Art. 1. What is a unit? 2. What is a number? 3. What is arithmetic ?

4. What is notation? 5. What is numeration? 6. What are figures? 7. What does zero, or cipher, express? What do the other nine figures express ?

9. When has a figure a simple name and value? When has it a place-name and value?

10. What is the place of a figure? 11. If in the first place, what place-name has a figure? What units does it express? If in the second place, what place-name has a figure? What units does it express?

12. What place-name has a figure at the left of tens? What units does it express?

13. What place-name has a figure at the left of hundreds? What units does it express?

15. Give the place-names beginning with ones. Give the corresponding orders of units.

16. What form a group for convenience in reading and writing numbers? How is each group named? Name groups beginning with ones. What is used to mark off the groups? 17. What does each complete group contain?

18. What are principles of notation? 19. What is our system called? What do the successive orders of units form?

20. What is the decimal point? For what is it written? 21. What is the number at the left of the point?

26. How are numbers written in figures? 27. How are numbers written in figures read?

ADDITION.

28. 1. James has 9 apples and Henry has 3. How many apples have both?

2. Mary had 7 oranges and her brother gave her 5. How had she then?

many

3. A father gave to one of his children 8 cents, to another 5 cents, and to a third 6 cents.

them in all ?

How many cents did he give

4. How many are 9 and 3? 7 and 5? 8, 5, and 6? 5. How many dollars are 8 dollars, 7 dollars, and 3 dollars?

6. What is the unit of 8 dollars, 7 dollars, and 3 dollars?

29. The Unit of a number is one of that number. Thus,

One pound is the unit of 8 pounds, one quart is the unit of 27 quarts.

30. Like numbers are numbers having the same unit. Thus 3, 5, 7; and 6 cents, 4 cents and 5 cents, are like numbers.

31. Addition is finding a number equal to two or more given numbers.

32. The sum, or amount, is the result of an addition.

33. The sign of addition is +, named plus. It means more, and is generally read and. Thus,

4+ 5+ 6 is read four and five and six.

34. The sign of equality is =. It means equal, or equal to, and is often read are. Thus,

78 15 is read seven and eight are fifteen.

35. The sign, $, written before a number, means dollars. Thus,

$10 is read ten dollars.

36. Cents, expressed in figures, may occupy two decimal places, tenths and hundredths, and mills one place, thousandths. Thus,

$0.53, or $.53, is read fifty-three cents, and $28.005 is read twenty-eight dollars and five mills.

ORAL EXERCISES.

7. How many dollars are $7, $ 6, and $2 ?

8. If you pay 10 cents for a slate, 9 cents for paper, and 3 cents for a pencil, how much do you pay for the whole?

9. 12 boys are at play in one place, 6 in another, and 5 in another. How many boys are at play in all?

10. John one day caught 8 trout, another day 9, and a third day 4. How many did he catch in the three days?

29. Add by 2's from 0 to 24, naming only results.

Solution. 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24.

Add:

42. How many are 8+ 6 + 5? 5 + 6 +8? 8+ 5+ 6? 6+8+5?

37. Principles of Addition.

1. Only like numbers, and units of the same order can be added.

2. The sum is the same in whatever order the numbers are added.

WRITTEN EXERCISES.

43. What is the sum of 142, 16, 201, and 410?

142
16

201

410

769

Solution. We write the numbers so that units of the same order may be in the same column.

Beginning with ones, we add, naming results, thus: 0, 1, 7, 9, and writing the 9 beneath in ones' place.

Adding the tens, 1, 0, 2, 6, the sum, 6 tens, we write beneath in tens' place.

Adding the hundreds, 4, 6, 7, the sum, 7 hundreds, we write beneath in hundreds' place.

The sum, then, is 7 hundreds 6 tens 9 ones, or 769.

To test or prove the work we add the columns downward, and have, as before, the sum 769.

44. What is the sum of 121, 516, 361, and 11 ?

45. What is the sum of 231 + 114 + 324?

46. How many are 235 + 321 + 142 ?

47. Sold 416 bushels of corn to one man, 301 to another, and 42 to a third. How many bushels were sold in all ?

48. Paid for labor $104, for boards $530, for timber $243, and for hardware $112. How much was paid for all?

49. Bought a horse for $150, a carriage for $200, a harness for $45, and hay and grain for $104. What was the cost of the whole?

50. Mr. Smith, in his will, gave to his son Arthur $500; to his son John $365; to his daughters $475, and to his brother $125. How much did he give them all?

ORAL EXERCISES.

51. In one basket there are 20 apples, in another 9, and in a third 7. How many are there in all?

66. Add by 9's from 3 to 48; from 4 to 49; from 5 to 50; from 6 to 51; from 7 to 52.

67. Add by 7's from 0 to 42; by 8's from 0 to 48; by 9's from 0 to 54.

How many are:

68. 17 + 2 + 5+ 6 ?

69. 21 + 5 + 8 + 2 ?

70. 13+2 +7+4?

71. 32 + 6 + 3 + 9 ?

72. What is the sum of 67 and 25?

73. If you should travel one day 20 miles and the next day 24 miles, how far would you travel in the two days?

74. A man earned in one week $11, in another $16, and in a third $13. How much did he earn in all?

75. A father gave to one of his sons 30 cents, to another 14 cents, and to his daughter 12 cents. How much did he give them in all ?

76. In one field there are 55 acres, in another 40, and in the third 17. How many acres are there in the three fields?