4. One hundred forty-eight thousandths. 5. Two hundred eleven thousandths.

6. Six hundred ninety-three thousandths. 7. Nine ten-thousandths.

8. Four ten-thousandths.

9. Thirty-two ten-thousandths.

10. One hundred eighty-three ten-thousandths.

11. Nine hundred seven ten-thousandths.

12. One thousand five hundred seventy-six ten thou sandths.

13. Nine thousand four hundred three ten-thousandths. 14. Eight hundred-thousandths.

15. Five hundred-thousandths.

16. Forty-five hundred-thousandths.

17. Ninety-four hundred-thousandths.

18. Three hundred fifty-two hundred-thousandths.

19. Eight hundred ten hundred-thousandths.

20. Four thousand seven hundred nineteen hundred-thousandths.

21. Seven thousand twenty-three hundred-thousandths. 22. Two thousand six hundred-thousandths.

23. Thirty-four thousand six hundred twenty-one hundredthousandths.

24. Fifty-nine thousand one hundred six hundred-thousandths.

25. Nineteen thousand three hundred-thousandths.

26. Fifty thousand one hundred-thousandths.

27. 25 millionths.

28. 8 millionths.

29. 63 millionths.

30. 478 millionths. 31. 2895 millionths.

32. 5008 millionths.

33. 37592 millionths.

34. 809066 millionths:

35. 26 and 68 hundredths. 36. 94 and 39 thousandths.

37. 290 and 463 hundred-thousandths.

38. 40073 and 50093 millionths.

39. 61 and 13 millionths.

40. Two thousand five and three thousand forty-six mil lionths.

25. Numbers like exercises 1 to 30, Art. 22, are called Decimal Fractions. Numbers 31 to 39 are called Mixed Decimals. Name the Decimal Fractions in Art. 24. Name the Mixed Decimals in the same section.

26. REDUCTIONS.

1. In .6 there are how many hundredths? How many thousandths? Write each of the numbers. How many tenthousandths? Write the number. How many millionths? Write the number. Read 3.5 as hundredths, as thousandths, ten-thousandths, hundred-thousandths, millionths. Write each of the numbers. In .600000 there are how many tenths? ten-thousandths? hundredths? hundred-thousandths? millionths?

2. In 3.2 there are how many hundredths? How many ten-thousandths? How many millionths? Write each of the numbers. In 5.000000 how many hundred-thousandths? hundredths? thousandths? tenths? Write each of the numbers.

3. In 400000, there are how many tens? How many hundreds? How many ten-thousands? How many thousands?

SECTION II.

ADDITION.

27. Like numbers are numbers that are made by repeating the same unit.

28. The Sum of two or more like numbers is a number which contains all of their units.

29. The sign + (plus) between two numbers shows that their sum is to be found.

30. At first, to unite two numbers, we count the units of the second upon the first, thus: In uniting four blocks and three blocks, we think (or say) four, five, six, seven, as we place the three blocks one at a time with the four. way, by counting objects, we learn and

the following forty-five sums:

3

In this

commit to memory

711

8

5

761

9

9

31. This series of forty-five sums of the nine primary numbers taken in twos is called the Addition Table.

8

91

841

651

611

631

741

9 61

774

The last twenty sums in the addition table may be learned without objects by uniting with the first number enough of the second to make ten; thus, 8 + 5 = 8 + 2 + 3 = 10 + 3 = 13.

32. Addition is the process of finding the sum of two or more like numbers.

Since 7+ 5 = 12, 17+ 5 = 22, 27 + 5 = 32, etc. Practice similarly with all of the "endings."

33. As a preparation for "column addition" give frequent exercises in adding by twos, threes, fours, etc., starting with one, two, three, etc., and carrying the work to 50.

34. EXERCISES.

The following problems are for seat, board, or home work, and for oral practice in recitation. Practice upon them until they can be performed with great rapidity. They contain frequent repetitions of the work in the addition table. Add from the bottom, naming results only, thus: (first problem) 7, 13, 21, 24, 26, etc. To test the accuracy of the work add downward.