4. In January, 1903, a merchant bought goods to the amount of $2675; in February, $4375; and in March, $1897. After making one payment of $3000, and another of $4947, how much did he still owe? $1000.

5. Mr. Jones deposited in a bank on Monday $450; on Tuesday, $725; on Wednesday, $1235; on Thursday, $4675; and on Friday, $1727. On Saturday morning he drew out $5935, and Saturday afternoon, $877. How much money had he left in bank? $2000.

6. At the end of one year I found I had spent $2300. Of this amount, $350 was paid for board, $125 for clothing, $375 for books, $150 for incidentals, and the remainder for two acres of ground. How much did the two acres cost? $1300.

For the first he

7. A speculator bought three houses. paid $4875; for the second, $2250 more than for the first; and for the third, $3725. He afterward sold them all for $20,838. How much did he gain? $5113.

8. A man owns property valued at $49570, of which $16785 are in personal property, and $24937 in real estate; the remainder is deposited in bank. How much has he in bank? $7848.

9. A merchant bought a bill of goods for $7895, and paid $175 for freight, and $3 for cartage. He sold the goods for $10093. How much did he gain? $2020.

10. The following is Mr. Brown's private account for two weeks: First week, received $50 for salary, and spent $25 for clothing, $8 for board, $1 for washing, and $5 for sundries. Second week, received $50 for salary, loaned $35 to Tom Jones, paid $8 for board, $1 for washing, and $8 for sundries. How much did Mr. Brown have at the end of the two weeks? $9.

57. The minuend is 15649, which is 2408 more than the subtrahend. What is the subtrahend?

13241.

58. In 1900 the population of New York City was 3437202, and that of Chicago 1698575. How many more people were there in New York than in Chicago?

1738627.

59. How far apart are two cities, one of which is 2346 miles from Boston, and the other 4335 miles in the same direction from Boston? 1989 mi.

60. A man invested $30000 in business; at the end of the first year all his assets amounted to only $26967. How much had he lost?

$3033.

61. Mr. Beard has $297420 less than Mr. Hall, who has 456721. How much has Mr. Beard? $159301.

62. If I borrow $32450 and pay back $19275, how much do I still owe? $13175. 63. The sum of two numbers is 619346, and the greater is 452020. What is the less?

167326.

64. The 250th anniversary of the founding of a society was celebrated in 1903. When was the society founded? 1653.

65. Previous to a fire the contents of a store was valued at $25690; after the fire at $18040. How much was lost by the fire?

Examples in Addition and Subtraction

$7650.

3. I owe three notes, whose sum is $1300, one note being for $250, and another for $650. What is the amount of the third note?

$400.

4. In January, 1903, a merchant bought goods to the amount of $2675; in February, $4375; and in March, $1897. After making one payment of $3000, and another of $4947, how much did he still owe? $1000.

5. Mr. Jones deposited in a bank on Monday $450; on Tuesday, $725; on Wednesday, $1235; on Thursday, $4675; and on Friday, $1727. On Saturday morning he drew out $5935, and Saturday afternoon, $877. How much money had he left in bank? $2000.

6. At the end of one year I found I had spent $2300. Of this amount, $350 was paid for board, $125 for clothing, $375 for books, $150 for incidentals, and the remainder for two acres of ground. How much did the two acres cost? $1300.

7. A speculator bought three houses. For the first he paid $4875; for the second, $2250 more than for the first; and for the third, $3725. He afterward sold them all for $20,838. How much did he gain? $5113.

8. A man owns property valued at $49570, of which $16785 are in personal property, and $24937 in real estate; the remainder is deposited in bank. How much has he in bank? $7848.

9. A merchant bought a bill of goods for $7895, and paid $175 for freight, and $3 for cartage. He sold the goods for $10093. How much did he gain? $2020.

10. The following is Mr. Brown's private account for two weeks: First week, received $50 for salary, and spent $25 for clothing, $8 for board, $1 for washing, and $5 for sundries. Second week, received $50 for salary, loaned $35 to Tom Jones, paid $8 for board, $1 for washing, and $8 for sundries. How much did Mr. Brown have at the end of the two weeks? $9.

11. A farmer invested $10000, as follows: in land, $5750; in horses, $925; in cattle, $1575; in hogs, $675; and the remainder in implements and tools. How much did he invest in implements and tools? $1075.

12. A speculator on Monday gained $4625; on Tuesday, $3785; on Wednesday he lost $6955; on Thursday he lost $895; on Friday he gained $985; and on Saturday he lost $1375. How much did he gain during the entire week? $170.

13. A farmer raised 2040 bushels of rye and 1059 bushels of wheat. After selling 1050 bushels of rye and 985 bushels of wheat, how many bushels of both together had he left? 1064 bu.

14. There are 21360 newspapers printed in the United States and Canada, 8000 in Great Britain, 6000 in Germany, and 4300 in France. How many more are printed in the United States and Canada than in Great Britain, Germany, and France together? 3060.

15. If 111100000 people in the world speak English, 51200000 French, and 42800000 Spanish, how many more people speak English than French and Spanish together? 17100000.

16. The area of North America is 9363235 square miles; of South America, 6887794 square miles; of Europe, 3857504 square miles. How much greater is the area of North and South America together than that of Europe? 12393525 sq. mi.

17. Congress voted $200000 for the relief of the victims of the volcanic eruption in the island of Martinique. If $110075 were spent for food and $46025 for clothing, how much remained for other expenses?

$43900.

MULTIPLICATION

27. 1. If one orange costs 2 cents, how much will 3 oranges cost?

SOLUTION. Three oranges will cost 3 times as much as one orange; that is, 2 cents taken 3 times: 2+2 + 2 = 6.

2. If one lemon costs 3 cents, how many cents will 4 lemons cost? Ans. 3+3 +3 + 3 = 12.

3. At 4 cents apiece, how much will 6 pencils cost? Ans. 4+4+4+4+4+ 4 = 24.

4. In an orchard there are 4 rows of trees, and in each row, 21 trees. How many trees are there in the orchard?

SOLUTION. 1. By writing 21 four times, as in the margin, and adding, the whole number of trees is 84.

2. Instead of writing 21 four times, write it once, place the number 4 underneath, to indicate the number of times 21 is to be taken, and say, 4 times 1 are 4, which put in units' place; then, 4 times 2 are 8, which put in tens' place; the result is 84, the same as found by addition.

1st row, 21 trees.

2d row, 21 trees. 3d row, 21 trees. 4th row, 21 trees.

84

OPERATION.

21

4

84

The latter method of obtaining the result is called multiplication. Therefore,

Multiplication is a short method of performing many additions of the same number.

28. Multiplication is the process of taking one number as many times as there are units in another.