Ans. 1188.

59

8. 96492 583217

9.

#382864 what?

NOTE.- In example 11, divide 15 by 9, then reduce the remainder to an improper fraction, and divide the fraction by 9.

12. Divide 288 by 18. I

For Dictation Exercises, see Key.

13. Divide 411 by 368.

133. DIVISION OF WHOLE NUMBERS AND FRACTIONS BY FRACTIONS.

ILL. EX., I. How many times is contained in 3?

SOLUTION. is contained in any number twice as many times as 1 is contained in it. 1 is contained in 3, 3 times; .. is contained in 3, 2 X 3 6 times.

1. How many times is 2. How many times is

EXAMPLES.

contained in 6?

contained in 18?

Ans. 18.

Ans. 126.

3. How many times is

contained in 8?

How do you divide by a fraction having 1 for its numerator?

Divide

5.

100 by 15.

6. 31 by z's.

9.

13. If it takes of a yard of cloth to make a vest, how many

vests can be made from 8 yards?

14. If a man walks 1 mile in of an hour, how many miles will he walk in 8 hours?

15. If the cars can run a mile in of an hour, how many miles can they run in 10 hours?

16. At ₫ of a dollar a dozen, how many dozen eggs can be bought for 10 dollars?

ILL. EX., II. Divide 4 by ; that is, see how many times

1 is contained in 4, 4 times; is con6, Ans. tained in 4, 5 times as many times as 1 is contained in it, or 5 × 4 times, and §,

which is 3 times, can be contained in it only as many times as of 5 X 4 times.

is contained in it, or

ILL. EX., III.

1 is contained in 3, 3 of a time; † is contained in, 6× times; § (which is 5 times) is contained in it of 6 x times. The expression then becomes 2X6; after cancelling, 2X2, Ans.

3 X 5

Hence the

4

RULE. To divide a whole number or a fraction by a frac tion; Multiply the dividend by the denominator of the divisor, and divide by the numerator; or,

Invert the divisor, and proceed as in Multiplication.

NOTE. — Reduce mixed numbers to improper fractions before dividing.

--

39. 713 × ÷ † of 71?

40. How many sevenths are there in 3 of 71%÷63? 41. How many times of 14 in 2% X & of 81?

For Dictation Exercises, see Key.

Ans. 12

135. TO FIND THE WHOLE NUMBER WHEN A FRACTIONAL

PART OF IT IS GIVEN.

ILL. EX. 38 is of what number?

1 of 116, and §, or

the entire number, is 5 times of 114; cancelling, the expression be

29X5=48}, Ans.

comes

3

5.

of is

of what number?

Ans. 18.

Ans. 38.

Ans. 1

Ans. 13.

6. 277 is 3 times what number (or of what number)?

7. 182 ÷ 12 × 24 is 34 times what number?

8. From New York to Troy is 150 miles, which is of the distance from New York to Rouse's Point; what is the distance from New York to Rouse's Point?

Ans. 350 miles.

9. Mr. Aborn owns of an acre of land; his neighbor Jones owns as much, which is & of what Mr. Green owns; what does Mr. Green own?

10. If of a piece of work be performed in 25 days, what number of days will be required to do the remainder?

11. Paid $6 a week for board in Boston, which was of what I paid in New York; this was of what I paid in Philadelphia; and this was of what I paid in Washington. What did I pay in Washington?

12. A vessel having lost of her cable, has 200 feet remaining; how many feet had she at first?

SOLUTION. If be lost, will remain; if 200 feet, and, or the whole cable,

13. A ship's crew having lost subsist on 14 ounces a day; what

of

of their bread, are obliged to 5 of 200 feet, = 250 feet. were they allowed at first?

of my money in trade, I now have

14. Having lost $2476.50; what had I at first?

15. A mother and her son together have $45 in a purse; the son's part is as great as the mother's. Required the part of each?

SOLUTION. The purse contained once the mother's money and as much more, (the son's). If 1 (§) times the mother's part = $45, of $45, and 3 × } of $45, = $27, the mother's part; $18, the son's part.

= 2 × of $45,

son's

16. The sum of the ages of a father and son is 155 years, the age being the age of the father; what is the age of each? 17. A body of 4800 troops has as many cavalry as infantry; what is the number of each?

18. A lot of land yielded 4140 bushels of grain in two years, yielding as much the second year as the first; what was the yield each year?

19. What number is that to which if of itself be added the sum will equal 275?

20. A carpenter, who has a number of floors to lay, estimates that it will cost more to lay them with hard pine, worth $28 a thousand feet, than with white pine; what is the price of white pine per thousand?

21. In counting his fowls, a farmer finds that he has 396 in all, which is more than he had the previous year; how many had he then?

22. He has sold his eggs at an average of 134 cents per dozen, which is higher than the previous year; what did they average then?

less than he

23. He is paid for grain $1 per bag, which is was paid last year; what was he paid last year? 24. Mr. Ober owns 50 acres of wood land, of which he exchanges with Mr. Fay for 404 acres of meadow land, which is of what Mr. Fay owned; how much meadow land did Mr. Fay have at first? How much wood land after the exchange was made?

For Dictation Exercises, see Key.