22. How many times will 4 gallons of camphene fill a vessel that holds off of 1 gallon? Ans. 101. 23. If 14 acres of meadow land produce 32 tons of hay, how many tons will 5 acres produce? Ans. 11. 24. If 2 yards of silk cost $31, how much less than $17 will 9 yards cost? Ans. $28. 25. If of a yard of cloth cost of a dollar, what will yard cost?

26. A man, having $10, gave of his money for clover seed at $34 a bushel; how much did he buy? Ans. 2 bush. 27. How many tons of hay can be purchased for $119, at $9 per ton? Ans. 12.

PROMISCUOUS EXAMPLES.

1. Reduce,,, and to equivalent fractions whose denominators shall be 24. Ans. H, H, & A. 2. Change to an equivalent fraction having 91 for its denominator. Ans. ff.

3. Find the least common denominator of , 13, 1 of †, 2, 1 of 1 of 1.

4. Add 41, 3, 4 of 13, 3, and 1.

5. Find the difference between of 6 and 4 of 4.

Ans. 1188.

Ans. 4885

6. The less of two numbers is 47564, and their difference

is 128; what is the greater number?

7. What is the difference between the continued products

of 3, 3, †, 4%, and 37, †, 4, ‡ ?

4

Ans. 317.

8. Reduce the fractions and to their simplest form

吾

11

9. What number multiplied by will produce 18257?

10. A farmer had of his sheep in one pasture, in

another, and the remainder, which were 77, in a third pasture; how many sheep had he?

Ans. 140.

11. What will 7 cords of wood cost at of 94 dollars per cord ? Ans. $2411.

12. At of a dollar per bushel, how many bushels of ap1 ples can be bought for 54 dollars?

13. Paid $1837 for 7350 bushels of oats; how much was that per bushel? Ans. of a dollar. 14. If 235 acres of land cost $47253, what will 628 acres cost? Ans. $12601. 15. A man, owning of an iron foundry, sold of his hare for $5404; what was the value of the foundry?

16. 14 less

of 88 14%

Ans. $40555.

is of 3 of what number? Ans. 27.

17. A merchant bought 44 cords of wood at $34 per cord, and paid for it in cloth at of a dollar per yard; how many yards were required to pay for the wood?

18. How many yards of cloth, of a yard wide, will line 201 yards, 11 yards wide?

Ans. 341. 19. If the dividend be, and the quotient, what is the divisor?

20. If the sum of two fractions be §, and one of them be %, what is the other?

Ans.

21. If the smaller of two fractions bet, and their difference, what is the greater?

Ans.

22. If 3 pounds of sugar cost 33 cents, what must be paid for 65 pounds?

23. If 324 bushels of barley can be had for 2591 bushels of corn, how much barley can be had for 2000 bushels of corn? Ans. 2500 bushels.

24. A certain sum of money is to be divided among 5 per sons; A is to have 1, B, C, D, and E the remainder, which is 20 dollars; what is the whole sum to be divided?

Ans. $50.

Ans. 40.

25. What number, diminished by the difference between and of itself, leaves a remainder of 34 ? 26. If of a farm be valued at $1728, what is the value of the whole?

27. Bought 320 sheep at $2 per head; afterward bought 435 at $1 per head; then sold of the whole number at $12 per head, and the remainder at $24; did I gain or lose, and how much? Ans. Lost $44.

28. If 5 be added to both terms of the fraction, will its value be increased or diminished? Ans. Increased

29. If 5 be added to both terms of the fraction, will its value be increased or diminished? Ans. Diminished

30. How many times can a bottle holding of of a gallon, be filled from a demijohn containing of 14 gallons? Ans. 7.

31. Bought of 7 cords of wood for of $32; what did 1 cord cost?

32. Purchased 728 pounds of candles at 163 cents a pound; had they been purchased for 33 cents less a pound, how many pounds could have been purchased for the same money? Ans. 95317. 33. What number, divided by 13, will give a quotient of 91? Ans. 124. 34. The product of two numbers is 6, and one of them is 1846; what is the other?

Ans.

35. A stone mason worked 11 days, and after paying his board and other expenses with of his earnings, he had $20 left; how much did he receive a day?

36. If of 4 tons of coal cost $54, what will of 2 tons cost?

Ans. $5. 37. In an orchard of the trees are apple trees, peach trees, and the remainder are pear trees, which are 20 more than of the whole; how many trees in the orchard?

Ans. 800.

38. A man gave 6 pounds of butter, at 12 cents a pound, for of a gallon of oil; what was the oil worth a gallon? 442 Ans. 100 cents.

39. A gentleman, having 271 acres of land, sold of it, and gave of it to his son; what was the value of the remainder, at $574 per acre? Ans. $4577.

40. A horse and wagon cost $270; the horse cost 14 times as much as the wagon; what was the cost of the wagon? 41. What number taken from 2 times 12 will leave 203? Ans. 111. 42. A merchant bought a cargo of flour for $21733, and sold it for of the cost, thereby losing of a dollar per barrel; how many barrels did he purchase? Ans. 126. 43. A and B can do a piece of work in 14 days; A can do as much as B; in how many days can each do it?

Ans. A, 32 days; B, 24 days.

44. How many yards of cloth of a yard wide, are equal to 12 yards of a yard wide? Ans. 111.

45. A, B, and C can do a piece of work in 5 days; B and C can do it in 8 days; in what time can A do it?

46. A man put his money into 4 packages; in the first he put, in the second, in the third, and in the fourth the remainder, which was $24 more than of the whole; how much money had he? Ans. $720.

47. If $7 will buy 31 cords of wood, how many cords can be bought for $101? Ans. 4. 48. How many times is of 4 of 27 contained in 3 of of 42?

49. A boy lost of his kite string, and then added 30 feet, when it was just of its original length; what was the length at first? Ans. 100 feet.

50. Bought of a box of candles, and having used of 1 them, sold the remainder for 18 of a dollar; how much would a box cost at the same rate? Ans. $53.

51. A post stands in the mud, in the water, and 21 feet above the water; what is its length?

52. A father left his eldest son of his estate, his youngest son of the remainder, and his daughter the remainder, who received $1723 less than the youngest son; what was the value of the estate? Ans. $21114.

DECIMAL FRACTIONS.

143. Decimal Fractions are fractions which have for their denominator 10, 100, 1000, or 1 with any number of ciphers annexed.

1. The word decimal is derived from the Latin decem, which signifies ten.

2. Decimal fractions are commonly called decimals.

=

3. Since 0%, 100 = 1000, etc., the denominators of decimal fractions increase and decrease in a tenfold ratio, the same as simple numbers.

DECIMAL NOTATION AND NUMERATION.

144. Common Fractions are the common divisions of a unit into any number of equal parts, as into halves, fifths, twenty-fourths, etc.

Decimal Fractions are the decimal divisions of a unit, thus: A unit is divided into ten equal parts, called tenths; each of these tenths is divided into ten other equal parts, called hundredths; each of these hundredths into ten other equal parts, called thousandths; and so on. Since the denominators of decimal fractions increase and decrease by the scale of 10, the same as simple numbers, in writing decimals the denominators may be omitted.

In simple numbers, the unit, 1, is the starting point of notation and numeration; and so also is it in decimals. We extend the scale of notation to the left of units' place in writing integers, and to the right of units' place in writing decimals. Thus, the first place at the left of units is tens, and the first place at the right of units is tenths; the second place at the left is hundreds, and the second place at the right is hundredths; the third place at the left is thousands, and the third place at the right is thousandths; and so on.

What are decimal fractions? How do they differ from common fractions? How are they written?