MULTIPLICATION AND DIVISION OF DECIMALS. 83

5. From three thousand, and three thousandths take three hundred, and three hundredths. Ans. 2699.973. 6. From 3471.3471 take 325.325. Ans. 3146.0221.

7. From 3004.3004 take 305.305. Ans. 2698.9954. 8. From 3000004.3000004 take 20001.20001.

Ans. 2980003.0999904.

9. From 4001.4001 take 401.401. Ans. 3599.9991.

3. Multiply 2000001.2000001 by 2001.2001. Ans. 4002402601.44032012001.

8. Divide .036 by .12; by .006. by .0006.

Ans. .3; 6; 60.

9. Divide .225 by .9; by .003; by .025.

Ans. .25; 75; 9.

10. Divide 1.11 by .1; by .001; by .00001.

Ans. 11.1; 1110; 111000.

11. Divide 3.43 by .7; by .07; by .0014.

Ans. 4.9 49; 2450.

12. Divide 271.26 by .003; by .9; by .0009.

Ans. 90420; 301.4; 301400.

13. Divide .000121 by 1.1; by .011; by .00011.

Ans. .00011; .011; 1.1.

FRACTIONS.

PRACTICAL EXAMPLES.

1. The dividend is and the quotient §; what is the divisor?

Ans. 1

2. The product of two numbers is 34 and one of the numbers is 53; what is the other number?

Ans. .

3. If 2 be added to each term of ğ, will the fraction be increased or diminished?

Ans. Increased by

4. If 2 be added to each term of g, will the fraction be increased or diminished?

Ans. Diminished by.

COR.-If both terms of a proper fraction be increased by the same number, the value of the fraction is increased; but if both terms of an improper fraction be similarly increased, the value is diminished.

5. Received from one man $56, from a second one $95, and then paid a third $124; how much remained? Ans. $28.

6. A gentleman bought a horse, buggy, and harness for $360; the harness cost as much as the buggy, and the buggy one-half as much as the horse; what did each cost? Ans. Harness $36, buggy $108, horse $216. 7. A and B together have $204; and of A's is equal to of B's; how much has each ?

Ans. A has $108, B $96.

8. A, B, and C bought a farm for $6000. A paid %, B, and C the balance; what did each pay?

Ans. A $2400, B $2000, C $1600. 9. If 3 tons of coal cost $241, what will 25 tons. cost? Ans. $178. 10. If 5 cords of wood cost $254, what will 1 cord cost? What will 26 cords cost? What will 57 cords cost? Ans. $4, $120, and $257%. 11. If 94 barrels of flour cost $511, what cost 1 barrel? What cost 38 barrels ? Ans. $5 and $212.

12. A can dig a ditch in 6 days, B in 9 days; how much will each do in 1 day? How much will both do in 1 day? How long will it take the two to do the work?

Ans. A can do and Bin a day = both in a day, and both can do it in 3 days.

13. Divide $60 between A, B, and C, so that A gets }, B, and C the balance; what part will C receive?

Ans. C gets 2.

14. Reduce × 88 × 45 × 15 to a simple frac

2

16. Find the greatest common divisor of 105, 231, and 1001. Ans. 7. REM.-First find the greatest common divisor of two numbers, then of the G. C. D. found and of the other number.

17. The product of two numbers diminished by 914 is 153; one of the nnmbers is 17; what is the other number? Ans. 14.

18. A farmer sold of his cows and of his sheep, and then had 22 cows and 27 sheep left: how many had he at first? Ans. 66 cows and 108 sheep. 19. If 7 lbs. of sugar cost 714 cents, what is the cost of 105 lbs.? Ans. 1002 cents. 20. What will 83 barrels flour cost at $6 per barrel ?

Ans. $57.

21. What cost 136 lb. ham at 124 ct. per lb.?

Ans. 1708 cents.

22. What cost 180 tons coal at $5 per ton?

Ans. $9921.

23. What cost 571 lb. flour at 41 ct. per lb. ?

Ans. 2583 cents.

24. A and B together have $372, and † of A's money is equal to of B's; how much has each ?

Ans. A $192, B $180.

25. If of a ton of coal cost $1, what will a ton cost?

Ans. $7.

26. If of a ton of coal cost $2, what will a ton cost?

Ans. $7.

27. If of a cord of wood cost $, what will a cord cost? Ans. $41. 28. If of a cord of wood cost $5, what will a cord Ans. $6.

cost?

COR.

When a given number of articles of the same value costs a certain sum of money, in order to find the cost of one article, divide the certain sum by the given number, whether integral or fractional; and in order to get the cost of any required number, multiply the cost of one article by the required number.

29. If one acre of land is worth $374, what is the cost of 1254 acres? Ans. $46963. 30. If of a farm cost $4250, what did the whole farm cost? Ans. $6375. 31. If of a house is worth $4949, what is of it worth? What is the whole house worth?

Ans. is worth $707, and the house $6363. 32. A watch and chain are worth $150, and the chain. is worth the price of the watch; what is the value of each? Ans. Watch $105, chain $45.

33. Two-thirds the value of the house is equal to the value of the lot; both are worth $8500; what is the value of each? Ans. House $4500, lot $4000. 34. One-third of A's money is equal to of B's; both have $160; how many has each?

Ans. A has $90 and B $70. 35. If of a yard of cloth cost $24, how many yards can be bought for $1434 ? Ans. 34 yd. 36. If a man travel 33 miles an hour, how long will it take him to travel 48 miles? Ans. 13 hours. 37. A cistern has two pipes of supply and one for discharge; the first alone will fill it in 5 hours, the second in 8 hours, and the third will empty it in 9 hours; in what time will it be filled if all run together? Ans. 44 hours.