laborers, giving them

33. If $27 be divided among some

each, how many laborers will receive a share?

34. At $33 a cord, how many cords of wood can be bought for $40? For $150?

35. How many bushels of pears at $ a bushel can be bought for $18? For $39?

36. At $6 a ton, how many tons of coal can be bought for $160? For $248?

37. At $1 a yard, how many yards of cloth can be bought for $9? For $24? For $64 ?

46. If of a farm cost $6270, what did the whole cost?

47. How many pounds of tea at $1 a pound, can be bought for $151 ?

48. At $31 a cord, how many cords of wood can be bought for $25 ?

49. If a man spend $3 a day for cigars, in what time will he spend $5} ?

50. If 14 bushels of oats cost $8, what costs 1 bushe!? 51. How many barrels of flour at $9 a barrel, can be bought for of $370?

REVIEW.

ORAL EXERCISES.

249. 1. How many sixths in 4? In 54 ? In 81? 2. Express in higher terms? &; † ; J; fb.

3. Express

in lower terms; 18; 38; 28.

and to their lowest terms.

and to twelftha

or ? or ?

or ?

4. Reduce 5 Change and to twentieths; 6. Which is greater, 7. Name 3 equivalent fractions for ; for ; for 2. 8. Change,t, and to fractions having 48 for a common denominator.

9. Find the least common denominator of the same. 10. For name 3 equivalent fractions in lower terms? 11. Change, 1 and 2 to sixths; and 24 to twentieths. 12. A farmer sold of his grain to one man; to another, and to another; what part of his grain did he sell, and what part had he left?

13. A lady paid of her money for a bonnet, for a shawl, and for a pair of gaiters. What had she left?

14. From 4 tons of coal of a ton was used one month and 14 tons the next; how much was left?

15. If of a box of raisins cost $212, what will of a box cost?

16. If of a yard of silk cost $3, how many yards can be bought for $15 ?

17. Henry bought a box of figs, and John as many. What part of a whole box did both buy?

18. Bought a watch and chain. which was of what the watch cost.

The chain cost $30,

What did both cost"

WRITTEN EXERCISES.

9504

250. 1. Reduce to their lowest terms ; 10368.

25

39

2. Change to integers or mixed numbers, 88; 85,841. 3. Reduce to improper fractions 164; 474; 104. 4. Change 21 to a fraction having 25 for its denominator; 34 to 50ths; 75 to 18ths.

5. Reduce

of 2,, 14 to equivalent fractions having the least common denominator

6. What is the difference between of 64 and 41 + § ? 7. A farmer had of his wheat in 1 bin, in another, and 60 bushels in the third. How many bushels had he? 8. Paid $1 a bushel for 10 bushels of wheat, and $1⁄2 a bushel for 14 bushels of corn; which cost the more? 9. How many yards of cloth of a yard wide, are equal to 12 yards of a yard wide?

10. How many pounds of tea at $3 a pound will pay for 10% baskets of peaches, at $ a basket?

11. If of an acre of land cost $791, what cost 1 acre? 12. At $ a pound, how many pounds of coffee can be bought for $61 ?

13. If 7 barrels of pork cost $60, how many barrels can be bought for $156 at the same rate?

14. A pole stands feet above the water. 15. A certain sum sons. A has, B,

in the mud, in the water, and 35
What is the length of the pole ?
of money is divided among 4 per-
C, and D has the remainder,

which is $30. What was the whole sum divided?

16. If 3 yards of velvet cost $74, how much more than $10 will 5 yards cost?

tions. Take

DRILL EXERCISES.

251. 1. Practice pupils in halving and doubling fracTeacher dictates, "Half of;" "Half of ;""Half of 1," the pupils naming the successive results to 1 (See Art. 28.)

8

2. Reverse the exercise; thus, "Twice ;" "Twice " etc., the pupils naming results as before.

96'

3. In like manner, dictate "One-fifth of 1," etc., and

reverse.

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4. Also, "One-tenth of ; "One-tenth of to' "One-tenth of 101‰0; and reverse the process, beginning, "Ten times 10000;" "Ten times Too" "Ten "Ten times o; times; "Ten times 1;" "Ten times 10;" "Ten times 100;" "Ten times 1000," to "Ten times 100000."

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5. Compare the scales of increase and decrease in the following examples:

Observe, that only when the scale of increase is 10, the successive

products at the left of 1 correspond with the successive orders in numeration of integers.

6. Begin at 8 and halve to .

7. Begin at and double to 8.

8. In the same manner with the scales of 5 and 10.

When this page, together with Pages 94 and 125, are thoroughly mastered, the principles of decimal notation as applied to fractions in the following pages will be easily understood.

DECIMALS.

252. The numbers 100, 10, 1, 10, 100, 100, etc., increase from right to left and decrease from left to right, by the same uniform scale of ten. Thus, 100 is ten times 10; 10 is ten times 1; 1 is ten times, etc. Also, 100 is one-tenth of 6; is one-tenth of 1; 1 is one-tenth of 10, etc. The value of any decimal figure is always of the value of the same figure in the next place to the left. 253. As the decimal multiples of a unit are expressed in orders at the left of the order of units, so the decimal divisions of a unit can be expressed in orders at the right of the order of units without their denominators.

These fractions, when so written, are called Decimals.

254. At the left of the order of units, the orders are called tens, hundreds, thousands, etc. At the right, they are called tenths, hundredths, thousandths, etc. By extending the orders to the left, we may express any number however large, and by extending the orders to the right, we may express any decimal division of a number however small.

255. The unit is the standard by which we compare all numbers. Therefore, to determine the order of units at a glance, a point is placed on the right of the order of units, and before the order of tenths.