9 Mahogany chairs, each 5 dollars. 5 French bedsteads, each 7 dollars.

Ans. 480 dollars.

7. If the railroad extending between Albany and Buffalo, a distance of 326 miles, cost 25649 dollars per mile, what was the entire cost? Ans. 8361574 dollars. 8. How many bushels of potatoes may be produced from 13 acres of land, if each acre produces 212 bushels? Ans. 2756 bushels.

9. How much must be paid for constructing 18 miles of plank-road, at 4211 dollars per mile? Ans. 75798 dollars. 10. How much will 543 cords of wood cost, at 5 dollars per cord ? Ans. 2715 dollars.

11. In one year there are 8766 hours, how many hours in 1848 years? Ans. 16199568 hours.

12. In one cubic foot there are 1728 cubic inches, how many cubic inches in 17 cords of wood, each cord containing 128 cubic feet? Ans. 3760128 cubic inches. 13. What will 13 square miles of land cost, at 17 dollars per acre, there being 640 acres in one mile?

Ans. 141440 dollars.

14. How many miles will a steam locomotive pass in 7 days of 24 hours each, if it move at the rate of 45 miles each hour? Ans. 7560 miles.

15. If the earth move in its orbit 68000 miles per hour, how far will it move in 365 days of 24 hours each?

Ans. 595680000 miles.

16. If one mile of railroad require 116 tons of iron, worth 53 dollars per ton, what will be the cost of sufficient iron to construct a road of 78 miles in length?

Ans. 479544 dollars.

17. In an orchard of 105 apple trees the average pro

50

duce of each tree is 7 barrels of fruit, worth 3 dollars per barrel. What was the income of the orchard?

Ans. 2205 dollars.

DIVISION OF SIMPLE NUMBERS.

22. DIVISION teaches the method of finding how many times one number is contained in another.

The number to be divided is called the dividend.

The number by which we divide is called the divisor. The number of times which the dividend contains the divisor is called the quotient.

Besides these three parts there is sometimes a remainder, which is of the same name as the dividend, since it is a part of it.

The sign usually employed to indicate division is Thus, 12÷ 3, denotes that 12 is to be divided by 3. By using this sign we may form the following

23. Division may also be represented by placing the divisor under the dividend, with a short horizontal line between them; thus, 10 denotes that 10 is to be divided by 2. In the same way we have

2122;

13-3; 7-17-5; 2-53-7.

This method is employed, when in division there is a remainder, to express accurately the value of the quotient.

What does division teach? What is the number to be divided called? What is the number by which we divide called? What is the number of times which the dividend contains the divisor called? There is sometimes another part, what is it? Of what name is the remainder? What is the symbol of division? By what other method is division denoted?

When the divisor consists of only one figure, we proceed as follows:

Divide 973 by 7.

Having placed the divisor at the left of the dividend, keeping them separate by means of a curved line, we draw a straight horizontal line underneath.

OPERATION.

7)973

139 quotient.

We then say, 7 is contained in 9, 1 time and 2 remainder; we write the 1 underneath. As the 9 occupies the hundreds' place, the 2 remainder must be 2 hundreds. The next figure, 7, to be divided, is tens, to which we add the 2 hundreds, or 20 tens, making 27 tens; which result is obtained by prefixing the 2 to the 7. Next, we see how many times 7 is contained in 27, which is 3 times and 6 remainder; we place the 3 for the next figure of the quotient, and conceive the 6 to be prefixed to the next figure of the dividend, making 63; which is the same as adding 6 tens or 60 units to the 3 units. Finally, we find 7 is contained in 63, 9 times.

Thus 7 is contained 139 times in 973. Hence, 139 repeated 7 times must equal 973.

24. Suppose we wish to know how many times 8 is contained in 32. We might proceed as follows: since 32 is greater than 8, we know that 8 is contained in it, at least once; therefore, subtracting 8 from 32, we find 24 for a remainder. Again, we know that 8 is contained at least once in 24; therefore, subtracting 8 from 24, we have 16, from which, subtracting 8, we have left 8; finally, from 8 subtracting 8, we have no remainder. Hence, we perceive that 8 has been subtracted 4 times from 32, that is, 8 is contained just four times in 32. It is obvious that by continued subtractions any operation in division may be performed.

For this reason division is said to be a concise way of performing several subtractions.

CASE I.

25. Short Division is the method of operation when the divisor consists of only one figure.

From the preceding operation we infer the following

RULE.

1. Place the divisor at the left of the dividend, keeping them separate by a curved line, and draw a straight line underneath the dividend.

II. Seek how many times the divisor is contained in the left-hand figure or figures of the dividend, and place the result directly beneath, for the first figure of the quotient.

III. If there is no remainder, divide the next figure of the dividend for the next figure of the quotient. But when there is a remainder, conceive it to be prefixed to the next succeeding figure of the dividend before making the next division. If a figure of the dividend, which is required to be divided, is less than the divisor, we must write 0 in the quotient, and consider that figure as a remainder.

Division is said to be a concise way of performing what? What is Short Division ? Repeat the rule.

EXAMPLES.

1. Divide 2345675 by 8.

OPERATION.

Divisor 8)2345675 dividend.

Quotient 293209 with 3 remainder.

26. When there is a remainder, we may place it over the divisor, with a short horizontal line between them, thus