45. To Read Numbers expressed by Figures:

Separate the number into periods of three figures each, counting each way from units place. Begin at the left, read each period separately, and add the name to each, except units period.

When there are decimals, read the figures on the right of the decimal point as if whole numbers, and add the name of the lowest order.

Thus, the figures 256,347.259 are read, "Two fifty-six thousand, three forty-seven, and two hundred fifty-nine thousandths."

NOTES.-1. In numerating decimals as well as whole numbers, the units place should always be made the starting point.

2. In reading whole numbers and decimals, the word and should be used between the whole number and the decimals.

Write the following numbers in figures:

1. One thousand, forty-two.

2. Thirty thousand, nine hundred seven.

3. Forty-six thousand, four hundred.

4. Ninety-two thousand, one hundred eight.

5. Sixty-eight thousand, seventy.

6. One hundred twenty-four thousand, six hundred.
7. Two hundred thousand, one hundred sixty.
8. Four hundred five thousand, forty-five.

9. Three hundred forty thousand.

10. Nine hundred thousand, seven hundred twenty. 11. One million, seven hundred thousand.

12. Thirty million, twenty thousand, fifty. 13. Three, and seven tenths.

14. Forty-five hundredths.

15. Twenty-eight, and three hundredths.

16. Two hundred fifty, and seven thousandths.

17. Thirty-five, and twenty-four thousandths.

18. Four hundred two thousand, and eight tenths.

19. Seventeen hundred, and twenty-five thousandths.

20. Nine thousand, two hundred five, and twenty-three hundredths.

Point off, numerate, and read the following numbers:

[For Rom. Notation and Eng. Numeration, see Arts. 860-863, Appendix.]

QUESTIONS.

1. What is a unit? 2. Number? 3. The unit of a number? 4. An abstract numbers? 5. Concrete? 6. Like numbers? 7. Unlike?

9. What is Arithmetic ? 10. Notation? 11. Numeration? 12. The Arabic Notation? 15. What is the value of a figure? 19. What does the first figure at the right denote? 20. In the second place? What called? 23. In the third place? What called? 24. What is the largest number expressed by three figures?

25. How are larger numbers expressed? 26. What does a figure in the fourth place denote? 27. In the fifth? 28. In the sixth ? 29. In the seventh? 30. If any orders are omitted, what is to be done?

31. What are the different values expressed by figures called? How determined? 32. What is the simple value of a figure? 33. The local value?

34. Name the three principles of Notation? 35. What is the great law of the Arabic Notation? What is it often called? Why? 36. Explain how this law is applied in expressing parts of one?

37. What is the first place at the right of units called? The second? Third? 38. How are these orders separated from units? 39. What are the orders at the left called? Those at the right ?

40. Repeat the Numeration Table? 41. What is the first period on the left of the decimal point called? The second? The third? 42. The first period on the right of units? 43. How are larger numbers expressed? 44. How express numbers by figures? 45. How read them?

D'DITION.

46.

ORAL EXERCISES.*

1. How many are 7 marbles, 5 marbles, and 9 marbles? Ans. 21 marbles.

SOLUTION.-7 and 5 are 12 and 9 are 21.

2. How many dollars are 15 dollars, 10 dollars and 6 dollars?

3. How many are 12 books, 8 books, and 7 books?

4. How many units are 15 units, 6 units, and 10 units? 5. How many are 6, 8, and 4? 7, 5, and 6?

6. If one tree bears 12 peaches, another 9, another 6, how many peaches will all bear?

7. A dairy-woman put 17 pounds of butter into a stone jar, and afterwards added 8 pounds more; how many pounds of butter did the jar contain?

8. If you have 12 pens in your box, and afterwards add 7 more, how many pens will your box contain ?

9. If a class of 12 pupils is united with a class of 15 pupils, how many will be in the class?

10. If 9 units and 7 units and 8 units are united in one number, how many units will the number contain?

DEFINITIONS.

47. Addition is uniting two or more numbers in one. The answer or number found by addition is called the Sum or Amount.

NOTE. The Sum or Amount contains as many units as all the numbers added.

48. The Sign of Addition is +. It is called Plus, which means more, and shows that the numbers between which it is placed are to be added. It is read "and," or "added to."

Thus, 5 3 is read, "5 plus 3," "5 and 3," or "5 added to 3."

49. The Sign of Equality is =. It is read, "equal" or "is equal to," and shows that the numbers between which it is placed are equal.

35. If you pay 10 cents for an inkstand, 8 cents for paper, 4 cents for pens, how much will you pay for all?

36. If you pick 7 apples from one tree, 5 from another, and 6 from another, how many apples will you have?

37. What is the sum of 9 dollars, 7 dollars, and 4 dollars? 38. How many are 11 books, 10 books, and 6 books?

39. If you pay 10 cents for fare, 15 cents for lunch, and 8 cents for fruit, how much will you have spent?

SLATE EXERCISES.

50. Write the following in columns and add each up and down several times, naming results only.

1. Add 4, 2, 6, 3, 5, 6, 4, 5, 3, 4, and 2.

Thus, 4, 6, 12, 15, 20, 26, etc.

2. Add 5, 3, 4, 2, 3, 5, 6, 2, 7, 4, and 3.
3. Add 4, 3, 5, 7, 6, 2, 3, 7, 4, 6, 4, and 5.
4. Add 2, 5, 4, 3, 7, 6, 4, 3, 2, 4, 5, and 6.
5. Add 8, 2, 7, 6, 5, 3, 1, 7, 6, 8, 7, 4, 3, and 7.
6. Add 9, 4, 2, 7, 3, 4, 5, 6, 8, 4, 6, 5, 4, and 8.
7. Add 7, 5, 3, 6, 4, 2, 5, 3, 8, 1, 6, 3, 4, and 9.
8. Add 6, 3, 4, 7, 2, 9, 4, 3, 7, 8, 5, 2, 6, 4, and 7.

9. Add 8, 4, 2, 7, 5, 3, 6, 2, 4, 6, 5, 8, 1, 9, 5, 6, and 8. 10. Add 6, 8, 3, 5, 2, 7, 4, 6, 3, 1, 7, 6, 5, 4, 6, 8, and 9. 11. What is the sum of 3232, 20, 4314, and 2123?

EXPLANATION.-We write the numbers so that units of the same order stand in the same column, and naming results only, proceed thus, 3, 7, 9 units. Write the 9 under units column.

Adding the tens in the same manner, 2, 3, 5, 8 tens. Write the 8 under tens column, and add the hundreds and thousands in like manner.

OPERATION.

3232

20

4314

2123

Ans. 9689

We prove the work by beginning at the top and adding each column downward. The two results agree, therefore the work is

16. A man paid 5423 dollars for a house, 325 dollars for repairs, and 430 dollars for painting; what did the whole cost?

17. If a steamer goes 243 miles in one day, 321 miles the next, and 402 miles the third, how far does she go in 3 days?

18. A father gave 314 acres to one son, 241 acres to another, and 432 acres to another; how many acres did he give to all?

ORAL DRILL.

51. 1. Add by 2's from 0 to 50, naming results only.

Thus, two, four, six, eight, ten, etc.

10. Add the other digits 5, 6, 7, 8, 9 in the same manner, till

the result becomes as large as may be deemed desirable.