196. Simplifying complex fractions.

Since division may be indicated by a fraction, 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 ÷ 4 like this,; 9-- 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.

FRACTIONAL RELATIONS

198. Finding what part one number is of another.

1. What part of 6 is 4?

EXERCISES

SOLUTION. Since 1 is of 6, 4 is 4 times of 6, or of 6; that is, 4 is

14. Of 12 boys camping at Moose Lake, 4 went fishing and the rest hunting. What part of the party went fishing? what part went hunting?

15. One boy caught 12 fish, another 8, and another 4. The fourth boy caught none. The hunters shot nothing. What part of the fish did each of the first three boys catch? what part of the whole party was unsuccessful?

16. Three boys went home after one week, the rest stayed two weeks. What part stayed one week? two weeks?

17. A grocer's boy delivered 48 packages-8 at one house, 4 at another, 6 at another, and the rest at the Home Restaurant. What part did he deliver at each place?

18. He solicited orders at 30 houses and received 18 orders. What part of his visits resulted in orders? what part did not?

19. Out of a class of 50 girls and 30 boys graduating from a grammar school, 44 girls and 20 boys entered the high school. What part of the girls entered the high school? what part of the boys? what part of the class?

of 12; but is the same part of 12 that the numerator 9 is of the numerator 10.

Observe that the same result may be obtained by dividing by .

SUGGESTION.

Reduce both numbers to fourths, or divide 5 by 61.

cars would there have been if it had been of a mile long?

SUGGESTION. What part of is?

24. The winner of a 5-mile automobile race covered the distance in 2 minutes. How far did he go in 13 minutes?

25. If one square foot of sheet iron of an inch thick weighs 20.141 pounds, find the weight, to the nearest thousandth of a pound, of a square foot of an inch in thickness.

26. If a machine makes 350 grape baskets in of an hour, how many baskets does it make in 44 hours?

27. If 220 trees in the Philippine Islands yield 180 pounds of hemp fiber for cordage, how many trees are necessary to provide fiber for a bale of 270 pounds?

28. The average time of transmitting a 20-word cable mes

sage on the first cable was 63 minutes. now be transmitted in of a minute.

Such a message can

What part of the origi

nal speed of transmission is the present speed?

200. Finding the whole when a fractional part of it is given. 1. If of a number is 20, what is of it? of it?

2. If of a number is 16, what is of the number? What is the number?

EXERCISES

201. 1. Our football team won & of the games that it played. It won 12 games. How many games did it play?

SOLUTION.

of the number of games played

= 12.

of the number of games played = } of 12, or 4.
The number of games played = 4 × 4, or 16.

2. One fourth of the domestic reindeer of Alaska one year were fawns. If 2000 were fawns, how many reindeer were

there?

3. The balcony of a music hall holds 400 people. If this is of the hall's capacity, how many people will the hall hold ?

4. A certain steamship can accommodate 300 first-class passengers. This is of the total number that can be carried. How many passengers can the vessel accommodate?

5. In a test for silver of a ton of ore yielded 6 pounds of silver. What was the yield of silver per ton?

6. A ball, or "loaf," of raw rubber when cleansed of impurities for manufacture weighed 9 pounds, or of its original weight. How much did it weigh at first?

7. When a balloon had traveled 800 miles it had completed of its journey. How far did it travel?

8. Of the people who lost their lives in one year in vessels wrecked on our shores, or 20, perished on the Atlantic coast. How many lost their lives in all?

THIRD PROG. AR.- - 7

as many

18. If Holland has 1500 miles of railroad, and only

miles of railroad as of canals, what length of canals has she? 19. Find the cost of the German North Sea Canal, if of the cost, or 17 million dollars, was paid for excavating.

20. The buildings of the great Krupp steel works in Germany cover 150 acres. If this is of the land owned by the company, how many acres do they own?

21. The cost of a British third-class cruiser was $675,000. This was $5000 more than of the cost of a German warship of the same type. How much did the German cruiser cost?

22. One section of a 50-ton anchor chain is 180 feet long. If this section is of the chain, how long is the chain?

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23. Ordinarily the cruiser Charleston has a coal supply of 650 tons, but this is only 3 of her capacity. How many tons of coal can she carry?

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24. In the menagerie Harold saw a test in which a horse pulled a weight of 1875 pounds, or of the weight pulled by an elephant. A camel pulled as much as the horse. What was the pulling strength of each animal?