REVIEW.

1. If 37 trees yield 13 bushels of apples each, and 41 others yield 11 bushels each, how many bushels do they

They all yield as many bushels as 37 times 13

bushels, and 41 times 11 bushels.

37 times 13 bushels are 481 bushels, and 41 times 11 bushels are 451 bushels; and 481 bushels and 451 bushels are 932 bushels. Therefore, they all yield 932 bushels.

2. Bought 713 tons of coal for 2852 dollars, and sold it at 6 dollars a ton; how much was gained by the operation? Ans. 1426 dollars.

3. Sold 325 barrels of apples at 3 dollars a barrel, and received 650 dollars in cash, and a note for the balance. For what sum was the note?

4. A farmer bought 32 sheep at 6 dollars each, 31 cows at 45 dollars each, and 3 horses at 162 dollars each. He sold the whole for 2500 dollars; how much did he gain? Ans. 427 dollars.

5. A merchant bought 7 rolls of carpeting, each containing 27 yards, and 4 rolls each containing 18 yards. How many yards did he buy in all? Ans. 261 yards.

6. If a man earn 950 dollars a year, and his expenses are 2 dollars a day, how much can he save in a year, or 365 days?

7. Jones and Smith start from the same place and travel in opposite directions, Jones at the rate of 32 miles a day, and Smith at the rate of 34 miles a day. How far apart will they be at the end of 6 days? Ans. 396 miles.

REVIEW. - What is the larger of the two given numbers called in Subtraction? Ans. The Minuend. In Multiplication, what is the result called? (49.)

8. Arthur has 135 dollars and his brother has 4 times as much, lacking 15 dollars; how much has his brother? Ans. 525 dollars.

9. Bought a dictionary for 6 dollars, a set of histories. for 22 dollars, and a select library for 137 dollars; and gave in payment a check for 63 dollars, and three 50-dollar bills. How much should be received back? Ans. 48 dollars.

10. Bought one farm of 63 acres at 105 dollars per acre, and another of 240 acres at 95 dollars per acre. What did both farms cost me?

11. Bought 31 parlor organs at 145 dollars each; and gave in payment 21 United States bonds at 111 dollars each, four 500-dollar bills, and my note for the balance. For what sum did I give my note? Ans. 164 dollars.

12. Sold 560 tons of coal at 9 dollars a ton, and received in payment 875 bushels of wheat at 2 dollars per bushel, and the balance in money. How much money did

I receive?

13. A merchant had in a bank 8000 dollars, drew out 7563 dollars, and afterwards put in 1550 dollars; how much had he then in the bank? Ans. 1987 dollars.

14. Two steamers start at the same time to meet each other, the one from Boston and the other from Liverpool, which places are 2883 miles apart. Provided that one sails at the rate of 192 miles a day, and the other at the rate of 168 miles a day, how many miles will they be from each other at the end of 5 days? Ans. 1083 miles.

REVIEW.

What is Multiplication? (49.) The Product? (49.) The Multiplicand? (49.) The Multiplier? (49.)

DIVISION.

55. 1. At 2 cents each, how many apples can be bought for 8 cents?

2. How many times 2 cents are there in 8 cents?

3. How many times 2 cents are 8 cents?

4. If 9 marbles be divided equally among 3 boys, how many marbles will each boy have?

5. Into how many equal parts of 3 marbles each, can 9 marbles be separated?

6. How many times 3 marbles are 9 marbles?

7. What is one of the 3 equal parts of 9 marbles?

8. What is one of the 4 equal parts of 8 cents?

9. If 4 barrels be a dray load, how many dray loads will be 12 barrels ?

10. How many times 4 barrels are 12 barrels ? 11. How many times 3 barrels are 12 barrels ? 12. How many times 4 in 12? 3 in 12?

REVIEW. How do you prove Addition? (42.) How do you prove Subtraction? (47.) How do you prove Multiplication? (53.)

56. One of two equal parts of a number is called one half. Thus, one half of two is one.

One of three equal parts of a number is called one third. Thus, one third of six is two.

One of four equal parts of a number is called one fourth. Thus, one fourth of four is one.

In like manner, one of the five equal parts of a number is called one fifth; one of the six equal parts is called one sixth; one of the ten equal parts is called one tenth, etc. Hence,

57.

A Whole Number has two halves, three thirds, four fourths, five fifths, ten tenths, etc.

58. One or more equal parts of a unit are called Fractions, to distinguish them from unbroken or whole numbers, which are called Integers, or Integral Numbers.

59. Division is the process of finding how many times one number is contained in another; or of finding one of the equal parts of a number.

The DIVIDEND is the number to be divided.

The DIVISOR is the number by which we divide.

The QUOTIENT is the result or number obtained by the division.

60. The REMAINDER is that part of the dividend which is left after finding the exact whole number of the quotient.

Thus,

3 is contained in 7, 2 times and 1 remainder. The division of this 1, indicated, gives, which, written after

What is one of the two equal parts of a number called? One of three equal parts? One of four equal parts? One of five? One of six? What is Division? What is the Dividend? The Divisor? The Quotient? The Remainder?

the whole number of the quotient, makes the complete quotient 23, which is read two and one-third.

61. The Sign of Division is a short horizontal line with a dot above and below it,, or a curved line,), and is read, divided by. Thus,

62 is read, 6 divided by 2; and 2)6 is read, 6 divided by 2, or 2 in 6.

What is the Sign of Division? Recite the column 1 in 1. 2 in 2. 3 in 3. 4 in 4. 5 in 5. 6 in 6. 7 in 7. 8 in 8. 9 in 9. 10