RULE. I. Reduce integers and mixed numbers to improper fractions.

II. Invert the terms of the divisor, and proceed as in multiplication.

of J.

Ans. 1.

17. At of a dollar a pound, how many pounds of sugar

can be bought for 4 of a dollar?

Ans. 5 pounds.

18. At of a dollar a pint, how much wine can be bought for of a dollar? Ans. of a pint. 19. At of of a dollar a yard, how many yards of ribbon can be bought for of a dollar? Ans. 2 yards. 20. At of a dollar a yard, how many yards of silk can be bought for of a dollar? Ans. 24 yards.

21. A man owning of a copper mine, divided his share equally among his sons, giving them each; how many sons had he? 22. If of a bushel of pears cost of a dollar, what 异

will 1 bushel cost?

Ans.

Ans. 2.

of a dollar. bushel, can be

23. How much corn at of a dollar a

bought for of a dollar.

PROMISCUOUS EXAMPLES.

1. In 25 pounds how many 16ths of a pound?

2. Reduce 41 to a mixed number.

3. Reduce to its lowest terms.

Ans. 11.

Ans. .

4. In 1852 of a day how many days?

5. Change 42 pounds to sevenths of a pound. 6. Reduce 21 to an improper fraction.

7. Reduce 126 to thirds.

Ans. 12.

Ans. 380.

8. Reduce & to its lowest terms.

Ans.

9. Reduce and to a common denominator.

10. Reduce 36 to a fraction whose denominator is 12.

11. What is the sum of, and ?

12. Add together, and 3.

13. What is the difference between and ?

Ans. 13.

Ans. 48.

14. Reduce, and to a common denominator. 15. Sold 93 cords of wood to one man, and 12 to another; how much did I sell to both?

16. Paid 87% dollars for a horse, and 624 dollars for a wagon; how much more was paid for the horse than for the wagon? Ans. 25 dollars.

17. A farmer having 2341 acres of land, sells at one time 42 acres, at another time 61, and at another 704 acres; how many acres has he left? Ans. 60 acres. 18. A speculator bought 120 bushels of wheat, for 136 dollars, and sold it for 1974 dollars; what did he gain? 19. Bought 12 pounds of coffee at of a dollar a pound, and 9 pounds of tea at of a dollar a pound; what was the cost of the whole? Ans. 8 dollars.

20. Bought 10 bushels of wheat, at 14 dollars a bushel, and 14 bushels of corn, at of a dollar a bushel; which cost the more,.and how much?

Ans. The wheat, 34 dollars.

21. Paid 12 dollars for some cloth, at the rate of 3 of a dollar a yard; how many yards were purchased?

22. If 8 oranges cost of 14 dollars, what will 1 orange cost? Ans. of a dollar.

23. A man bought of a farm and sold of his share; what part of the whole farm did he sell? what part had he left? Ans. Sold 14. 24. If a barrel of sugar is worth 22 dollars, what is of it worth? Ans. 15 dollars. 25. How many hours will it take a man to travel 136 miles, if he travel 34 miles an hour? Ans. 41 hours. 26. How many barrels of apples can be bought for 18 dollars, at 1 dollars a barrel? Ans. 15 barrels. 27. If the smaller of two fractions be, and the difference, what is the greater? Ans. .

Ans.

28. If the sum of two fractions is 1, and one of them is, what is the other? 29. If the dividend be, and the quotient, what is the divisor? Ans. 13. 30. If the divisor be, and the quotient 33, what is the dividend? Ans. 2 31. How many bushels of oats worth of a dollar a bushel, will pay for of a barrel of flour worth 9 dollars a barrel? Ans. 15 bushels.

32. At of a dollar a rod, what will it cost to dig of of 5 rods of ditch? Ans. dollars.

33. If a man has 243 bushels of clover seed, and he sells of it, how much has he left?

34. A man had 6 lots of land,

Ans. 6 bushels.

each containing 37

acres ; how many acres did they all contain ?

35. If of a ton of hay can be bought for 15 dollars,

what part of a ton can be bought for 1 dollar?

DECIMAL FRACTIONS.

NOTATION AND NUMERATION.

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

Decimal fractions are commonly called decimals.

Since, 180 = 1886, etc., the denominators of decimal fractions increase and decrease in a tenfold ratio, the same as simple numbers.

104. In the formation of Decimals a unit is divided into 10 equal parts, called tenths; each of these tenths is divided into 10 other equal parts called hundredths; each of these hundredths into 10 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.

105. The Decimal sign (.) is always placed before decimal figures to distinguish them from integers. It is commonly called the decimal point. Thus,

And universally, the value of a figure in any decimal place is the value of the same figure in the next left hand place.

106. The relation of decimals and integers to each other is clearly shown by the following

DECIMAL NUMERATION TABLE.

Hund, of thousands.
Tens of thousands.
or Millions.

Thousands.
Hundreds.
Decimal Sign
Tenths.
Tens.
Units.

Hundredths.
Thousandths.
Ten-thousandths.

Hundred-thousandths.

• Millionths.

5 7 3 275 4.57325 6

By examining this table we see that

107. Since the denominator of tenths is 10, of hundredths 100, of thousandths 1000, and so on, a decimal may be expressed by writing the numerator only; but in this case the numerator or decimal must always contain as many decimal places as are equal to the number of ciphers in the denominator; and the denominator of a decimal will always be the unit 1, with as many ciphers annexed as are equal to the number of figures in the decimal or numerator. The decimal point must never be omitted.

4. Write one hundred twenty-five thousandths.

5. Write eighteen thousandths.