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DIVISION OF DECIMALS.

ORAL EXERCISES.

10

10

100.-1. What is 33?.6 ÷ 3? .8 ÷ 4?
2. What is o÷? .48÷.6? .56 ÷ .7?
3. What is Toooo? .024.8? .072.9?
4. What is ooooo? .081.09? .063.07?

÷

5. When hundredths are divided by tenths, how many deci mal places are there in the quotient? Thousandths by tenths? Thousandths by hundredths?

6. .36 ÷ 9.

7. .42 ÷ 6.

8. .64 ÷ 8. 9. .72 ÷ 9.

PROCESS.
6.4, Ans.

101. The quotient of two decimals contains as many decimal places as those in the dividend exceed those in the divisor.

.34)2.176

204

10. .36.9. | 14.
11. .42.6.
12. .56.7.

15.

.063 ÷.9.

16.
13. .81.9. | 17. .049 ÷ .7.

1. Divide 2.176 by .34.

136

136

.035 ÷ .7. | 18. .012 ÷.06.

.028 ÷ .4.

19. .027 ÷ .09. 20. .032 ÷ .08. 21. .054 ÷ .06.

WRITTEN EXERCISES.

1ST. 2176 divided by 34 is 64; but thousandths divided by hundredths give tenths: hence the quotient is 64 tenths, or 6.4.

2D. 2.176.34

2176 34 2176 100 X 1000 100 1000 34 2176 64 10 × 34 10

=

÷

=

=

6.4.

RULE.

Divide as in whole numbers, and point off as many decimal places in the quotient as those in the dividend exceed those in the divisor.

1. If the number of decimal places in the dividend is less than the number of decimal places in the divisor, make them equal before beginning the division.

2. If the quotient does not contain the required number of decimal places, supply the deficiency by prefixing ciphers.

2. Divide 16.5 by .25; and .29808 by 124.2.

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31. Divide 16000 by .0004.

32. Divide .00016 by 4000.

4968

4968

8. Divide 34.4088 by 1.62. 9. Divide .291624 by 2.32. 10. Divide .0014375 by 6.25. 11. Divide .3234 by 1470. 12. Divide 102.102 by 102.

28. Divide 1249383 by .023.
29. Divide 1 by .0125. By .375.

30. Divide .023 by 10. By 100. By 1000.

23. .016 400. 24. 160.004. 25. .0018÷.06. 26. 800.04. 27. 2.125.

33. Divide .2952, 99.63, and 1.3653 by .123.

34. Divide 7.1262, .96942, and 54.891 by 3.21.

35. Divide one, and one hundred-millionth by one ten-thou sandth.

APPLICATION OF DECIMALS.

102. The application of the principles of decimals and common fractions gives rise to several abbreviations in multiplication, division, and business transactions, of which the following are the most important:

CASE I.

103. To multiply by an aliquot part of 100.

An Aliquot Part of a number is the whole or mixed number which will exactly divide that number.

Thus, 50, 331, 25,

20, 16, 121, etc. are aliquot parts of 100.

1. To multiply by 25.

This is equivalent to multiplying by 100; hence the

RULE.

Annex two ciphers, or move the decimal point two places to the right, and divide by 4.

25 times

1. 512 51200

2. 10.24.

3. 3456.

=

= 12800.

4. 1.23456.

5. 968.424.

6. 12.3284.

2. To multiply by 121.

This is equivalent to multiplying by 100; hence the

RULE.

Annex two ciphers, or move the decimal point two places to the right, and divide by 8.

121 times

7. 512 51200 = 6400.

8. 6.32.

9. 7864.

10. 82.128.

11. 98.7656.

12. 4.248.

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3. To multiply by 331.

This is equivalent to multiplying by 100; hence the

RULE.

Annex two ciphers, or move the decimal point two places to the right, and divide by 3.

=

331 times

17. 55.5555.

13. 612 6130020400. | 15. 60.3045. 14. 9636.

16. 1357.11. 18. 123.456.

Similar rules may be made for other aliquot parts of 100.

CASE II.

104. To divide by an aliquot part of 100.

1. To divide by 25.

This is equivalent to multiplying by ; hence the

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2. 86752.

3. 2161.

4. 762.34.

5. 213.75.

6. 32125.

7.99975.

3950.

2. To divide by 121.

This is equivalent to multiplying by 18; hence the

RULE.

Multiply by 8 and divide by 100.

Divide 12 into

8. 10121

81.

9. 4625.

3. To divide by 331.

This is equivalent to multiplying by ; hence the

=

1012 × 8
100

=

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10. 345.216.

11. 1784.

12. 1256.

13. 475.

16. 12000.

17. 21.62.

18. 128.5.

19. 895400.

15. 4700.

Similar rules may be made for other aliquot parts of 100.

PROBLEMS.

1. What will 72 yards of muslin cost at 12 cents a yard? 2. What will 32 yards of calico cost at 63 cents a yard? 3. What will 150 pounds of coffee cost at 33 cents a pound?

4. What will 48 pounds of butter cost at 333 cents a pound, and 64 dozen of eggs at 25 cents a dozen?

5. What is the cost of 24 yards of cloth at $1.16%, and 75 yards of muslin at 12 cents a yard?

6. What will 216 tons of ore cost at $163 a ton?

7. What will 429 tons of rails cost at $331 a ton ?

8. What will 840 bushels of oats cost at 25 cents a bushel?

9. What will 215 pounds of beef cost at 20 cents a pound?

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