19. A coal dealer paid $375 freight for transporting coal from Scranton to Hudson. If the price was $3 per

ton, how many tons were transported?

20. How many pounds of beef, at 18 cents per pound, can be bought for $17.48?

21. A farmer hires an equal number of men and boys, and

pays for a man and boy $2 a day. If the pay roll

is $84 a day, how many men and boys does he hire? 22. When 815 acres of land cost $1297, what will of an acre cost?

23. A city speculator in land divided of an acre into lots of of an acre each, and sold them all for $13,426. What was the average price per lot?

24. For of of a ship the sum of $6394 was received; what is the value of the ship?

25. A vessel sails 17 miles per hour; how many miles will she sail in 263 hours?

26. George is 13 years old, Henry is as old as George, and John's age is 14 that of Henry; what is the age of John?

27. There are 16 feet in one rod; how many feet are there in 845 rods?

28.

How many feet around a field, each one of whose four

sides measures 75 rods?

29. A schooner sails on the average 175 miles a day; how far will she sail in a week?

30. At the rate of 83 miles per hour, how many miles will a ship sail from a quarter past three A.M. to a quarter before six P.M.?

31. Reduce of 5 of 7 of 15 to a simple fraction in its lowest terms.

32. George Ward inherited from his father of a farm containing 377 acres. He divided his share equally among his four sons; how many acres would each

one of the sons receive?

33. How many pounds of sugar, at 93 cents a pound, can be bought for $1.52?

34. For 23 baskets of peaches, a grocer gave $20.59; what was the price per basket?

35. A farmer sold 42 bushels of potatoes for $26.58; what was the average price per bushel?

36. At 371⁄2 cents per yard, how many yards of lace can be bought for $51?

37. A farmer sold 6 bushels of apples for $4.871; what was the price per bushel?

38. When 63 bushels of apples bring $3.90, what are they worth a peck? (Four pecks make a bushel.)

39. At 60 cents a pound, how many pounds of tea can be bought for $4.65 ?

40. If of a yard of cloth cost 80 cents, what should be paid for of a yard?

41. The cost of fencing a lot 8 rods in circuit is $64, what is the rate per rod?

42. A roll of carpeting containing 202 yards is cut into pieces of 25 yards each, and each piece is sold for $321. Required the number of pieces, and the price per yard.

43. When 35 bushels of turnips cost $28.60, what should be paid for of a bushel?

44. How many yards of cloth can be bought for $10.80, if of a yard cost 63 cents?

LEAST COMMON DENOMINATOR.

123. A fraction is changed to higher terms by multiplication.

In either of the two forms & or the value of the fraction is 2.

124. Hence, to reduce a fraction to higher terms,

Multiply both terms of the fraction by that number which will change the given denominator to the required denomi

nator.

The required multiplier is found by dividing the required denominator by the denominator of the given fraction.

125. Similar fractions are fractions that have a common denominator.

All fractions must be expressed as similar fractions before they can be added or subtracted, and in all cases it is best to express them with the least common denominator. (L.C.D.)

126. The least common denominator of two or more fractions is the least common multiple of their denominators. Reduce, to similar fractions.

The least common multiple of the denominators 2, 3, 4 is 12. It is therefore necessary to reduce 1, 1, 1 to 12ths, by the method explained in 124, and we have f f f

127. Hence, to reduce fractions to similar fractions,

Find the least common multiple of the denominators ; this will be the required denominator. Divide this denominator by the denominator of each fraction.

Multiply the first numerator by the first quotient, the second numerator by the second quotient, and so on.

The products will be the numerators of the equivalent fractions.

128. Add 3, 4, 5.

ADDITION OF FRACTIONS.

These fractions reduced to similar fractions become 12, 12, 12, and f1⁄2 + 12 + 12 = }} = 21⁄2 = 24.

129. Hence, to add fractions,

21. Ans.

Reduce the fractions to similar fractions, and write the sum of the numerators over the common denominator.

130. If any of the expressions are integers or mixed numbers, add together separately the integers and the fractions, and find the sum of the results.

Find the sum of 2,8%, 17, 511.