24. How many bushels of oats at $3 a bushel, will pay for of a barrel of flour at $9 a barrel?

25. A man at his death left his wife $12500, which was of of his estate. At her death she left of her share to her daughter. What part of the father's estate did the daughter receive from her mother?

26. Paid $1837 for 3675 bushels of oats. the cost a bushel?

What was

27. A merchant bought a cargo of flour for $21731, and sold it for of the cost, thereby losing $.25 on a barrel. How many barrels of flour did he purchase?

28. A man owning of 156 acres of land, sold of of his share.

How many acres did he sell, and what was the value of the remainder of his share, at $42 an acre? 29. A horse and wagon cost $360; the horse cost 2 times as much as the wagon. Find the cost of the wagon. 30. If $7 will buy 3 cords of wood, how many cords can be bought for $311⁄2?

31. A dealer sold 7 barrels of apples for $32, which was as much as he received for all he had left, at $4 a barrel. How many barrels in all did he sell?

32. If of 9 bushels of wheat cost $131, what will of a bushel cost?

33. A man engaging in trade lost of the money he invested, after which he gained $740, and then, had $3500. What was his loss?

34. A boy having lost feet; the string was then was its original length ?

of his kite-string, added 45o of its original length. What

35. There are two numbers the sum of which is 4, and their difference . What are the numbers?

1383

36. A man invests of his money in cotton, in sugar, in molasses, and the remainder, which is $2542, in dried fruits. What is the amount of each investment, and the total amount?

37. If of 3 times 1, be multiplied by, the product divided by, the quotient increased by 41, and the sum diminished by of itself, what is the remainder?

Reduce to their simplest form :

44. (7+18+3)-(34+28÷32+143)=?

247. 1. If a unit be divided into 10 equal parts, what is each part called? What are 2 parts? 3 parts? 4 parts? 2. What is the fractional unit?

3. If 1 tenth of a unit be divided into 10 equal parts, what is each part called? What are 2 parts? 4 parts? 5 parts? 7 parts? 12 parts? 25 parts?

4. What is of ? of? 4 of 1? £ of 1? 5. If a unit be divided into 100 equal parts, or each tenth into 10 equal parts, what are the parts called?

6. What part of 1 tenth is 1 hundredth ? How many hundredths in 1 tenth ?

7. If 1 hundredth of a unit be divided into 10 equal parts, what is each part called? What are 3 parts? What are 8 parts? 9 parts? 15 parts?

8. What is of of ?

of too? fo of Too?

9. If a unit be divided into 1000 equal parts, or each hundredth into 10 equal parts, what are the parts called? What are 12 parts? 26 parts? 42 parts?

10. What part of 1 hundredth is 1 thousandth? How many 1 thousandths is 1 hundredth ?

NOTATION AND NUMERATION. 248. A Decimal Fraction is one or more of the decimal divisions of a unit. Thus, fo, 1, 10, 1880, etc., are decimal fractions.

109

Decimal Fractions are commonly called Decimals.* (16.)

249. Decimals are like other Fractions, except that their denominators increase and decrease by the uniform scale of 10. The fractional units are, therefore, always tenths, hundredths, thousandths, etc.

250. The Decimal Sign (.), called the decimal point, is used to distinguish a decimal from an integer, and must always be placed before the numerator of the decimal.

75

* The terms fraction and decimal will hereafter be used to distinguish the common from the decimal form of expression. Thus, 10%, and .75, are two forms of expressing the same thing. For convenience we shall call the first form a fraction, and the other a decimal.