58. 1. How many oranges in of an orange? In 7 In 10 thirds?

thirds? In 9 thirds?

2. How many yards in

10? In 12? In 15?

of a yard? In of a yard? In

3. Prepare the above, on slate or paper, in tabular form;

4. Extend the work to improper fractions whose denominators are 6, 7, 8, etc., to 12, and applying the fractions to bushels, gallons, miles, acres, etc.

5. If 3 books cost 12 fifths of a dollar, what is the cost of 1 book?

SOLUTION. One book will cost 1 third of 12 fifths, or $3.

6. Divide the above by 2, or take of each fraction, by dividing the numerator; thus, of 1; of fofo, etc.

=

7. Prepare table-work on slate or paper;

=

1,

thus,

8. If 4 pounds of coffee cost

of a dollar, what will

1 pound cost? What will 5 pounds cost? 9. If 3 yards of muslin cost

of a dollar, what will 4 yards

cost? 5 yards? 7 yards? 10 yards?

10. If a man walks of 12 miles in 1 hour, how far can he walk in 3 hours? How far in of an hour?

11. If 3 pounds of coffee cost $1%, what will 1 pound cost? What will 5 pounds cost?

12. If 4 yd. of ribbon cost $8, what will 3 yd. cost? 5 yd.?

7 yd.? 10 yd.?

13. If a man walks

of

6 mi. in 1 hour, how far can he of an hour?

walk in 3 hr.? How far in

14. If 5 bu. of oats are worth $15, what is 1 bushel worth? 3 bu.? 6 bu.? 10 bu.?

15. If 3 fourths of a bushel of cranberries are worth $3, what is of 6 bushels worth?

16. At $4 a yard, what will 24 yd. of cloth cost?

SOLUTION. 2 yards will cost 24 times $4; 2 times $4 are $8, and of $4 is $2, which added to $8 make $10.

17. At $10 a barrel, what will bbl. of flour cost? What will of a barrel cost? 24 bbl. ?

18. At of 16 cents a pound, what will of a pound of sugar cost? of a pound? 14 pounds? 21 pounds?

19. At $15 a ton, what will of a ton of hay cost? of a ton? 1 tons? 1 tons?

20. If a barrel of pork cost $15, what will of it cost?? 21. What will § of a bushel of chestnuts cost, at 10 cents a quart? of a bushel at 8 cents a quart?

22. If 10 lb. of sugar cost $.80, what part of 80 cts. will 3 lb. cost? 5 lb. ?

23. If 3 lb. of raisins cost $4, what will 1 lb. cost?

24. If 4 slates cost $8, what will 1 slate cost?

25. If 5 lb. of sugar cost $5, what will 1 lb. cost?

26. At $1 a basket, what will 2 baskets of peaches cost? 5 baskets? 10 baskets?

27. If 2 yd. of cloth cost $10, what is the cost of a yard? Of 1 yd.? Of 2 yd.?

59. 1. Harry paid $2 for a knife, $3 for a book, and $1 for a necktie. What did he pay for all?

WRITTEN SOLUTION. $+$}+$} =what he paid for all.

ORAL SOLUTION. He paid the sum of $3, $3, and $1, which is $11. 2. A grocer sells of a box of tea from a box full. What part of the whole box is left ?

ORAL. There was left the difference between & and §, which is

3. If a man earn $1% a day, what will he earn in 6 days?

WRITTEN. $% 6 = what he will earn in 6 days.

ORAL. He will earn 6 times $1, or $54, equal to $5%.

4. If of a barrel of flour is divided equally among 3 poor families, what part of a barrel will each receive?

WRITTEN. bbl.÷3, or of = what each will receive.

ORAL. Each family will receive of bbl., or of a barrel of flour. 5. If a man earns $15 a week, and spends does he save?

of it, how much

6. If 3 oranges are worth of a melon, what part of the melon is 1 orange worth?

7. Rollin had 18 marbles, and gave of them to Martin. How many marbles did he give Martin, and how many did he keep for himself?

8. Andrew is 18 years old, and his sister Jane is § as old. How old is Jane?

9. Paid $36 for 1 acre of land. What is of it worth? q? ? ?

3

10. If 1 man consume of a pound of meat in a day, how many pounds would 6 men consume?

11. Oliver having 20 qt. of blueberries, sold of them for $. What was that a quart?

DECIMALS.

0;

60. The numbers 1000, 100, 10, 1, 10, 100, 100, etc., increase from right to left, and decrease from left to right, by the same uniform scale of ten. Thus, 1000 is ten times 100 100 is 10 times 10; 10 is ten times 1; 1 is ten times, etc. Also, Too is one tenth of To; To is one tenth of;is one tenth of 1; 1 is one tenth of 10, etc. The value of any decimal figure is always of the value of the same figure in the next place to the left.

61. Decimal fractions may be written in two ways; either as other fractions, the denominator being expressed, or in decimal notation, the denominator being omitted. Thus,

The name of the first order at the right of units is tenths;

of the second, hundredths; of the third, thousandths.

62. The unit is the standard by which we compare all numbers. Therefore, to determine the order of units at a glance, a point is placed on the right of the order of units, and before the order of tenths.

It is written thus, (.), and is called the decimal point. Its only purpose is to determine the place of the order of units, and it must never be omitted.

Thus, in the number 62.55, the point shows the order of units, 2; and as we read sixty-two units, so we read fifty-five hundredths, giving to it the name of the lowest order.

63. When an integer and decimal are written together, the expression is a mixed number (52, 4).

Mixed numbers involving decimals are read in the same manner as mixed numbers involving common fractions.

Thus, .07 is read seven hundredths, .58 is read fifty-eight hundredths, 25.34 is read, twenty-five and thirty-four hundredths.

64. The relation of decimals and integers is clearly shown in the following Table:

Read as follows, always using the word "and" between the integer and decimal:

425 and 37 hundredths. 1046 and 65 thousandths. 32400 and 456 thousandths.

87 and 75 ten-thousandths. 4328 and 169 thousandths.

7000 and

Ten-thousands.

Thousands.
Hundreds.

Tens.

UNITS.

Ten-thousandths.

Thousandths.
Hnndredths.

Tenths.

ten-thousandths.

INTEGERS.