DEMONSTRATION OF THE RULE. The number 700=100×7. Hence it is a composite number of which the factors are 100 and 7. In striking off the two figures 89, from the right of the dividend, we divide it by 100; we then divide the 673 by the other factor 7. We then multiply the remainder 1 by 100 and add 89 to the product, giving 189 for the true remainder, (see § 37.) 2. Divide 8749632 by 37000. 37/000)87491632(236 Q. How do you divide by 10, 100, 1000, &c.? (see § 38.) Which part is the quotient? Which part is the remainder? When there are ciphers on the right of the divisor, how do you form the true remainder? APPLICATIONS IN DIVISION. OPERATION. 1. Divide 80 dollars equally among four men. Here the 80 dollars is to be divided into 4 equal parts, and the quotient 20 dollars expresses the value of one of the equal parts. 4)80 20 dollars. 2. Four persons buy a lottery ticket; it draws a prize of 10000 dollars: what is each one's share? 3. A person dying leaves an estate of 4500 dollars to be divided equally among 5 children: what is each one's share? Ans. 900 dollars. 4. There are 1560 eggs to be packed in 24 baskets: how many eggs will be put in each basket? Ans. 5. What number must be multiplied by 124 to produce 40796? Ans. 329. 6. How many times can 24 be subtracted from 1416? Ans. 7. The sum of 19125 dollars is to be distributed among a certain number of men, each is to receive 425 dollars : how many men are to receive the money? Ans. 8. By the census of 1840 the whole population of the 26 States was 16,890,320: if each one had contained an equal number of inhabitants, how many would there have been in each state? Ans. 649,62718. 9. If a man walks 12775 miles in a year, or 365 days, how far does he walk each day? Ans. miles. 10. A farmer sells a drove of sheep for 2 dollars a head, and receives 1250 dollars: how many sheep did he sell? Ans. 625. 11. It is computed that the distance to the sun is 95,000,000 of miles, and that light is 8 minutes travelling from the sun to the earth: how many miles does it travel per minute? Ans. 12. By the census of 1840 it appeared that the City of New York contained 312710 inhabitants; allowing 5 to each house, how many houses were there in the city at that time? Ans. 62,542. 13. A merchant has 5100 pounds of tea, and wishes to 'pack it in 60 chests: how many pounds must he put in each chest? Ans. 14. A person goes to a store and buys a piece of cloth containing 36 yards, for which he pays 288 dollars: how much does he pay per yard? Ans. dollars. 15. There are 7 days in a week: how many weeks in Ans. 52 weeks and 1 day over. 16. There are 24 hours in a day: how many days in 2040 hours? Ans. days. 17. Twenty-three persons dined together, their bill was 92 dollars: how much had each one to pay? a year of 365 ? Ans. 4 dollars. GENERAL REMARKS. § 40. Numeration, Addition, Subtraction, Multiplication, and Division, are called the five ground rules of Arithmetic. Q. How many principal rules are their in Arithmetic? What are hey? Can Multiplication be performed by Addition? Can Division be performed by Subtraction? By how many rules, then, may all the operations in Arithmetic be performed? § 41. The preceding rules furnish answers to the following questions. Ques. 1. When the cost of each one of several things is given, how do you find their entire cost? Ans. Add the costs of the several things together, the sum will be the entire cost. What is the entire cost of a bag of coffee at 6 dollars, a chest of tea at 4 dollars, a box of raisins at 2 dollars, and a barrel of sugar at 12 dollars? Ans. 24 dollars. Q. 2. When you have two unequal numbers, how do you find their difference ? A. By subtracting the less from the greater. Q. 3. When the subtrahend and remainder are given, or known, how do you find the minuend? A. By adding the remainder and subtrahend together. Hence the following principles. 1st. If the sum of two numbers be diminished by one of them, the remainder will be the other number. 2d. The less of two numbers added to their difference, will give the greater. The sum of two numbers is 56, one of the numbers is 12: what is the other? Ans. 44. The less of two numbers is 25, and their difference 30: what is the greater? Ans. The less of two numbers is 35, and their difference 35: what is the greater? Ans. 70. Q. 4. When you have the cost of a single thing, how will you find the entire cost of any number of things at the same rate? A. Multiply the cost of the single thing by the number of things. What is the cost of 35 pears at 2 cents each? What is the cost of 45 yards of cloth at 3 dollars per yard? Q. 5. When you know the number of things, and their entire cost, how do you find the cost of a single thing of the same kind? A. Divide the entire cost by the number of things, the quotient will be the cost of a single thing. If 60 oranges cost 360 cents, how much do they cost apiece? If 40 yards of cloth cost 200 dollars, how much is it a yard? APPLICATIONS IN THE PRECEDING RULES. 1. A Farmer sells a yoke of oxen for 90 dollars, 3 cows for 25 dollars each, 9 calves for 4 dollars each, and 65 sheep at 3 dollars a head. How much did he receive for them all? Ans. dollars. 2. The sum of two numbers is 365, one of the numbers is 221; what is the other number? Ans. 144. 3. The difference of two numbers is 95, the less number is 327; what is the greater number? Ans. 4. A farmer sells 4 tons of hay at 12 dollars per ton, 80 bushels of wheat at 1 dollar per bushel, and takes in part payment a horse worth 65 dollars, a wagon worth 40 dollars, and the rest in cash. How much money did he receive? Ans. 23 dollars. 5. A farmer has 14 calves worth 4 dollars each, 40 sheep worth 3 dollars each; he gives them all for a horse worth 150 dollars: does he make or lose by the bargain? 6. The product of two numbers is 51679680, and one of the factors is 615: what is the other factor? Ans. 84032. 7. When the divisor is 67941, and the quotient 30620, what is the dividend? Ans. 2080353420. 8. When the dividend is 1213193, the quotient 37, is the divisor? Ans. what 9. A piece of cloth containing 65 yards costs 455 dollars what does it cost per yard? : Ans. dollars. 10. A man has 6 children, all of whom are married, and each has four children; two of these grand-children are married, and each has one child: how many children, grand-children, and great grand-children are there? Ans. 11. The distance around the earth is computed to be about 25000 miles: how long would it take a man to travel it, supposing him to travel at the rate of 35 miles a day? Ans. 71438 days. 12. The earth moves around the sun at the rate of 68000 miles an hour: how many miles does it travel in a day, and how many in a year? 1632000 in a day. Ans. 595680000 in a year. 13. A farmer purchased a farm for which he paid 18050 dollars. He sold 50 acres for 60 dollars an acre, and the remainder stood him in 50 dollars per acre: how much land did he purchase? Ans. 351 acres. OF FRACTIONS. § 42. The unit 1 represents an entire thing; as 1 apple, 1 chair, 1 pound of tea. If we suppose 1 thing, as one apple, or one pound of tea, to be divided into two equal parts, each part is called one half of the thing. If the unit be divided into 3 equal parts, each part is called one third. If the unit be divided into 4 equal parts, each part is called one fourth. If the unit be divided into 12 equal parts, each part is called one twelfth; and when it is divided into any number of equal parts, we have a similar expression for each of the parts. The equal parts of a thing are expressed thus: is read one half. |