DEFINITIONS.

54. The Difference between two numbers is the number which, when added to the less, will make the greater.

55. Subtraction is the process of finding the difference between two numbers.

56. The Minuend is the number from which the subtraction is made.

57. The Subtrahend is the number which is subtracted. 58. The Sign of Subtraction is —, and is called minus. When placed between two numbers it denotes that the one on the right of it is to be taken from that on the left. Thus, 13 — 5 is read, thirteen minus five, and means that 5 is to be subtracted from 13.

MENTAL EXERCISES.

59.-1. If a boy had 16 dollars and lost 9 of them, how many had he left?

SOLUTION.-If a boy had 16 dollars, and lost 9 of them, he had left as many as the difference between 16 and 9, which is 7, the answer required.

2. I bought a book for 20 cents and sold it for 12 cents. How many cents did I lose by the sale?

3. William has 14 dollars in one purse and 24 dollars in another. If he should take 5 dollars from each, how many dollars would be left in them?

4. A farmer having 17 dollars, paid 10 dollars for flour. How many dollars had he left? 10 and how many are 17?

5. I paid 19 dollars for a coat and 7 dollars for a

vest. How many dollars more were paid for the coat than for the vest? 7 and how many are 19?

Principles of Subtraction.

60.-1. Only similar numbers can be subtracted, the one from the other.

2. The difference and the subtrahend are together equal to the minuend.

WRITTEN EXERCISES.

61. Write and subtract

From
Take

(1.)

49

26

Difference, 23

SOLUTION.-Write the numbers for sub

tracting so that the figures representing ones stand in one column, and the figures representing tens stand in another column at the left.

Begin with the ones, and subtract the ones and the tens separately.

Write the difference of the ones, which is 3, under the line at the bottom of the column of ones.

Write the difference of the tens, which is 2, under the line at the bottom of the column of tens.

The result is 23, which is the difference required.

Add the subtrahend and difference in each of the last

four problems. Their sum should be equal to the minuend.

MENTAL EXERCISES.

62.-1. How many are 12 less 5?

less 8?

2. How many are 10 less five? less 9?

3. Count backward by 2's, or by subtracting 2 successively, from 22 to 2.

SOLUTION.-22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2.

4. Count backward by 3's from 60 to 30. From 30 to 3.

5. Count backward by 4's from 48 to 8. From 96 to 72.

6. Count backward by 5's from 40 to 10. From 80 to 55.

7. Count backward by 6's from 90 to 12. From 35 to 11.

8. Count backward by 7's from 61 to 5. From 70 to 35.

9. Count backward by 9's from 45 to 9. From 72 to 45.

10. How many will remain if 2 be taken from 11? 2 from 21? 2 from 31? 2 from 41?

11. How many will remain if 3 be taken from 11? 3 from 21? 3 from 41? 3 from 61?

12. How many will remain if 4 be taken from 11? 4 from 21? 4 from 31? 4 from 51 ?

63.-1. What number must be added to 7 to make 13? To make 23? To make 33?

2. What number must be added to 6 to make 14?

3. If the subtrahend is 9 and the difference 8, what is the minuend?

4. What number is 19—8? 17-9? 16-7?

5. What number must be added to 8 to make 13? To make 23? To make 33?

6. How many are 21 less 9? 13 less 9?

7. What number must be added to 9 to make 13? To make 23?

8. If you have 9 dollars, how many more must you have to make 16 dollars? To make 26 dollars?

9. If you are

will you be 14?

now 8 years old, in how many years In how many will you be 24?

10. Jacob has 6

lambs; how many more must he

have to make 12? To make 22?

11. 2 tens from 4 tens leave how many tens? 2 tens from 6 tens? 5 tens from 9 tens? 7 tens from 11 tens?

12. A shepherd has 20 sheep in one fold, and 30 in another. How many more has he in the second than in the first?

13. John has 50 cents; how many more must he have to make 70 cents?

WRITTEN EXERCISES.

64.-1. What is the difference between 86 and 47 ?

7. 16.

Minuend, 86
Subtrahend, 47

Difference, 39
Proof, 86

SOLUTION. Write the figures of the subtrahend under the figures of the same order in the minuend.

Since 7 units cannot be taken from 6 units, take 1 ten from the 8 tens of the minuend, leaving 7 tens, and add 10 ones, which are equal to the 1 ten, to the 6 ones, thus making the minuend the same as 7 tens, 16

ones.

Subtract 7 ones from 16 ones, leaving 9 ones, which write under the line at the bottom of the ones.

Subtract 4 tens from 7 tens, leaving 3 tens, which write under the line at the bottom of the tens.

The result is 39, which is the difference required.

Prove the solution by adding the difference to the subtrahend, which gives 86, the minuend.

Subtract, explain in like manner and prove

65.—1. A farmer had 25 bushels of wheat, and sold 12 bushels. How many bushels had he left?

=

SOLUTION.-He had left as many bushels as the difference between 25 and 12; 12: 102; 10 from 25 leaves 15, and 2 from 15 leaves 13, which is the answer required.

2. If you had 29 dollars, how many dollars would you have left after spending 16 dollars?

3. What number must be added to 21 to make 40? 4. What number must be added to 13 to make 61 ? 5. What number must be added to 49 to make 76 ? 6. Arthur had 28 cents, and his father gave him enough more to make 50. father give him?

How many cents did his