9. Two men start from the same place and travel in the same direction, one goes 125 miles, the other 876, how far apart are they? How far if they had travelled in opposite directions?

10. From 7,000,000 subtract 8901 +101.

Ans. 6990998. 11. A man purchased a farm for $ 6890, and having paid $575 for an additional picce of land, he sells the whole for $7500; does he gain or lose, and how much?

12. In a Union school there are four departments; in the first there are 125 scholars, in the second 379, in the third 437, and in the fourth 487; how many scholars does it contain? If 692 are boys, how many are girls?

13. A general started out on a campaign with three regiments of soldiers, the first numbered 1025 men, the second 975, the third 875; after a battle he finds but 2575 in all reported fit for duty; how many men has he lost?

14. How many are 687 +594 +369 -918?

15. In 1850, the population of New York was 515547; that of Philadelphia, 340045; of Baltimore, 169054; and of Boston, 136881. At the same time, the population of London was about 2363241; what was the difference between the population of London and the aggregate population of the four cities named in the United States? Ans. 1201714. 16. A merchant bought some flour for $347, some rye for $236, and some oats for $ 563; he sold the whole for $1275. Did he gain or lose? How much?

17. Mr. Jones gives $2376.43 to his four sons, as follows: to Daniel, $534.68; to James, $354.68; to Thomas, $ 486.39; and the rest to David. What does David receive?

Ans. $1000.68.

MULTIPLICATION.

50. In 1 bushel there are 32 quarts; how many quarts are there in 8 bushels?

1st Method,

BY ADDITION.

32

2d Method,

This example may be solved

BY MULTIPLICATION. by addition, as by the 1st

32

32

32

2d method; thus, 8 times 2 units are 16 units, 1 ten and 6 units; write the 6 units in the place of units, and then say 8 times 3 tens are 24 tens, which, increased by the 1 ten previously obtained, make 25 tens, = 2 hundreds and 5 tens, and when these are written in their proper places we have 256 quarts for the true result. This, when solved by the 2d method, is a question in multiplication.

Sum, 256

51. MULTIPLICATION is a short method of adding equal numbers; or, it is a short method of finding how many units there are in any number of times a given number.

The number repeated is called the MULTIPLICAND; the number showing how many times the multiplicand is taken is the MULTIPLIER; the sum, or result of the multiplication, is the PRODUCT. The Multiplicand and Multiplier are called FAC

TORS.

50. Explain the two methods of solving the above example. Which is best?

51. What is Multiplication? cand?

Another definition.

What is the Multipli. Multiplier? Product? Factors? 52. Repeat the Multiplication

Table.

MENTAL EXERCISES.

1. How many leaves will 7 sheets of paper make if each sheet is folded in 8 leaves? Ans. 56.

2. In how many days can I do as much work as 9 men can do in 5 days?

3. One peck contains 8 quarts; how many quarts are there in 3 pecks?

4. If 9 yards of cloth are required to make 1 garment, how many yards are required to make 8 such garments?

5. How many men can do as much work in 1 day as 6 men can do in 9 days?

Ans. 54. 6. If you solve 9 examples each hour, how many examples will you solve in 9 hours?

7. When flour is worth $10 per barrel, how much must be paid for 7 barrels?

8. If 12 inches make 1 foot, how many inches are there in 3 feet?

Ans. 36.

9. In 1 year there are 12 months; how many months are there in 2 years? 4 years? 3 years? 7 years? 5 years? 8 years?

10. If I deposit $10 a month in a savings bank, how much shall I deposit in 5 months? In 4 months? In 8 months? In 9 months?

53. The sign of multiplication, X, signifies that the two numbers between which it stands are to be multiplied together; thus, 6 x 530; that is, six multiplied by five equals thirty, or six times five are thirty.

Ex. 11. How many are 7 × 4?

Ans. 28.

53. Make the sign of multiplication on the black-board. What does it signify?