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(a) Find the sum of the nine quotients. *

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See page 106, problems 29 and 30.

7. 11

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(b) Find the sum of the nine quotients. †

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*Why is the sum of the nine quotients equal to (46 +375 + 196) × 5? + Why is the sum of the nine quotients equal to (+12+11) × 4?

Fractions.

196. TO REDuce Complex FRACTIONS TO SIMPLE

FRACTIONS.

Observe that every reduction of a complex fraction may be regarded as a problem in division.

014100

is read, divided by . J = 2 of 4 = 1 = 4.

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(a) Find the sum of the four fractions.

Observe that a complex fraction may be reduced to a simple fraction by multiplying its numerator and denominator by some number that will in each case give an integral product. When this number can be easily discovered by inspection this is a convenient method of reduction: thus ==

2 1 7 X 2

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2. Peter Lundy earned $650 in one year; of thi expended $520. What part of his earnings did he Page 85, problems 1 and 2.

3. A lady owned § of an acre of land. How man of an acre did she own?

4. Benton walked of a mile. Express the dis walked in 160ths of a mile.

Page 91, problems 1 and 6.

5. In a certain furnace of a ton of coal was co in one day, and of a ton the next day.

ton was consumed in the two days?

What p

6. Mr. Luker has three lots of land ; in the first 1 are of an acre; in the second, of an acre, and third, of an acre. How many acres in all?

Page 91, Art. 186, problems 3 and 4.

7. Of of a mile of board fence of a mile was What part of a mile remained?

8. Mr. Reynolds had put into the bank of his salary; he drew from this money a sum equal to salary. What part of his salary remained in the ban Page 92, Art. 187, I., problems 4 and 5.

tons.

9. From 52 tons of hay, were sold and deliver How many tons remained of the unsold hay? 10. On Monday James rode on his wheel 47 mil Tuesday he rode 18 miles. How much further did Monday than Tuesday?

Page 93, Art. 188, I., problems 1 and 5.

12

11. If a street car makes a round trip in of an hour, how long a time can it make 4 such trips?

in

12. If yd. of ribbon are required to trim a hat, how much ribbon will be required to trim 8 such hats?

Page 93, Art. 188, II., problems 1 and 5.

13. At 3 dollars a cord, what is the cost of 7 cords of wood?

14. If Henry rides his wheel at the rate of 43 miles an hour, how far does he ride in 5 hours?

Page 94, Art. 189, I., problems 1 and 4.

15. If of a yd. of ribbon is cut into 4 equal pieces, what part of a yard is each piece?

16. John hoes 4 rows of corn in § of an hour. In what part of an hour does he hoe 1 row?

Page 94, Art. 189, II., problems 1 and 5.

17. A horse traveled 17 miles in 3 hours. What was his rate per hour?

18. A farmer divided a field containing 18 acres into 4 equal lots. How many acres in each lot?

Page 96, Art. 190, I., problems 1 and 5.

19. At $345 an acre, what is the cost of acre?

20. At $263 an acre, what is the cost of

acre?

Page 96, Art. 190, II., problems 1 and 9.

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21. A piece of land in the form of a rectangle is of a mile long and of a mile wide. The piece is what part of a square mile?

22. Ata dollar per yard, what is the cost of of a yard of silk?

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