239. Numbers to be compared with each other, must be so far of the same nature, that one may properly be said to be a part of the other.

Thus, we may compare a day with a week, since the one is the seventh part of the other; but we cannot say, that a day is any part of a mile, therefore a day cannot be compared with a mile.

240. PRINCIPLE.-Only like numbers are so related as to be compared with each other.

241. To find what part one number is of another.

2. What part of 9 is 5? Of 12 is 7? Of 24 is 18 ? 3. 10 yards are what part of 25 yards? 8 pounds, of 20 pounds? 9 eggs, of a dozen ? 4. $15 are what part of $50? of 90 days? 6 days, of a week?

10 ounces, of a pound? $60, of $72? 9 days, 7 months, of a year?

5. If an acre of land can be bought for $48, what part of an acre cabe bought for $8? For $12? $16? $24? 6. What part of 3 is ?

ANALYSIS.-1 is of 3, and § of 1 is § of of 3, or 1× =

Or, 3 = 24; the relation of 24 to § is the same as that of their numerators 24 and 5, or. Hence is of 3.

7. What part of 9 is ? Of 8 is? Of 20 is ?

8. What part of 15 is 14?

Of 18 is 24? Of 25 is 61?

9. of a month is what part of 8 months?

10. What part of is ?

ANALYSIS.—1 fifth is 4 of 4 fifths, and 1, or 5 fifths, is 5 times

or; hence is of, or 19, equal to §.

Or, =1, and

that of 10 to 12, or

18, and the relation of to is the same as

13. A man having $150, gave $25 for a robe, and of the remainder for a harness. What part of $150 had he left?

14. Bought a horse for $275, and sold him for $160. For what part of the cost was he sold?

15. If from 18 yards of cloth 23 yards are cut, what part of the whole is taken?

16. If 15 tons of coal cost $112, what part of $1121 will of a ton cost?

243. To find a number when a fractional part of it is given.

1. 7 is of what number?

ANALYSIS.-7 is of 5 times 7, which is 35. Hence 7 is of 35.

ANALYSIS.

of 36, or 12;

Since 36 is of a certain number, of the number is and the number is 4 times 12, or 48.

13. 36 is of how many times 4? ANALYSIS. 36 is of 8 times of 36 which is 32, and 4 is con tained in 32, 8 times. Hence 36 is of 8 times 4.

?

of?

17. is of how many times of

18. of 56 is of what number?

ANALYSIS.-3 of 56 is 3 times of 56, which is 21; and 21 is of 10 times of 21, which is 30. Hence of 56 is 1 of 30.

19. of 27 is of what number?

20. of of 64 is of what number?

of what number?

21. of of 72 is of of what number?

22. of 54 is of how many times 5? 7? 8? 9? 23. of of 63 is of of how many times 10? 9? 24. of 56 is of 3 times what number?

ANALYSIS.— of 56 is 32, and 32 is of 36, and 36 is 3 times of 36, which is 12. Hence of 56 is of 3 times 12.

25. of 64 is

of 9 times what number?

26. § of 21 is

of 8 times what number?

27. Paid $60

of a bookcase.

for a sideboard, which was of the cost What was the cost of the bookcase?

28. A scarf cost $1%, which was of the cost of a vest What was the cost of the vest?

29. Paid $100 for a sleigh, which was of 3 times what Į paid for a harness. What did I pay for the harness? Written Exercises of this kind are included in the review examples

REVIEW OF FRACTIONS.

ORAL

EXAMPLES.

244. 1. What fraction added to

2. What number taken from 25

3. If the sum of two fractions is

, what is the other?

will make § ?

will leave 7?

and one of them is

4. From what number must 3§ be taken to leave 51 ? 5. A boy spends of his earnings for board, and clothing. What part has he left?

for

6. The less of two numbers is 5%, and their difference 7. What is the greater?

7. What number divided by will give a quotient of 1? 8. The product of two numbers is 4, and one of them is 18? What is the other?

9. If 2 be added to both terms of the fraction, will its value be increased, or diminished, and how much?

10. If 2 be added to both terms of the fraction §, will its value be increased, or diminished, and how much?

11. If a box of tea cost $213, what will of a box cost? 12. A man owning of a steam-mill sold of his share. What part of the whole mill does he still own?

13. A farmer sold 40 acres of land, which was of his whole farm. How many acres were there in his farm? 14. A man sold of his farm, and had 100 acres left. How many acres had he at first?

15. Bought a watch and chain for $120, the chain costingas much as the watch. What did each cost?

16. A, B, and C together own a yacht. A owns of-it, and B. of it. What part does C own?

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