Each man's share will be equal to the number of tens contained in the whole sum, and, if one of the figures be cut off at the right hand, all the figures to the left may be considered so many tens; therefore, each man's share will be 247 dollars. It is evident, also, that if 2 figures had been cut off from the right, all the remaining figures would have been so many hundreds; if 3 figures, so many thousands, &c. Hence we derive this general RULE for dividing by 10, 100, 1000, &c. Cut off from the right of the dividend so many figures as there are ciphers in the divisor; the figures to the left of the point will express the quotient, and those to the right, the remaindler. 2. In one dollar are 100 cents; how many dollars in 42400 Ans. 424 dollars. cents? 424100 Here the divisor is 100; we therefore cut off 2 figures on the right hand, and all the figures to the left (424) express the dollars. 3. How many dollars in 34567 cents? Ans. 345 dollars. 4. How many dollars in 4567840 cents? 5. How many dollars in 345600 cents? 6. How many dollars in 42604 cents? Ans. 426. 7. 1000 mills make one dollar; how many dollars in 4000 mills? in 25000 mills? in 845000? 8. How many dollars in 6487 mills? Ans. 648 9. How many dollars in 42863 mills? in 96842378 mills? 10. In one cent are 10 mills; mills? mills? in 400 mills? in 4784 mills? mills? dollars. in 368456 how many cents in 40 in 20 mills? in 34640 mills? in 468 III. When there are CIPHERS on the right hand of the divisor. 22. 1. Divide 480 dollars among 40 men? OPERATION. 4|0)48|0 In this example, our divisor, (40,) is a composite number, (10 × 4 = 40;) we may, therefore, divide by one component part, (10,) and that quotient by the other, (4;) but to divide by 10, we have seen, is but to cut off the right hand figure, leaving the figures to the left 12 dolls. Ans. of the point for the quotient, which we divide by 4, and the work is done. It is evident, that, if our divisor had been 400, we should have cut off 2 figures, and have divided in the same manner; if 4000, 3 figures, &c. Hence this general RULE:- When there are ciphers at the right hand of the di visor, cut them off, and also as many places in the dividend; divide the remaining figures in the dividend by the remaining figures in the divisor; then annex the figures, eut off from the dividend, to the remainder. 4. How many yards of cloth can be bought for 346500 dollars, at 20 dollars per yard? 5. Divide 76428400 by 900000. 6. Divide 345006000 by 84000. 7. Divide 4680000 by 20, 200, 2000, 20000, 300, 4000, 30, 600, 70000, and 80. 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 divi sion, and what does it show? 8. What is the other way of expressing division? 9. What is short division, and how is E 4 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 ic 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 30401 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 ?---in each house are 2 families; how many persons in each family? 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 20 days? in 40 days? in 120 days? 22. If a carriage wheel turns round 32870 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 in 2419200 seconds? seconds? 24. Sixty minutes make one hour; how many hours in 1440 minutes? in 10080 minutes? in 40320 25. Twenty-four hours make a day; how many days in 168 hours? in 672 hours? in 8766 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 (₹) of a bushel? for one fourth (†) of a bushel? eighth (1) of a bushel? for one Ans. to the last, 4 quarts. 29. How many is of 20? 2477 of 345578? of 48? of 204030648? Ans. to the last, 102015324, many walnuts are one third part (3) of 3 walof 6 walnuts ? 30. How nuts? of 12? of 30? 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 foun dation of all other rules. 1. A man bought a chaise for 218 dollars, and a horse for 142 dollars; what did they both cost? 2. If a horse and chaise cost 360 dollars, and the chaise cost 218 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 4361, 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 differ ence given, how do you find the greater number? |