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19. In a garden are 57 fruit trees; 15 of them are peach trees, 12 plum trees, and the remainder pear trees. How many pear trees are there?

What is the difference between

20. 17 and 4+6? | 23. 20 and 6+6?

26.

125 and 25+3?

21. 24 and 9+5? 24. 35 and 9+20? 27.

27-8 and 14+8? 22. 18 and 7+7? 25. 28 and 9+9? 28. 30-10 and 9+8?

Find the omitted terms in the following equations:

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45. To find the difference between two like numbers.

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Since 6 units cannot be taken from 3 units, increase the 3 units by 10 units (1 ten) taken from the next higher order, making 13 units; 6 units from 13 units leave 7 units, which write in the units' place.

Since 1 of the tens was united with the units, there are 4 tens left. As 7 tens cannot be subtracted from 4 tens, increase the 4 tens by 10 tens (1 hundred) taken from the next higher order, making 14 tens; 7 tens from 14 tens leave 7 tens, which write in tens' place.

Since 1 of the hundreds was united with the tens, there are 5 hundreds left; and 4 hundreds from 5 hundreds leave 1 hundred, which write in hundreds' place. Hence, the difference between 653 and 476 is 177.

RULE.-1. Write the subtrahend under the minuend, placing units of the same order in the same column.

2. Begin at the right hand, and take each figure of the subtrahend from the figure above it, and write the result underneath.

3. If any order of the subtrahend is greater than the same order of the minuend, add 10 to the latter, and subtract.

4. Then diminish by 1 the next higher order of the minuend, and proceed as before.

PROOF.-Add the remainder to the subtrahend; if the sum is equal to the minuend, the work is correct.

Instead of diminishing by 1 the next higher order of the minuend, practically we add 1 to the next higher order of the subtrahend.

Copy, solve, and prove the following:

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How many years from the date of each of the following events to the year 1887?

7. Printing was invented in 1441.

8. The telescope was invented by Galileo in 1610. 9. First use of a locomotive in this country in 1820. 10. First railway in the United States built in 1827. 11. The first iron steamship was built in 1830. 12. The first steamboat plied the Hudson in 1807. 13. The first passage of the Atlantic by steam in 1839. 14. The first lucifer match was made in 1829.

15. The first steel pen was made in 1830.

16. The first newspaper published in America in 1704. 17. The electric telegraph first used in the U. S. in 1844.

Numbers composed of dollars and cents must be written as in addition.

When one of the given numbers contains cents, and the other does not, fill the vacant places with two ciphers.

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40. 2762+10341 and 44701 +1200 = ?

41. 3000+42301 and 720+1684+7342 = ?

42. What is the sum of 4062 and 12356, increased by the difference between 15000 and 975?

43. From the sum of 23462 and 9030, subtract the difference between 34000 and 7640.

44. From the difference between 19876 and 6032, subtract the difference between 12000 and 673.

45. A man has $10000. How much must he add to this, to be able to pay for a farm worth $13640?

46. California contains 158933 square miles, and Texas 237321 square miles. How much larger is Texas than California?

47. A man having $15740.80, gave $5085 for a store, and $7640.75 for goods. How much money had he left?

48. A merchant bought a quantity of goods for $1248.65, and sold them for $1540. What did he gain?

49. A man bought a western farm for $22700; he expended $4375 for improvements, and $2862 for stock: he sold the whole for $32000. Did he gain or lose, and how much?

50. A man willed $125000 to his wife and two children. To his son he gave $44675, to his daughter $26380, and the remainder to his wife. What was his wife's share?

A convenient method of subtracting the sum of two or more numbers from another:

51. From 948 subtract (325+106+82).

EXPLANATION.-Write the numbers as in addition, placing the minuend at the top.

Then add and subtract, thus: 2, 8, 13, and 5 more make 18; write 5 in the remainder, and carry 1 to the next col

umn.

948

325

106

82

435

1, 9, 11, and 3 more make 14; write 3 in the remainder, and carry 1 to the next column. 1, 2, 5, and 4 more make 9; write 4 in the remainder.

If the work is correct, the sum of the remainder and the parts of the subtrahend will equal the minuend.

In like manner, solve and prove the following:

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56. Mr. Jones having $12470, paid $4070 for a house, $927

for furniture, and $1000 for improvements. How much money had he left?

57. lf a man's income is $10000 a year, and he pays $1500 for rent, $1250 for provisions, $375 for taxes, and $1463 for other expenses, how much has he left?

58. A merchant of Nashville goes to New Orleans with $21600. He invests $7638.50 in groceries, $3210.65 in crockery, $1245.18 in woodenware, and the remainder in hardware. How much does he invest in hardware?

59. A man owns property valued at $75860, of which $45640 is invested in real estate, $25175.75 in personal property, and the remainder he has in bank. How much has he in bank?

60. A man deposited in bank $8752; he drew out at one time $4234, at another $1700, at another $962, and at another $49. How much had he remaining in bank?

61. A man buys goods as follows: groceries for $9.68; dry goods for $7.49; clothing, $19.95; nails for $2.58; and a plow for $9.75, and pays for them with a 50-dollar bill. How much change does he receive?

62. A gentleman possessing $47840, at his death gave to each of his two sons $18755, and the remainder to his daughter. How much did the daughter receive?

63. Three persons bought a hotel valued at $42075. The first agreed to pay $8375.50, the second agreed to pay twice as much, and the third the remainder, How much was the third to pay?

64. A man invests in trade at one time $680; at another time $820; at a third time $1580; and on a fourth occasion $420. How much must he add to the sum of these that the amount may be $5000?

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