8. Find the sum of $305.08, $6.54, and $296.03.

9. A farmer sold a quantity of wheat for $97.75, of barley for $42.06, of oats for $39.50. How much did he receive for the whole ? Ans. $179.31.

10. Bought a house for $4368.90, furniture for $790.07, carpeting $280.60, and made repairs on the house amounting to $307.05. How much did the whole cost? Ans. $5746.62. 11. A man bought a horse for $342.50, a carriage for $185.90, and sold them so as to gain on both $85.50. How much were they sold for? Ans. $613.90.

12. A furniture dealer sold a bedroom set for $135.86, a bookcase for $75.09, and 3 rocking-chairs for $5.75 each. How much did he receive for the whole ? Ans. $228.20.

13. A man is in debt to one man $873.60, to another $500.50, to another $75.08, to another $302.04; how much does he owe in all? Ans. $1751.22.

14. James Williams bought a saw-mill for $8394.75, and sold it so as to gain $590.85; for how much did he sell it? 15. A lady after paying $23.85 for a shawl, $25.50 for a dress, $2.40 for gloves, and $4.08 for ribbon, finds she has $14.28 left; how much had she at first? Ans. $70.11.

DEFINITIONS.

50. Addition is the process of uniting two or more numbers into one number.

51. Addends are the numbers added.

52. The Sum or Amount is the number found by addition.

53. The Process of Addition consists in forming units of the same order into groups of ten, so as to express their amount in terms of a higher order.

54. The Sign of Addition is +, and is read plus. When placed between two or more numbers; thus, 8+3+6 + 2 + 9, it means that they are to be added.

55. The Sign of Equality is, and is read equals, or equal to; thus, 9413 is read, nine plus four equals thirteen.

56. PRINCIPLES.-I. Only numbers of the same denomination and units of the same order can be added.

II. The sum is of the same denomination as the addends.

III. The whole is equal to the sum of all the parts.

REVIEW AND TEST QUESTIONS.

57. 1. Define Addition, Addends, and Sum or Amount. 2. Name each step in the process of Addition.

3. Why place the numbers, preparatory to adding, units under units, tens under tens, &c.?

4. Why commence adding with the units' column?

5. What objections to adding the columns in an irregular order? Illustrate by an example.

6. Construct, and explain the use of the addition table. 7. How many combinations in the table, and how found? 8. Explain carrying in addition. What objection to the use of the word?

9. Define counting and illustrate by an example.

10. Write five examples illustrating the general problem of addition, "Given all the parts to find the whole."

11. State the difference between the addition of objects and the addition of numbers.

12. Show how addition is performed by using the addition table.

13. What is meant by the denomination of a number? What by units of the same order?

14. Show by analysis that in adding numbers of two or more places, the orders are treated as independent of each other.

SUBTRACTION

PREPARATORY STEPS.

58. STEP 1.—To find the difference between two numbers when the smaller is expressed by one figure and the larger does not exceed the smaller by 10.

1. The difference between two numbers is the amount that one number is greater than the other. Thus, 7 is 2 greater than 5; hence 2 is the difference between 7 and 5.

2. The greater number is called the Minuend, the smaller the Subtrahend, and the process of finding the difference is called Subtraction.

3. Subtraction is an application of the Addition Table. From our knowledge of the parts that make up the numbers in the table, we can tell at once, if a number and one of its parts are given, what the other part is.

Thus, we know that 9 and 6 are equal to 15; hence if 15 be given and the part 9, we can name 6 at once as the other part, or difference between 15 and 9.

59. 1. Arrange on your slate in irregular order the numbers from 1 to 10, and write 1 under each number, thus:

1 5 2 8 4 7 3 10 6 9

1 1 1 1

111

1 1 1

Practice writing and pronouncing the differences between these pairs of numbers in the same manner as you did in addition. See (33).

Arrange on your slate in the same way and practice upon each of the following:

2. Numbers from 2 to 11 with 2 written under. 3. Numbers from 3 to 12 with 3 written under. 4. Numbers from 4 to 13 with 4 written under. 5. Numbers from 5 to 14 with 5 written under. 6. Numbers from 6 to 15 with 6 written under. 7. Numbers from 7 to 16 with 7 written under. 8. Numbers from 8 to 17 with 8 written under. 9. Numbers from 9 to 18 with 9 written under.

60. STEP 2.-To find the difference between two numbers when the smaller number is expressed by one figure and the greater by two, the units' figure of which is less than the smaller number

Observe carefully the following:

1. Numbers of two figures above 20 can at sight be made into two parts one of which contains 1 ten and the units. Thus, 7460 + 14; 90 = 80 + 10.

2. To subtract, for example, 9 from 85, we regard the 85 as 70 and 15, and take the 9 from the 15. We know at sight that 6 is the difference between 15 and 9. Uniting this 6 to 70 we have 76, the difference between 85 and 9.

3. Find the difference between 73 and 6, 32 and 5, 94 and 9, and explain the process as illustrated in 1 and 2.

61. 1. Write on your slate every number from 20 to 99, and make each into two parts one of which will contain 1 ten and the units.

2. Write on your slate in irregular order all the numbers from 20 to 30, with 4 under each number thus,

20 25 21 28 24 30 27 22 26 29 4 4 4 4 4 4 4 4 4 4

Subtract the 4 from each number and write the difference under. Erase and repeat the work until you can write the difference at sight of the numbers.

Practice in the same manner, on subtracting from the same numbers each number from 1 to 9 inclusive.

3. Write on your slate in the same way numbers from 30 to 40 inclusive; then from 40 to 50; 50 to 60; 60 to 70; 70 to 80; 80 to 90.

Practice on subtracting from each set in order numbers from 1 to 9 inclusive, as directed for numbers from 20 to 30. Continue the practice on each set until you can give the differences at sight.

62. 1. Frank had 9 apples in his basket, but he ate 2 and gave away 3 more; how many were left?

SOLUTION. -He had as many left as the difference between 9 and the sum of 2 and 3, which difference is 4. Hence he had 4 apples left.

2. Irving picked 16 cherries, and gave 4 to his sister and 5 to his mother; how many had he left?

3. A man bought some bacon for $6, and enough flour to make the whole cost $14; what did the flour cost him?

4. A man who had 20 dollars, spent 5 for a hat and 2 for a pair of rubbers; how many dollars had he left?

5. I bought a saddle for $14 and a bridle for $3, and paid $9; how much was left unpaid?

6. A farmer having 40 turkeys sold 3 to one man and 6 to another; how many had he left?