42. How many times can 5 gallons of vinegar be drawn from a barrel that contains 311⁄2 gallons?

43. A farmer received $2383 for some corn at $ § per bushel. How many bushels did he sell?

44. A certain kind of barbed wire weighs 1 lb. per rod. How much does it weigh per foot?

45. If it takes 185 yards of canvas to make a tent, how many tents can be made out of 150 yards?

46. If it requires 44 cubic yards of earth to level the lawn in front of Dr. Robinson's house, how many loads of 12 cubic yards will be needed?

47. If a corn-fed hog gains 11 pounds for each bushel of corn that he eats, how many bushels will increase his weight 701 pounds?

48. An experiment in feeding wheat showed that a hog gained 13 pounds for each bushel of wheat fed. How many bushels of wheat were required to increase his weight from 225 pounds to 3977 pounds?

250. Simplifying complex fractions.

You have learned that fractions indicate division, the numerator being the dividend and the denominator the divisor.

We may indicate the division of a fraction by an integer, of an integer by a fraction, or of a fraction by a fraction, in fractional form, by writing the dividend above a line and the divisor below.

We may write, 3 ÷ 6 like this,; 8 like this, and | ÷ ÷ like this,

Such indicated expressions of division are sometimes called complex fractions.

When the indicated division is performed, the complex fraction is said to be simplified.

252. Finding what part one number is of another.

1. What part of 4 is 3? of 6 is 2? of 12 is 8?

2. What part of $8 is $4? of 3 pints is 2 pints? of 4 fifths is 2 fifths? of is ? of is ? of is?

3. What part of 1 pound is 8 ounces? of 4 yards, or 12 feet, is 6 feet? of, or 2, is ? of § is 1, or ?

4. Tell how to find what part one number is of another.

2. What part of 144 is 80? of is? of 12 is ?

PROG. COMPL. AR.- - 10

19. If 26 pounds of cream produced 63 pounds of butter fat, what part of the cream was butter fat?

20. The celery from an acre of land sold for $2183 and the cost of raising it was $871. What part of the selling price was

the cost?

21. The height of the Statue of Liberty is about 150 feet, and the length of the forefinger holding the torch 8 feet. What part of the whole height is the length of the forefinger? 22. A public park has an area of 325 acres, of which 108-7 acres are occupied by a lake. What fractional part of the park does the lake occupy?

254. Comparison of fractions.

1. Compare within this way: ÷ = 2; that is, is 2 times.

In the same way compare with ; with ; 1 with 1; } with; with; with 1.

of 3.

2. Compare with in this way: 1; that is, is

=

In the same way compare with ; with; with; with with ; with 2.

3. Compare with ; with; with ; with §; with 1; with 1; 14 with 1; with 11.

17. Compare 1 with. When of a dozen bananas costs 5 cents, find the cost of 14 dozen.

18. Compare with 14. When 15 quarts of strawberries cost $11, how many quarts can be bought for $4?

19. If my watch gains of a minute in 3 days, in how many days will it gain 1 minutes?

20. If 24 bunches of celery cost $23, how many bunches can be bought for $3?

21. If 3 pounds of live cocoons yield of a pound of silk, how many pounds of cocoons are required for of a pound of

silk?

22. John walked 21 miles in of an hour. how long would it take him to walk 14 miles?

At that rate,

13. Compare with

8. 61 with 74

11. If of a barrel of flour makes

231 loaves of bread, how many loaves will of a barrel make? 14. When 18 barrels of cabbages can be bought for $221, how many barrels can be bought for $71?

15. Compare 3 with 3. If a woman receives $3 for picking 40 quarts of strawberries, how many quarts must she pick to earn $33 ?

16. A farmer raised 63 tons of hay on 4 acres.

crop was 861 tons, how many acres of hay had he?

If his whole

17. If an automobile runs 8 miles while a train runs 261 miles, how far does it go while the train runs 77 miles?

18. When the cost of transporting 90 cans of milk from Medina, Ohio, to Cleveland is $131, how many can be transported for $11?

19. If it takes 3 bushels of seed to sow 41 acres of land, how many bushels are needed to sow 28 acres?

20. An orchard yielded 4271⁄2 barrels of apples, averaging 313 barrels to 10 trees. Find the number of trees in the orchard.

MISCELLANEOUS EXERCISES

257. 1. Find the cost of 48 yards of linen at $ per yard.

2. At a certain gold mine it costs $ a ton to mine the ore. How many tons of gold ore can be mined for $611? Find the cost of crushing this quantity of ore at $1 per ton.

3. A train running from Boston to Providence averages 61 miles every 7 minutes. What is its rate per hour? How long does it take the train to go from one city to the other, the distance being 49 miles?

4. The coal used one year to run the trains of a Texas railroad was estimated to be equivalent to 910,938 barrels of oil, reckoning 1 ton of coal to 31 barrels of oil. How much coal was used?

5. A woman in Ceylon picks 16 pounds of tea leaves in one day from full-grown plants, but only 7 pounds from young plants. At per pound, how much more does she earn per day by picking from old plants?