it contain? Ans. 36. 26. A man bought a farm for 22464 dollars; he sold one half of it for 12480 dollars, at the rate of 20 dollars per acre; how many acres did he buy? and what did it cost him per acre? 27. A boy bought a sled for 86 cents, and sold it again for 8 quarts of walnuts; he sold one half of the nuts at 12 cents a quart, and gave the rest for a penknife, which he sold for 34 cents; how many cents did he lose by his bargains? 23. In a certain school-house there are 5 rows of desks; in each row are 6 seats, and each seat will accommodate 2 pupils; there are also 2 rows, of 3 seats each, of the same size as the others, and one long seat where 8 pupils may sit; how many scholars will this house accommodate? Ans. 80. 29. How many square feet of boards will it take for the floor of a room 16 feet long, and 15 feet wide, if we allow 12 square feet for waste? 30. There is a room 6 yards long and 5 yards wide; how many yards of carpeting, a yard wide, will be sufficient to cover the flours, if the hearth and fireplace occupy 3 square yards? 31. A board, 14 feet long, contains 28 square feet; what is its breadth? 32. How many pounds of pork, worth 6 cents a pound, can be bought for 144 cents? 33. How many pounds of butter, at 15 cents per pound, must be paid for 25 pounds of tea, at 42 cents per pound' 34. 456+1+8 35. how many? 4310—2—4+6—7—how many? 36. A man divides 30 bushels of potatoes among 3 poor inen; how many bushels does each man receive? What is of thirty? How many are (two thirds) of 30? 37. How many are one third () of 3? of 45674312? 9? 39. 38. How many are two thirds (3) of 3? of 6? of of 45674312? of 124 ? of 246376? of 80? of 100? of 282 ? twelfth part () of a foot; how many feet in 24 inches in 36 inches? 42. If 4 pounds of tea cost 128 cents, what does 1 pound cost? 2 pounds? 100 pounds? 3 pounds? 5 pounds? 43. When oranges are worth 4 cents apiece, how many can be bought for 4 pistareens, (or 20 cent pieces?) 44. The earth, in moving round the sun, travels at the rate of 68000 miles an hour; how many miles does it travel in one day, (24 hours?) how many miles in one year. (365 days?) and how many days would it take a man to travel this last distance at the rate of 40 miles a day? how many years ? Ans. to the last, 40800 years. 45. How much can a man earn in 20 weeks, at 80 cents per day, Sundays excepted? 46. A man married at the age of 23; he lived with his wife 14 years; she then died, leaving him a daughter 12 years of age; 8 years after, the daughter was married to a man 5 years older than |