SUBTRACTION

INDUCTIVE EXERCISES.

56. 1. James had 4 apples, but he ate 2 of them. How many had he left?

2. Mr. Dane had 5 horses, but sold 3 of them. How many had he left?

3. A hen hatched 6 chickens, but 3 of them died. How many lived?

4. A boy had 7 cents, of which he spent 4. How many had he left?

5. A man earned $10 per week, and spent $5 of it. How much had he left?

6. Nine men fell from a scaffold, and 4 of them were killed. How many were not killed?

7. A freight train of 10 cars contained 4 open cars, and the rest were closed cars. How many closed cars were there in the train?

8. William bought a slate for 10 cents and sold it for 7 cents. How much did he lose?

9. In a certain class there are 9 girls and 5 boys. How many more girls are there than boys?

10. George is 11 years of age and Henry is 6. What is the difference between their ages? What is the difference between 11 and 6? Between 10 and 5?

11. What is the difference between 6 dollars and 3 dolBetween 6 men and 3 dollars?

lars?

12. Why can you not find the difference between 6 men and 3 dollars?

13. Between what kind of numbers can you find the dif ference?

14. Hiram worked 8 days and William worked 5 days. How many days more did Hiram work than William ?

15. Henry spent 12 cents and Jane spent 8 cents. How much more did Henry spend than Jane? What is the difference between 12 and 8?

16. If the difference between 12 and 8 is added to 8, the smaller number, what will be the result?

17. If the difference between any two numbers is added to the smaller number, to what will the result be equal?

DEFINITIONS.

57. Subtraction is the process of taking one number from another.

58. The Minuend is the number from which another is to be subtracted.

59. The Subtrahend is the number to be subtracted.

60. The Remainder, or Difference, is the result obtained by subtracting.

61. The Sign of Subtraction is a short horizontal line: It is called minus.

When it is placed between two numbers it shows that the one after it is to be subtracted from the one before it.

Thus, 8-3 is read 8 minus 3, and means that 3 is to be sub、 tracted from 8.

62. PRINCIPLES.-1. Only like numbers can be subtracted. 2. The sum of the subtrahend and remainder must be equal to the minuend.

9-1-8 10-2- 8 11-3 8 12-4 8 13—5— 8 10-19 11-2 9 12-3- 9 13-4 9 14 5 9 11-1-10 12-2-10 13-3-10 144-10 15- 5-10

6-6-0 7-7-0 8-8- 0

=

1

9-9-010-10-0

9. 1 10- -9 111-10- 1 210-8- 2 11-9 2 12-10-2 311-83 12-9 3 13—10— 3

4

10-64 11-7: 4 12-8 4 13-9 4 14-10 11-6 512--7- 5 13-85 14-9- 5 15-10-5 12-6-613-7- 6 14-8 6 15-9- 6 16—10— 6 13-6714-7- 7 15-8-7 16-9- 7 17—10— 7 14-6 8 15-7- 816-8- 817-9 8 18-10- 8 15-6 9 16-7 917-8-9 18-9- 9 19-10= 9 16-6-10 17-7-10 18-8-10 | 19-9-10 20-10-10

ORAL EXERCISES.

63. 1. I bought a writing-book for 15 cents and a slate for 10 cents. How much more did the writing-book cost

than the slate?

2. A boy solved 12 examples on Monday and 15 on Tuesday. How many more did he solve on Tuesday than on Monday?

3. A horse traveled 9 miles the first hour and 7 miles the second. How much farther did he travel the first hour than the second?

4. Henry earned 14 cents and spent 7 of them. How much had he left?

5. A merchant has a piece of cloth containing 16 yards. If he sells 8 yards, how much will he have left?

6. A farmer who had 16 bushels of seed corn planted 7 bushels of it. How much had he left?

7. A boy who had 13 marbles lost eight of them. How many had he left?

8. William hoed 15 rows of corn while Henry hoed 7. How many more rows did William hoe than Henry?

9. I bought 16 pencils and sold 8 of them. How many had I left?

10. Henry's mother found that in 15 days at school he had perfect lessons on 7 days. On how many days did he have imperfect lessons?

11. A librarian loaned 14 books, of which all but 6 were story-books. How many story-books did he loan?

12. A news-boy who had purchased 17 papers sold all but 5. How many did he sell?

13. Two boys together caught 17 fishes. If one of them caught 8, how many did the other catch?

14. Fourteen sailors were wrecked and 5 of the number were drowned. How many were saved?

15. Seventeen criminals escaped from a jail, but 8 of them were caught. How many were not caught?

16. In a city there are 18 newspapers published, all but 6 of which are weeklies. How many weekly papers are published in that city?

17. A woman had 20 rose-bushes, but only 7 of them bloomed. How many did not bloom?

WRITTEN EXERCISES.

64. When no figure of the subtrahend has a greater value than the corresponding figure of the minuend. 1. From 869 subtract 423.

PROCESS.

Minuend 869

Subtrahend 423

Remainder 446

ANALYSIS. For convenience the less number is written under the greater, units under units, tens under tens, etc.

Beginning at the right, each order of units in the subtrahend is subtracted separately from the same order in the minuend.

Thus, 9 units-3 units are 6 units, which are written under the units. 6 tens-2 tens are 4 tens, which are written under the tens.

8 hundreds-4 hundreds are 4 hundreds, which are written under the hundreds. Hence the remainder is 446.

PROOF.-446, the remainder, plus 423, the subtrahend, equals 869, the minuend. Hence the result is correct. (Prin. 2.)