10. What is the unit of 18 yards? Of 9 days? Are the units of 18 yards and 9 days like, or unlike? Can 9 days be taken from 18 yards? Why?

In each of the preceding questions there are given two numbers to find the difference between them, or to find the remainder of the larger after taking away the smaller.

Definitions.

64. Subtraction is the process of taking one of two numbers from the other.

65. The Difference, or Remainder, is the number obtained by subtracting one of two numbers from the other. 66. The Minuend is that one of two numbers from which the other is taken.

67. The Subtrahend is that one of two numbers which is taken from the other.

Thus, if 12 pounds are taken from 20 pounds, 20 pounds is the minuend, 12 pounds is the subtrahend, and 8 pounds is the remainder, or difference.

68. The Sign of Subtraction is a short horizontal line, It is named minus, and means less.

When the sign of subtraction is placed between two numbers, it shows that the number placed after it is to be taken from the number placed before it.

Thus, 20 pounds 8 pounds is read 20 pounds minus 8 pounds, and means that 8 pounds are to be taken or subtracted from 20 pounds.

69. Principles.

I. Subtraction is the reverse operation of addition.

II. Only similar numbers, and only like orders of units, can be taken one from another.

III. The difference or remainder is a number similar to the minuend and the subtrahend.

1. When the Subtrahend is less than 10.

1. A basket has in it 3 apples. How many apples must be added that it may contain 7 apples?

70. Analysis. If a basket has in it 3 apples, that it may contain 7 apples, there must be added 4 apples, because 3 apples and 4 apples are 7 apples. Hence, etc.

2. Ada has 8 cents, and Emma has 5 cents. How many cents more has Ada than Emma?

3. Charles had 6 dollars, and earned enough to make his money equal 10 dollars. What did he earn?

4. James is eleven years old, and his brother five years old. What is the difference in their ages?

5. If a dressmaker earns 12 dollars a week, and spends 7 dollars, how much does she save?

71. Analysis.

If a dressmaker earns 12 dollars a week, and spends 7 dollars, she saves the difference between 12 dollars and 7 dollars, which is 5 dollars. Hence, etc.

6. From a lot of 13 pails, a tinsmith sold 6 pails. How many pails had he remaining?

7. Ellen is 14 years old, and Henry is 7 years younger. What is Henry's age?

8. From a pile of wood containing 15 cords, a farmer sold 6 cords. How many cords remained?

9. A newsboy bought some papers for 9 cents, and sold them for 16 cents. How many cents did he clear?

10. If a freight-train had in it 17 cars, and 8 of them were empty, how many were loaded?

How many are

11. 10 tons less 7 tons?
12. 11 boys less 6 boys?
13. 13 bushels less 5 bushels?

14. 15 years less 8 years?

16. 15 cows less 9 cows?
17. 16 cords less 7 cords?
18. 16 baskets less 8 baskets?
19. 17 books less 9 books?

15. 14 dollars less 7 dollars? 20. 18 melons less 9 melons?

21. Mary had 14 cents, and spent 3 cents for paper and 5 cents for a pencil. How much had she left?

72. Analysis. Since Mary had 14 cents, and spent 3 cents for paper, she had left the difference between 14 cents and 3 cents, which is 11 cents; and if she then spent 5 cents more for a pencil, she had left the difference between 11 cents and 5 cents, which is 6 cents. 22. From a bin containing 16 bushels were sold 4 bushels for seed and 7 bushels to a miller. How many remained? 23. How much of 17 tons of coal remains after taking away 5 tons and 8 tons? 9 tons and 6 tons?

24. A farmer had 9 cows, bought 7 cows more, and then sold 8. How many had he then ?

25. From the sum of 8 and 9 take 8. To the difference between 18 and 9 add 7.

Exercises.

1. Subtract 1 from 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and back.

73. Model. -1 from 1 leaves 0; 1 from 2 leaves 1; 1 from 3 leaves 2; 1 from 4 leaves 3; 1 from 5 leaves 4; 1 from 6 leaves 5; 1 from 7 leaves 6; 1 from 8 leaves 7; 1 from 9 leaves 8; 1 froin 10 leaves 9. 1 from 9 leaves 8; etc.

2. Subtract 2 from 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and reverse.

6 from

3. Subtract 3 from 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12, and reverse.

4. Subtract 4 from each number from 4 to 13 inclusive, and reverse. 5. Subtract 5 from each number from 5 to 14, and reverse. each number from 6 to 15, and reverse.

6. Subtract 7 from each number from 7 to 16, and reverse. each number from 8 to 17; 9 from 9 to 9 from 18.

8 from

7. Subtract, rapidly, 3 from 8; 5 from 9; 4 from 11; 5 from 12; 6 from 12; 6 from 15; 7 from 14; 7 from 16; 8 from 15; 8 from 17; 9 from 15; 9 from 16; 9 from 18.

8. Tell, promptly, the remainder of

2. When the Subtrahend is more than 9.

1. By selling a cow for 23 dollars, a farmer cleared 5 dollars. What did the cow cost him?

74. Analysis. - Since a farmer sold a cow for 23 dollars, and cleared 5 dollars, the cow cost him the difference between 23 dollars and 5 dollars, which is 18 dollars. Hence, etc.

2. A man bought a watch for 31 dollars, and sold it at a loss of 5 dollars. What did he get for it?

3. From a cask containing 42 gallons, 7 gallons leaked How many gallons were left in it?

out.

4. From a 50-cent note, John received 6 cents in change. How much money had he spent?

5. Alice is 7 years old, and her father is 61 years old. What is the difference in their ages?

6. John's grandfather is now 65 years old. How old was he 8 years ago? How old 6 years ago?

7. The sum of two numbers is 73, and the less number is 7. What is the greater number? If the less is 9?

8. If the minuend is 75 dollars, and the subtrahend is 8 dollars, what is the remainder?

9. If the minuend is 82 miles, and the remainder is 8 miles, what is the subtrahend? If the minuend is 91 miles? 10. What is the remainder of the minuend 93 pounds after taking from it 9 pounds? After taking 8 pounds?

How many are

11. 25 roses less 6 roses? 12. 33 pinks less 5 pinks?

13. 42 lilies less 4 lilies? 14. 54 lilacs less 6 lilacs?

15. 65 shrubs less 7 shrubs?

16. 53 nails less 6 nails? 17. 64 knobs less 8 knobs? 18. 77 doors less 8 doors?

19. 86 panes less 7 panes ? 20. 98 locks less 9 locks?

21. A merchant sold some goods that cost him $30 at a What did he receive for them?

loss of $10.

22. If a coal-dealer buys 40 tons of coal, and sells 20 tons the same day, how many tons has he left?

23. From a flock of 58 sheep, a drover sold 30 sheep. How many then remained in the flock?

24. Henry's father is 64 years old, and Henry is 40 years younger. How old is Henry?

25. A clerk was paid $35, and he spent $19 for some clothing. What had he remaining?

75. Analysis. - Since the clerk was paid $35, and he spent $19 for some clothing, he had remaining the difference between $35 and $19. $19 equal $10 and $9; $10 from $35 leave $25; and $9 from $25 leave $16. Hence, etc.

26. A man bought a watch for $42, and sold it for $14 less than the cost. How much did he get for it? 27. If I live 17 more years, I shall be 51 years of age. How old am I now? How old was I 15 years ago?

28. Of 63 passengers on a ferry-boat, 24 were women. How many of the passengers were men?

29. A fence was put up at a cost of $70. If the material cost $35, what was paid for the labor?

30. I exchanged a watch worth $48 for a horse worth $85, and paid the difference in cash. How much did I pay?

31. If a dollar-note is offered in payment for a bushel of potatoes worth 75 cents, what change must be given?

32. What is the remainder of the minuend 83 barrels after taking from it 49 barrels? After taking 54 barrels ?

33. What is the excess of the minuend 94 acres over the subtrahend 55 acres? Over the remainder 66 acres?

34. What is the difference between the tens in 30 and the tens in 60? Between the tens and ones in 40 and 75?

35. How many tens and ones in 35 less 8? In 46 less 20? In 60 less 45? In 75 less 57? In 82 less 63? 91 less 74?