2. Multiply 43,01 by 6,04. Prod. 259,7804. 3. What is the product of two hundred and twenty-eight and sixty-five hundredths, multiplied by three and six hundredths? Ans. 699,669.

4. If a yoke of oxen eat,45 of 1 cwt. of hay in one day how much hay will be required to keep them 150 days? Ans. 67,5 cwt.=3 T. 7,5 cwt. 5. Ifa man build 16,6 rods of fence in one day, how many rods will he build in 11 days, working at the same rate?

Explanation. Change the vulgar fraction to a de

cimal.

Ans. 190,9. 6. What will 79 barrels of flour cost, at $4,37 per barrel?

Explanation.-37 cents are 37 hundredths of a dollar, consequently there will be two decimal places in the product, that is, two places of cents. Or if we call the whole price of each barrel 437 cents, which it is, the whole product will be cents, for the 437 cents will be placed in the product once for each barrel. But if we divide the whole number of cents in the product by 100, the number of cents in a dollar, the quotient will be dollars, and the remainder, if any, cents; but the remainder will always be the two right hand figures. From this it appears, that when two places of figures are pointed from the right of any number of cents, the figures to the left of the point, will be dollars, and those to the right of it cents. Ans. $345,23.

7. What cost 79,4 yards of cloth, at $2,36 per yard? Ans. $187,384.

Note 3.--There being one decimal place in the quantity and two in the price of a 1 yard, there will be three decimal places in the product. The three decimal places will be thousandths of a dollar, which are mills. The two left hand decimals are hundredths of a dollar, and the whole decimal may be read three hundred eighty-four mills, or thirty-eight cents and four mills; for dividing the whole number of mills by 10 the number of mills in a cent, the quotient would be cents and the remainder mills, but the two left hand figures would form the quotient and the right hand one the

remainder.

8. What is the product of 379765 into seventy-nine thousandths? Ans. 30001,435.

mills per gal.?

9. What cost 118 gal. of molasses, at 28 cents 4 Ans. $33,512. 10. What cost 503 yards of tape, at 7 mills per Ans. $3,521.

yard?

11. What cost 1174 lb. of butter, at 15 cents per pound?

Explanation. In most cases, when a vulgar frac tion is reduced to a decimal, it is not necessary to carry the decimal to more than two or three places. In this question we carry the decimal to two places only in the multiplicand. The of a centand the cents themselves are decimals of a dollar; the decimals therefore obtained by reducing the are decimals of a cent, and the whole multiplier decimals of a dollar.

The decimals to the right of mills, being only thousandths of a mill, may be omitted.

12. What will 26 barrels of cider come to at a dollar 27 cents and 9 mills per barrel ? Ans. $33,676+. 13. What cost 678 yards of riband, at 13 cents per yard? Ans. $88,14. 14. What is the product of nine million, seventyone ten millionths, multiplied by itself? Ans. ,81001278005041. 15. What is the product of $6,50, multiplied by Ans. $27,365.

$4,21?

16. What is the product of 10 dollars, eight cents into 92 cents? Ans. $9,273+.

Note 4.-The 6 tenths of a mill are omitted.

17. What is the product of 92 cents into 8 cents?

Ans. $,073+.

18. Multiply 92 cents by 8 mills.

Prod. $0,007+.

19. What will 5675 feet of boards come to at $9,75 per thousand ?

Operation.
5,6 7 5
9,7 5

2 8 3 7 5

397 25 51075

5 5 3 3 1 2 5

Ans. $55,331+.

Explanation.-Boards, plank, and joist, are calculated by the thousand. Any number of feet less than 1000 are thousandths of 1000, and the price must be found accordingly. When we read figures denoting any number of feet of boards, plank, or joist, the decimal expression is not generally used. We say five thousand six hundred and seventy-five feet of boards; but in finding the price we must consider 675 feet as thousandths of 1 thousand, for $9,75 being the price of one thousand feet, is to be taken as often as there are 1000 in the whole number of feet, and a proportional part of it for 675 feet.

20. What is the part of 100001 ? Ans. ,045728+. 21. What must I receive for 10609 feet of boards, at 10 dollars per thousand? Ans. $106,09. 22. Find what 259 feet of boards will come to, at $12 per thousand ? Ans. $3,108. 23. What must a ship-carpenter give for 62100 ft. of white oak plank, at $631 per thousand?

Ans. $3943,35.

24. What will 900 ft. of plank come te, at 50 dollars and 45 cents per thousand?

Ans. 45 dollars, 40 cents and 5 mills. 25. What will 8 feet of plank come to, at $70 per thousand ? Ans. 56 cents. 26. What will 1009 ft. of joist amount to, at $9,25 per thousand ?

Ans. $933 and 8,295 mills.

27. How many shillings in, 3 of a pound?

Operation.

20

,3

6,0

Explanation.-By Explanation to question 16th, page 148, it was shown that multiplying a number by the numerator and dividing by the denominator, the quotient would equal the same part of the number as was expressed by the fraction. 20 shillings equal 1 pound, therefore multiplying 20 by 3 the numerator of the fraction, and dividing by 10 the denominator, or pointing off the right hand figure, the quotient will express the same number of shillings as ,3 of a pound. Ans. 6 shillings.

28. How many hours in of a day?

Ans. 7 and,2 of an hour. 29. In ,26 of a cord of wood, how many solid inches?

Explanation.-First find the number of solid inches Ans. 57507,84.

in a cord.

30. If I buy ,09 of a ton of copperas, how many pounds do I buy?

Ans. 201,6.

31. How many inches in ,001 of a mile?
Ans. 63,36.

Note 5.--When the value of the decimal is required in several less denominations, reduce the decimal to the lowest denomination mentioned as directed in Rule, page 118, observing to multiply only the decimal each time.

32. What is the value of,126 of a pound?

Explanation. Multiplying,126 by 20 and pointing off the 3 right hand figures, gives 2 s. and 52 hundredths of a shilling which is the whole value. By multiplying the decimal of a shilling by 12, gives the value of that part of a shilling in the same manner as in the first part of the operation.

33. What is the value of ,37 of a day?

Ans. 8 h. 52 m. 48 s.

34. What is the value of ,0101 of a mile?

Ans. 3 r. 3 ft. 9,936 in.

SUBTRACTION OF DECIMAL FRACTIONS.

RULE.

Place each figure of the subtrahend under one of its own name in the minuend.

Subtract as in whole numbers.

The decimal point must stand directly under those in the given numbers.

Remark. As decimals increase by 10 the same as whole numbers, we must subtract in the same as in whole numbers. The same illustration is applicable to the subtraction of decimals, which was given for the subtraction of whole numbers. (See page 53.)