39. From 8 take 271.

In Ex. 38, take

81-211=714 — 27=5&, Ans. from , and 2 units from 6 units; but in

from

Ex. 39 we cannot take from,.. reduce one of the 8 units to, and add it to the, making 1, and then take the if, and the 2 units from the remaining 7 units.

to its lowest terms.

4. Add 8 to 611.

5. Subtract 1815 from 2517.

6. Reduce 23 to an improper fraction.

7. Reduce 8 to a fraction whose denominator is 27.

8. Reduce 9 to 6 fractional forms.

9. Divide

by 13.

10. Divide 16 by 23.

11. Divide by §.

12. Reduce of a day to hours, minutes, and seconds. 13. Reduce 3pk. 5qt. 1pt. to the fraction of a bushel. 14. Multiply 83 by 10.

15. Divide 93 by 4.

16. Divide by 9.

17. Divide 18 by .

18. Reduce 374 to a mixed number.

19. Reduce 112 to a whole number.

20. Multiply 21. Reduce

by 11.

of

off to a simple fraction.

22. Subtract

from 3.

153. Mode of taking a mixed number from a whole or mixed number?

23. Reducer, , and to equivalent fractions that have a common denominator.

24. Reduce 1, 14, and 37 to equivalent fractions having the least common denominator.

25. Reduce and to equivalent fractions having a common numerator.

26. Reduce, f, and 18 to equivalent fractions having the least common numerator.

27. Reduce to a simple fraction.

43
6층

38. Subtract

of a gill from † of a gallon.

39. Add 1, 5, 15, 15, and 15 together.

40. From 3 take 33.

41. Five gallons, 3 quarts, 1 pint, and 3 gills, are what part of 1 gallon? (See Art. 151, Note 3).

42. Three pecks are what part of 3 pecks?

EXAMPLES IN ANALYSIS.

154. We analyze an example when we proceed with it, step by step, according to its own conditions, without being guided by any particular rule.

Ex. 1. If 4 tons of hay cost $48, what will 7 tons cost?

SOLUTION. If 4 tons cost $48, then 1 ton will cost of $48, which is $12; and if 1 ton cost $12, then 7 tons will cost 7 times $12, which is $84, Ans,

2. What is the value of 12 acres of land, if 3 acres cost $81? Ans. $324.

3. What is the cost of 16 barrels of flour, if 3 barrels cost $24?

4. If a man can cut 8 cords of wood in 4 days, how much will he cut in 7 days?

5. If 1 ton of hay costs $15, what will of a ton cost? SOLUTION. One ton costs $15; .. of a ton costs of $15 $3, and cost 4 times $3 $12, Ans.

6. What is the value of

acre?

of an acre of land, at $40 per
Ans. $35.

7. If 6 men mow 12 acres of grass in a day, how many acres will they mow in & of a day?

8. If a man cradle 18 acres of wheat in 9 days, how many acres will he cradle in 5 days?

9. Paid $6 for 2 of a yard of velvet; what was the price per yard?

SOLUTION. Since $6 were paid for of a yard,

cost of $6 $2, and .. 4, or a whole yard, cost 4 times $2= $8, Ans. 10. If of a yard of ribbon cost 63 cents, what will a yard

cost?

11. If of an acre of land cost $75, what is the price per acre?

12. If 234 bushels of potatoes grow on of an acre, how many bushels will grow on an acre?

13. If of a farm cost $4200, what cost of it?

SOLUTION. If cost $4200, then costs $1400, and cost 4 times $1400 $5600. farm costs $5600, .. of it costs of $5600 = 5 times $800 $4000, Ans.

=

of $4200= Now the whole

$800, and cost

14. If of a cord of wood are bought for $33, what will of a cord cost?

15. If of a ship are worth $8769, what is the value of § of her?

16. If of the distance from A to B is 32 miles, what is of the distance from A to B?

17.

If 3 men build

of a rod of wall in an hour, how many

rods will 4 men build in 6 hours?

18. If 6 men can do a piece of work in 3 days, how long will it take 4 men to do the same work?

19. What cost 6 lb. of sugar, at 83c. per lb. ?

20. What shall I pay for 161lb. of rice, at 4c. per lb.? 21. Bought 4lb. of raisins, at 123c. per lb., and paid for them in eggs, at 16 c. per dozen; how many dozen did it take?

22. What cost 124lb. of pork, at 6c. per pound?

23. If g of a bushel of wheat cost $14, what is the cost of 121 bushels?

24. If 7 bbl. of flour cost $56, what will 34bbl. cost?

25. If 24 cords of wood will pay for 27 gallons of molasses, how many cords will pay for 4 times 27 gallons?

Ans. 4 times 2 cords, viz. 9 cords. 26. What cost 12 yards of silk at $14 per yard?

27. How many times will a wheel that is 9 feet in circumference turn round in running 20 miles?

28. How many cubic feet in a box that is 6ft. long, 5}ft. wide, and 33ft. deep? Ans. 117. (See Art. 104).

29. How many bottles containing 13 pints each are required to bottle 21 gallons of wine?

30. What costs a farm of 75 acres at $961 per acre?

31. If it costs $84 to carry 13cwt. 3qr. 53 lb. 8 miles, how far can the same be carried for $161⁄2?

32. Bought of a 20-acre lot, and sold of the part purchased; how much had I remaining?

33. If 33 bushels of oats will sow an acre, how many bushels will sow 7 acres ?

34. A staff 3ft. long cast a shadow of a foot at 12 o'clock; what is the length of a shadow cast by a steeple 125ft. high, at the same time?

35. If a staff 3ft. long casts a shadow of of a foot at 12 o'clock, what is the hight of a steeple that casts a shadow 31 ft., at the same time?

36. Sold a watch for $433, which was of its cost; what was its cost?

37. How many pounds of butter in 24 firkins containing 331 lb. each, and what is it worth at of a dollar per pound?

38. If 6 is of some number, what is 5 times that number? Ans. 44. ANALYSIS. If 6 is 2, then is of 6, which is 2, and are 4 times 2 8. Since 8 is the number, 5 times the number will be 5 times 8 = 44, Ans.

Ans. 4.

39. If 12 is of some number, what is 73 times that number? 40. Fifteen is of how many times 10? ANALYSIS. If 15 is, then is } of 15= = 5, and are 8 times 540. Now 40 is 4 times 10; .. 15 is 10, Ans.

of four times

Ans. 22.

41. Twenty-four is of how many times 2?
42. Thirty-five is of how many times 5?
43. Seven ninths of 72 are of how many times 7?

ANALYSIS. One ninth of 72 is 8, and if 56 is, then is 4 of 56, which is 14, and 70. Now 70 is 10 times 7; .. 3 of 72 are 44. Three eighths of 40 are

Ans. 10.

are 7 times 8=56; § are 5 times 14= of ten times 7, Ans.

of how many times 5?

Ans. 7.

45. Seven eighths of 48 are 4 of how many times 8? 46. Six fifths of 30 are g of how many sixths of 24?

Ans. 8.

=

:36;

ANALYSIS. One fifth of 30 is 6, and § are 6 times 6: if 36 is, then is of 36=4, and are 8 times 4 = 32. Now of 24 is 4, and 4 is contained 8 times in 32; .. § of 30 are of eight sixths of 24, Ans.

47. Five eighths of 64 are # of how many thirds of 75? 48. Four sevenths of 35 are of how many eighths of 40? 49. Of the inhabitants of a certain town, are farmers, 4 mechanics, manufacturers, students and professional men, and the remainder, numbering 246, are engaged in various occupations. What is the population of the town? Ans. 3280.

50. What would be the population of the town mentioned in Ex. 49, all the conditions remaining the same except that 246 shall be changed to 123?

Ans. 1640.