§ 41. What does division explain? What is the less number called? What is the greater called? What is the answer called? What is the number called which is left?

§ 42. How many signs are there in division? Make them. 43. How many times does any number contain 1 ?

44. When the divisor does not exceed 12, how do you set it down? How do you divide?

§ 45. If there is a remainder after division what do you do with it?

§ 46. When the divisor contains several figures, how do you set it down? How do you divide?

§ 47. How is division proved?

48. How is multiplication proved?

49. How do you divide when the divisor is a composite

number?

§ 50. What do you do with the remainders after division?" § 51. When the divisor is 1, 10, 100, &c. how do you di vide?

§ 52. When there are ciphers on the right of the divisor what do you do?

APPLICATIONS IN DIVISION.

53. The quotient after division shows how ma

ny times the dividend contains the divisor. And if we consider the dividend to be divided into as many equal parts as there are units in the divisor, the quotient will express the value of one of these parts. Ex. 1. Divide 80 dollars equally among four

men.

20 dollars.

Here the 80 dollars is to be divid- 4)80 ed into 4 equal parts, and the quotient 20 dollars expresses the value of one of the equal parts.

2. Four persons buy a lottery ticket: it draws a prize of 10000 dollars. What is each one's share? Ans. 2500 dollars. 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. 65.

5. Wha number must be multiplied by 124 to produce 40796?

Ans. 329.

6. How many times can 24 be subtracted from 1416?

Ans. 59.

7. The sum of 19125 dollars is to be distributed among a certain number of men, each to receive 425 dollars: how many men are to receive the money?

Ans. 45.

8. By the census of 1830 the whole population of the 24 States was 12,840,540: if each one had contained an equal number of inhabitants, how many would there have been in each state? Ans. 5350224.

9. If a man walks 12775 miles in a year, or 365 days, how far does he walk each day?

Ans. 35 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. 11875000.

12. By the census of 1830 it appeared that the City of New York contained 207020 inhabitants; allowing 5 to each house, how many houses were there in the city at that time?

Ans. 41404. 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. 85.

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. 8 dollars. 15. There are 7 days in a week: how many weeks in a year of 365 ?

Ans. 52 and 1 day over. 16. There are 24 hours in a day: how many days in 2040 hours?

Ans. 85.

17. Twenty three persons dined together, their bill was 92 dollars: how much had each one to pay? Ans. 4 dollars.

GENERAL REMARKS.

54. Numeration, Addition, Subtraction, M

plication and Division, are called the five ground rules of Arithmetic.

§ 55. 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.

Ques. 2. When you have two unequal numbers, how do you find their difference?

Ans. By subtracting the less from the greater. Ques. 3. When the subtrahend and remainder are given, or known, how do you find the minuend? Ans. 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.

Ques. 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?

Ans. Multiply the cost of the single thing by the number of things.

Ques. 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?

Ans. Divide the entire cost by the number of things, the quotient will be the cost of a single thing.

APPLICATIONS IN THE PRECEDING RULES.

1. A Farmer sells a yoke of oxen for 90 dollars, ws 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. 396 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. 422.

per

4. A farmer sells 4 tons of hay at 12 dollars ton, 80 bushels of wheat at 1 dollar per bushel, and takes in part payment a horse worth 65 dollars, a waggon 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?

Ans. He loses 26 dollars.

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, what is the divisor?

Ans. 32789.

9. A piece of cloth containing 65 yards cost 455 dollars; what did it cost per yard? Ans. 7 dollars.

10. A man has 6 children, all of whom are married, and each has four children; two of these grandchildren are married, and each has one child. How