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Reduce the following decimals to common fractions:

5. .375.

8. 10.10.

6. .625.

9. 4.3125.

7. .875.

10. 12.9375.

2. .25.

3. .85.

4. .64.

14. Reduce .163 to a common fraction.

PROCESS.-.163

163

100

[blocks in formation]

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1. Reduce to a decimal.

Ans.

31. .0225.

32. .6251.

33. 4.37.

34. 4.81.

35. .03.

36. 4.003.

37. 17.00.

38. 8.663.

WRITTEN EXERCISES.

11: 40.3750.

12. 2.00125.

13. 4.0125.

39. 12.04.

40. 26.03.

41. 75.75.

CASE II.

95. To reduce a common fraction to a decimal.

42. 400.875.

43. 375.375.

44. 112.0625.

45. 2.0025.

46. 45.455.

PROCESS.

equals of 3.

8)3.000

3 equals 30 tenths; of 30 tenths is 3 tenths, and 6 .375, Ans. tenths remaining; 6 tenths equals 60 hundredths; of 60 hundredths is 7 hundredths, and 4 hundredths remaining; 4 hundredths equals 40 thousandths; of 40 thousandths is 5 thousandths. Hence equals .375.

RULE.

Annex ciphers to the numerator and divide by the denominator; point off as many decimal places as there are ciphers annexed.

Reduce the following fractions to decimals:

2.1.

24. 183.

25. 925.

3. 4.

26. 4.

4. 3.

27. 5.

5. .

28. 776.

6.

.

29. 8.

7.5.

30. 9.

8. 7.

31.756.

5

9. f.

32. 427.

33. 17 17

34. 42.

12

10. 1.

11. 18.

12. 250. 19

13. 16

3

16

14. 25.

15..

16. .

6

17. 25.

18. 76.

19.

20. 17

32.

21. 5.

22.93.

23. 7.

ADDITION OF DECIMALS.

WRITTEN EXERCISES.

96.-1. Add 4.26, 12.005, and 126.4.

PROCESS.

4.26 12.005 126.4

142.665

Add

2. 28.32, 47.16, 35.08, 9.9, 12.001.

3. 126.2, 26.37, 7.425, .6243, 250.1256.

4. .7802, 6.321, 89.42, 172.8, 4216.

5. 40.002, 7.08, 123.4567, 400.005.
6. .9374, 13.21, 45.135, 1.0006, 82.16.
7. 4.2, 16.73, 141.154, 7832.1654.

12.

13.

35. 105635

36.

15.

8.

75.4

14. 4.81123.478 + 120.042 + 9. 63.45 + 2.3 +74.6 + 62.04 10. 100.027 + 52.67 + 634.842 + 4.7 11. 53.2 + 40.732 +

3.5 + 432.683

37. 164.

38. 4.00%.

39. 1.325.

40. 6.0031.

41. 2.001.

We write the numbers so that their decimal points are in the same vertical column, and add as in whole numbers, placing the decimal point between units and tenths.

42. 4.0621.

43. 8.703.

44. 1.003. 45. 40.0017.

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16.

17. Find the sum of 9 tenths, 18 hundredths, 125 thousandths, 62 ten-thousandths, 165 tenths, and 125 thousand.

18. Find the sum of five, and twenty-four hundredths, eight, and sixty-two ten-thousandths, ninety, and forty-one millionths, two hundred and five, and one thousand three hundred and seven ten-millionths.

19. A wagon cost $25.37, a horse $180.90, a set of harness $10.05, a mowing-machine $85.37, a cow $28.08, and a pair of mules $225.75; what was the entire cost?

20. What is the sum of $25 and 18 cents, $45 and 27 cents, $610 and 39 cents, $250 and 81 cents, and $1001 and 57 cents?

SUBTRACTION OF DECIMALS.

WRITTEN EXERCISES.

97.-1. Subtract 129.486 from 726.278.

PROCESS.

726.278 129.486

596.792, Ans.

2.

86.71

5.03

6.

27.004

8.2106

We write the numbers so that their decimal points are in the same vertical column, and subtract as in whole numbers, placing the decimal point between units and tenths.

[blocks in formation]

10. From 876.472 take 162.587.
11. From 800.719 take 49.62.
12. From 125.6 take 42.3478.
13. From 3.07 take 2.187654.
14. From 10 take 9.768745.
15. From 10.001 take 9.000001.

8.

2.0067

[blocks in formation]
[blocks in formation]

20. 4.28

21. 132.06

22. 400.

23. 216. .321862

18. .0017 .000218 =

19. 6.396.3899 = =

24. From 16 hundredths take 16 millionths. 25. From 10.32 take 17 ten-millionths.

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7. 3 X .2? 11. × | × 8. 6 X 4? 9. 7 X.3? 10. 8 × .6? |

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2 X 3? | 15. .7
.5 X .7?

16. .6
17. .8
18. .9

12.

13. .9 X .8?
14. .7 × .6?

3.002786 =

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100.0027 =

26. From four hundred, and four thousandths take four hundred and four thousandths.

362.0041 =

27. A farmer bought 102.26 acres of land from A, 140.216 acres from B, 47.025 acres from C, and enough from D to make in all 400 acres; how much did he buy from D?

28. A coal-dealer bought 1020 tons of coal: he sold A 40.025 tons, B 105.008 tons, C 208.125 tons, D 416.375 tons, and E 50.015 tons; how much was left?

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MULTIPLICATION OF DECIMALS.

ORAL EXERCISES.

98.-1. How much is 3 X? 4X.2? 3.3? 2. How much is ? 2 × .2? .3 × .3? 3. How much is to XT60? 2 x .03? 4 X .06? 4. How much is to X Tooo? 2 x .002? .6 .003? 5. How much is Too X TO? .02 .03? .06 × 04? 6. When tenths are multiplied by tenths, how many deci mal places are there in the product? Tenths by hundredths? Tenths by thousandths? Hundredths by hundredths?

.001? 19. .02 .03?
| X
.002? 20. .06 X .09?
.006? 21. .08 .07?
.004? 22. .04 X .09?

99. The product of two decimals contains as many decimal places as there are decimal places in both factors.

1. Multiply 24.6 by .24.

PROCESS.

24.6

.24

984

492

5.904, Ans.

WRITTEN EXERCISES.

1ST. 246 multiplied by 24 is 5904, but tenths multiplied by hundredths give thousandths; hence the result is 5904 thousandths, or 5.904.

2D. 24.6 x .24

246 × 20

Multiply

2. Multiply 42.8 by .31.
3. Multiply 4.26 by 2.8.
4. Multiply 62.85 by 3.15.

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RULE.

8. .4 by .625.

9. .8 by .068.

10. .9 by .899.

11. .7 by .039. 12. .6 by .079.

Multiply as in whole numbers, and point off as many decimal places in the product as there are in both factors.

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Prefix ciphers to the product if it does not contain the required number of figures.

5904

5.904.

13. .26 by .4216.
14. .09 by .0036.
15. .35 by .1024.
16. .73 by .0094.
17. .08 by .6213.

5. Multiply 7.214 by .316. 6. Multiply 40.206 by .027. 7. Multiply .0216 by .0042.

18. .321 by .8432. 19. .027 by .6215. 20. .061 by .0283. 21. .092 by .0063. 22. .007 by .0038.

23. Multiply 1.080502 by 3.216.
24. Multiply .00432 by .00037.
25. Multiply 8 by .074 by 10.
26. Multiply .05 by 14.162 by .02.

27. Multiply 6 by 73 by .81.

28. Multiply 0.305 by .00046.

29. Multiply .42, 3.04, .125, and .826 by .0031.
30. Multiply 12.63, .081, .073, and .0081 by .00093.

31. Multiply 10, 100, 1000, and 10000 by 8.6213.

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