12. A man spent of his money and had $21 left: how much money had he at first?

13. A boy gave 24 cents for a slate, which was of his money: how much money did he have? 14. A man pays $25 a month for house-rent, which is of his monthly salary: what is his salary?

15. A farmer sold a cow for $45, which was more than he paid for her: what was the cost of the cow? 16. A man sold of a farm for $1500: at this rate,

what was the value of the farm?

LESSON XVI.

Miscellaneous Problems.

1. Reduce 18 to an improper fraction.

2. Reduce 1 to a mixed number.

3. Reduce, §, and 7 to a common denominator. 4. Add †, †, 4, and 15.

5. Add 28%, 401, 633, and 193.

6. From
7. Multiply

take . From 28 take 163.
by 7; 13 by ; 2 by 4.
8. Multiply 137 by 15; 256 by 21g.

9. Divide 12 by ; by 12; by .

10. Divide 243 by 11; 256 by 51.

11. what? -? z × z? J÷j? 공

7 +

=

12. There are 5280 feet in a mile: how many feet

in of a mile?

13. A vessel is worth $6000, and the cargo is worth as much as the vessel: what is the value of the cargo?

14. A man sold of his farm to one neighbor and of it to another: what part of the farm has he left?

of a factory sold

15. A man owning of his share what part of the factory did he sell? What part does he still own?

16. There are 16 feet in a rod: how many feet in 66 rods?

17. There are 5 yards in a rod: how many rods in 66 yards?

18. At $6 a barrel, how many barrels of flour can be bought for $150?

19. If

of a ship is worth $12000, what is the whole ship worth?

20. A man owning of an estate sells of his share for $2400: at this rate, what would be the value of the estate?

21. A farmer had 2 fields of wheat; the first yielded 840 bushels, which was of the amount yielded by the second field: how many bushels did the second field yield?

22. A man owning of a ship sells of his share. for $4400 at this rate, what is the value of the ship?

23. The value of a certain ship is $9760, and

of the value of the ship is

of the value of the

cargo: what is the value of the cargo?

QUESTIONS FOR REVIEW.

What is a fraction? What does the denominator denote ? The numerator? What are the terms of a fraction?

What is a mixed number? What is meant by 183? Ans. 18+. When is a fraction called proper? When improper? When is the value of an improper fraction equal to 1?

How is an integer reduced to a fraction? How is a mixed number reduced to a fraction? What kind of a fraction is the result? Give examples. How is an improper fraction

reduced to a whole or mixed number?

How is a fraction reduced to lower terms? On what principle does the process depend? How may a fraction be reduced to its lowest terms by one division?

How are fractions having a common denominator added or subtracted? When fractions have different denominators, how are they added or subtracted? How may mixed numbers be added? How may they be subtracted?

In what two ways may a fraction be multiplied by an integer? How may an integer be multiplied by a fraction? Give the rule for multiplying a fraction by a fraction. What is a compound fraction? How is a compound fraction reduced to a simple fraction?

In what two ways may a fraction be divided by an integer? How may an integer be divided by a fraction? How may a fraction be divided by a fraction?

N. B.-If it is thought best to teach United States Money before Decimal Fractions, introduce Section IX at this point.

I. A.-8.

SECTION VIII.

DECIMAL FRACTIONS.

LESSON I.

Numeration and Notation.

1. If a unit be divided into ten equal parts, what is one part called?

2. If a tenth of a unit be divided into ten equal parts, what is one part? What is

of?

3. If a hundredth of a unit be divided into ten equal parts, what is one part? What is of Tho? 4. What part of one tenth is one hundredth? What part of one hundredth is one thousandth? 5. How do one tenth and one hundredth compare with cach other in value? and

5

?

6. How do one hundredth and one thousandth compare with each other in value?

and Too?

3 1000

7. How, then, do the fractional units, tenths, hundredths, and thousandths, compare in value?

Art. 79. The fractional units, tenths, hundredths, and thousandths may be expressed on a scale of tens, by writing the tenths in the first order at the right. of units, the hundredths in the second order, and the thousandths in the third order, and placing a period between the orders of units and tenths, to distinguish the fractional orders from the integral orders.

Thus, 2.5 denotes two units and five tenths; 4.06 denotes four units and six hundredths; .05 denotes five hundredths; and .004 denotes four thousandths.

8. How many tenths in .3? In .6? In .7? 9. How many hundredths in .02? In .04? .07? 10. How many thousandths in .005? In .008? 11. How many tenths and hundredths in .24? .06? 12. How many tenths, hundredths, and thousandths in .356? In .523? In .603? In .041?

Art. 80. Two tenths and five hundredths (25) denote twenty-five hundredths; and two hundredths and five thousandths (.025) denote twenty-five thousandths.

13. How many hundredths in .34? In .45? In .06? 14. How many thousandths in 246? In .048? In .605? In .007? In .403? In .075?

Art. 81. Such fractional numbers as 24 and 208 are called Decimal Fractions, or Decimals, and the orders of which they are composed are called Decimal Orders.

The first decimal order is tenths; the second, hundredths; and the third, thousandths.

Copy and read the following decimals:

Art. 82. When fractions denoting tenths, hundredths, thousandths, etc., are expressed on a scale of ten, they are said to be expressed decimally. The right-hand figure is written in the order indicated by the name of the decimal.

20. Express decimally 25 hundredths. 21. Express decimally 205 thousandths.