24. Multiply thirty-six units and forty-eight hundredths, by four hundred seventy-five thousandth.

DIVISION.

191. Since the dividend is equal to the product of the divisor and quotient, it must have as many decimal figures as there are in both divisor and quotient. Hence,

The quotient must have as many decimal figures as the number of decimal figures in the dividend exceeds that in the divisor.

2. Divide .00115 by .05.

OPERATION. .05).00115

.023

.00115 divided by 5 gives .00023; but, as the divisor is .05, the quotient must be one hundred times as large, and .00023 multiplied by 100, by removing the point two orders to the right, gives .023. Therefore,

the quotient of .00115 divided by .05 is .023.

Rule. Divide as in integers, and point off as many figures for decimals in the quotient as the number of decimal figures in the dividend exceeds that in the divisor, supplying the deficiency, if any, by prefixing ciphers; or,

What is the dividend equal to? How many decimal figures must the quotient have? Explain the operation. Recite the Rule.

If the divisor is a decimal, divide by its numerator, and multiply by its denominator.

When the divisor is 10, 100, 1000, etc., remove the point to the left as many orders as there are ciphers in the divisor.

193. When the number of decimal figures in the divisor exceeds that in the dividend, annex to the dividend as many ciphers for decimals, at least, as will make the number of decimal figures in both equal.

Here, in Example 14, the division does not terminate. In such cases, after carrying it to a sufficient exactness, denote the incompleteness by annexing the sign.

How do you proceed when the divisor is 10, 100, 1000, etc.? How do you proceed when the number of decimal figures in the divisor exceeds that in the dividend?

15. Divide 2.117 by .0073. 16. Divide 8 by .002.

17. Divide 7.43 by .0079.

18. Divide 89 by .003.

Ans. 290.

Ans. 4000.

Ans. 940.5063+.

Ans. 29666.66+.

19. Find the quotient of 80.3 divided by .22.

20. Find the quotient of 80.3 divided by 2.2.

Ans. 36.5.

21. If 3.5 acres produce 142.1 bushels of corn, what is the yield per acre? Ans. 40.6 bu. 22. How many yards of cotton cloth, at .125 dollars per yard, can be bought for $46.95?

Ans. 375.6 yd. 23. At .75 dollars a day, how many days must a boy work to earn $141? Ans. 188 days.

24. If you can walk 12.5 miles in one day, how many days will it take you to walk 102.5?

25. Bought 30 pounds of butter for $5.85; how much was that a pound?

Ans. $0.195.

26. Divide one hundredth by one ten-thousandth.

Ans. 100.

REVIEW.

1. Add seven hundred forty-three thousandths, seven hundredths, five units and sixteen ten-thousandths.

Ans. 5.8146.

2. Add eighty-seven units and twenty-nine hundredths, seventy-three units and forty-seven thousandths, three thousand five units and one hundred six ten-thousandths,

REVIEW.

- What is a Unit? (1.) What is the Unit of a Fraction? Ans. The unit or single thing divided into equal parts.

twenty-eight units and three hundredths, one unit and five thousandths. Ans. 3194.3826.

3. Reduce 5 to the decimal form. Ans. 5.1875. 4. Reduce 1 and 2 to decimals having a common denominator. Ans. .680 and .052.

5. From 100 subtract 101 thousandths.

Ans. 99.899.

6. From eighteen units and three hundred sixty-five thousandths, take eighteen hundred sixty-five ten-thousandths. Ans. 18.1785. 7. Change .68 to an equivalent common fraction.

Ans..

8. Change 5.25 to an equivalent common fraction.

Ans. 21

9. Multiply one hundred units and thirty-seven hundredths by nine tenths. Ans. 900.333.

10. What common fraction is equal to the sum of .125

13. At $1.25 a pair, how many pairs of shoes can be bought with $45?

Ans. 36 pairs.

14. If an acre produces 16.25 bushels of wheat, how much will 3.95 acres produce?

15. If $18.5625 is paid for 148.5 yards of calico, how much is paid per yard?

$.125. 16. If 3.5 cords of wood cost $22.4, how much will 4.25 cords cost? Ans. $27.20.

REVIEW. - What is a Decimal Fraction? (172.) What the Denominator of a Decimal Fraction? (174.) How many decimal figures has the product in Multiplication of Decimals? (190.) The quotient in Division of Decimals? (192.)

17. When $107.525 is paid for 114 barrels of flour, how much must be paid for 5.8 barrels? Ans. $54.23. 18. At .375 of a dollar a bushel, how many bushels of potatoes can be bought for $500?

Ans. 1333.33+ bushels.

19. If 51 pairs of shoes cost $133.875, how much will 67 pairs cost? Ans. $175.875.

QUESTIONS FOR ANALYSIS.

1. At $2.25 per hundred weight, or cental, what is a load of wheat, weighing 2564 pounds, worth?

SOLUTION.—2564 pounds reduced to hundred weight, or centals, by pointing off two orders from the right, is 25.64 centals. At $2.25 per cental, 25.64 centals of wheat will be worth 25.64 times $2.25, or $57.69. Therefore, etc.

2. What cost a cargo of corn weighing 156750 pounds, at $1.20 per cental?

Ans. $1881. 3. How much must be paid for 11023 pounds of corn, at $1.05 per cental? Ans. 115.74+.

4. At $1.20 per hundred weight, what is the freight on 6545 pounds of glass ware?

Ans. $78.54.

5. At $8 per thousand, what cost 19340 bricks? SOLUTION. 19340 reduced to thousands, by pointing off three orders from the right, is 19.34 thousands. At $8 per thousand, 19.34 thousands will cost 19.34 times $8, or $154.72. Therefore, etc.

6. What cost 42555 feet of boards, at $40 per thousand?

REVIEW. How many pounds make a cental? (110.) A bushel of wheat? (110.) Of corn? (110.)