number on the right of the sign is to be subtracted from the one on the left.

Thus, 12-9-3.

NOTE.-The difference is sometimes called the remainder, especially when a part of a number is to be subtracted from the whole number; as, 5 yards of muslin are cut from a piece containing 20 yards.

PRINCIPLE.

The minuend and subtrahend are always like numbers.

ORAL PROBLEMS INVOLVING BUT ONE PROCESS.

1. A boy had 20c., and paid 15c. for a slate. How much had he left?

ANALYSIS. Since he had 20c., and paid 15c. for a slate, he had left as many cents as 20c. is greater than 15c., which are 5c. Therefore he had 5c. left.

2. Paid 14c. for paper, and 9c. for a pencil. How much more was paid for the paper than for the pencil?

3. Mary is 16 years old, and her brother is 8 years old. What is the difference of their ages?

4. John bought 18 marbles, and James 12. How many more did John buy than James?

5. A lady having $19, paid $8 for a shawl. How much Idid she have left?

6. A boy gathered 21 quarts of nuts, and sold 12 quarts. How many quarts were left?

7. A man bought 28c. worth of meat, and gave the trader 35c. How much change should he receive?

8. Bought 38c. worth of cotton cloth, and gave the merchant 50c. How much change should I receive?

9. Bought a suit of clothes for $36, and gave the dealer $50. How much change should I receive?

10. There are two trees in my yard, one of which is 48 feet high, and the other is 13 feet less. How high is the other tree?

11. A gentleman is 60 years old, and his wife is 12 years younger. How old is the wife?

12. A farmer raised 75 bushels of corn is 15 bushels more than he raised last year. he raise last year?

this year, which

How much did

13. Paid $90 for a wagon, and sold it so that I lost $20. How much did I receive for the wagon?

14. Took 80 bushels of oats to market, which is 30 bushels more than I left at home. How many bushels did I leave at home?

15. Sold 100 bushels of wheat, which was 30 bushels more than I kept. How many bushels did I keep?

16. Bought 88c. worth of groceries, and gave the grocer $1. How much change should I receive?

ORAL PROBLEMS INVOLVING TWO PROCESSES.

17. Paid 7c. for a pencil, 12c. for a book, and gave 25c. to the dealer. How much change should I receive?

18. A lady had $12, found $10, and afterward lost $8. How much did she have left?

19. Had 50c., paid 30c. for a book, and 12c. for toys. How much had I left?

20. A farmer kept 45 hogs in 3 pens; in one pen were 20 hogs, in the second 15. How many were there in the third?

21. Mary had 12 peaches, Jane 9 peaches, and Sarah 30 peaches. How many peaches has Sarah more than both Mary and Jane?

22. A wagon cost $50, a sleigh $20, and harness $10. How much does the wagon cost more than both sleigh and harness?

23. Bought 40c. worth of sugar, and 30c. worth of coffee. How much change should I receive if I gave the. grocer $1.

24. A hogshead contains 63 gallons of water. If I pour

into it at one time 40 gallons, at another 14 gallons, how many gallons more will fill it?

25. A tree is 75 feet high. If 40 feet be broken off at one time, 20 feet at another, how much will yet remain?

26. A boy put 18 chickens into one coop, 12 into another, and enough in the third to make 45 altogether. How many did he put into the third coop?

27. A woman paid 50c. for some tea, 25c. for cheese, and enough for oil so that they all cost $1. How much did

she pay for oil?

28. A farmer planted an orchard of 100 apple trees in 4 days. The first day he planted 30 trees, the second 30 trees, the third 20 trees. How many did he plant the fourth day?

29. A hunter in 4 days shot 80 birds. The first day he shot 24 birds, the second 24 birds, and the third 12 birds. How many did he shoot the fourth day?

30. A gentleman lost $20 each day for 3 days, and enough the fourth day to make his whole loss $80. How much did he lose on the fourth day?

31. From a pile of wheat containing 72 bushels, 20 bushels were taken at one time, 30 bushels at another, and 10 bushels at another. How many bushels were left?

32. Gave 16c. for a pound of sugar, 20c. for a pound of coffee, and 45c. for meat. How much more was given for meat than for both sugar and coffee?

33. Gave 20c. for oranges, 30c. for lemons, and 41c. for How much less did I pay for candies than for the lemons and oranges?

candies.

34. Sold a pencil for 9c., a slate for 12c., and some toys for 8c. If I received a 25c. piece, and a 10c. piece, how much change should I give?

35. Bought a coat for $25, a pair of pants for $10, and a vest for $6. If I give a $50 bill, how much should I receive in change?

36. A lady put up at one time 22 quarts of cherries, at another 10 quarts, and at another 8 quarts. She lost at one

time 12 quarts, at another 9 quarts. How many quarts were left?

37. A boy had 9 marbles, found 3 more than he had. He afterward lost 6 less than he found. How many marbles did he have left?

38. A squirrel ran up a tree 20. feet, then down 8 feet, up 4 feet, down 12 feet, up 9 feet, up 7 feet, down 11 feet, up 7 feet, down 6 feet, down 9 feet, up 25 feet, down' 10 feet, down 9 feet, up 12 feet, down 16 feet. How high is the squirrel?

ORAL COMBINATIONS.

39. 15+7+8+9-7-6-4+8-5+9-7+6+9=? 40. 12+9-7+5+9-10+6-12+7+5+3-12+5=? 41. 7+8+6-9-3+6+11-10-8+5+4-6-5-? 42. 50-8-7-6-5+7-5+4-5+8-9+6-8+12=? 43. 18+12-8-8-8+12+5+4-10-7+5+3-9=? 44. 16+8-9+15-9-9+6-9+5-7+12+5-20=? 45. 24+8+8-20+7+9-8+6-4+9+6-5-10=? 46. 9+6-8+7+8+8-6-6+12+10+10-20=? 47. 12+5+5+5-7-7+6-5+9+9-8-6+8+6=? 48. 18-6-4-8+11+5-10+20+8+7+9-40=? 49. 12+5+4+3-5-5+9+8+9+8—5—5—5—5—? 50. 7+8+9-3+9-3+9−3+9−3+9+3—9—2=? 51. 17+7-12+7+6−5+9−4+8+7−8+6+6=? 52. 16+12+12-10-10+8−9+7−9+6−9+12=? 53. 8+9+6+6-11-9+12+5+4—10—9—8+6=? 54. 11+9-6+11-5+20+20-50+21+9-8-12=? 55. 60-4-4-4-4-4-4-4-4-4+8+8—7—7=? 56. 40+40+20+60-100-40+80-40-50+90=? 57. 12+12+12+12+12+12-2-10-20-30+90=? 58. 11+11+11+11+11+11-6+12+3-5-5-5-? 59. 25+10+5-8-7+11-12+6-20+19+6+7=? 60. 30+20-40+15+25+50+100+200+400+800=? 61. 500-300-100-50+25+25-30-30-30-10-? 62. 400-200-200+80+20+100+1000-200-500=? 63. 1000-400-300-200+300+400+200-1000=?

64. A boy had 144 chestnuts. He then took

away

each day until there was left a number less than five. How many were left?

65. If there are 133 apples in a barrel, and George should take out 8 each day, and James 9 every other day, how many apples will George get if he precedes James?

66. A man has 63 volumes of books in his library. 2 shelves contain 9 volumes each of poetry; 1 shelf Dickens' works in 13 volumes, and Hood's works in 5 volumes; another shelf Barnes' Notes in 11 volumes; the remainder consists of 3 Bibles and the "Little Classics." How many volumes of "Little Classics" in the library?

ANALYSIS OF SUBTRACTION.

67. From 9876 subtract 3452.

PROCESS.

9.876

3452

6424

ANALYSIS.-1. Write the numbers so that figures of the same order shall stand in the same column.

2. Begin at the order of units thus: 6 units less 2 units are 4 units. Write the 4 units beneath the column of units.

3. 7 tens less 5 tens are 2 tens. Write the 2 tens beneath the column of tens.

4. 8 hundreds less 4 hundreds are 4 hundreds. Write the 4 hundreds beneath the column of hundreds.

5. 9 thousands less 3 thousands are 6 thousands. Write the 6 thousands beneath the column of thousands.

Therefore, 9876-3452-6424.

68. From 8345 subtract 4879.

8345

ANALYSIS.-1. Write the numbers as above.

PROCESS. 2. 5 units of the minuend are less than 9 units of the subtrahend. To supply this deficiency, take 1 ten of the 4 tens of the minuend, and change it to units. 1 ten is equal to 10 units, which, added to the 5 units is equal to 15 units. 15 units less 9 units are 6 units. Write the 6 units in the order of units.

4879

3466

3. 1 ten having been taken from the 4 tens of the minuend, 3 tens are left. 3 tens of the minuend is less than 7 tens of the subtrahend.