462. If 1£. 17s. are paid for 7 yards of cloth, what is the price of one yard?

463. If

of a barrel of flour costs 1£. 13s. 7d., what

will be the cost of a whole barrel?

464. When $13.746 are paid for of a ton of hay, what will 1 ton cost?

465. When of a cargo of wheat costs $887.40, what sum will pay for the whole cargo?

466. If $73.60% are paid for of a ton of potash, what will 1 ton cost?

467. If of an acre produce 18 cwt. 12 lbs. of hay, what quantity will a whole acre produce?

468. If of a certain lot of land equals 12 A. 2 R. 303 sq. rds., what is the area of the field?

469. 1 of a ton of potash costs $83.409; what is the value of 3 tons?

QUESTIONS.-When both numerator and denominator are increased or decreased in any ratio, how is the value of the fraction affected? (137., a., b.) Why does dividing the numerator of a fraction decrease its value? (66., k.) Why does dividing the denominator of a fraction increase its value? (66., i.) Why does multiplying the numerator of a fraction increase its value? (66., j.) Why does multiplying the denominator of a fraction decrease its value? (66., h.)

LESSON XLVI.

470. If of a cwt. of sugar costs $7.40, what is the value of of a cwt.?

471. If

of a pound of opium costs $2.71, what is the value of of a pound?

472. When $80 are paid for of an acre of land, what will 3 of an acre cost?

473. If

of a cotton factory is worth $4370, what is

of it worth?

474. of a ship is worth $147.374; what is of it worth?

475. I sold of a farm for $1783; what is the remainder worth?

476. I sold of a farm for $371; what is of the remainder worth, at the same rate?

477. A man bought of a farm containing 1784 acres for $1728; what was the cost of one acre?

478. A man bought of a farm containing 231 acres for $4712; what was the cost of of an acre?

479. A man bought of a farm containing 437 acres for $2744.26; how much should he receive for 233 acres, in order that he may neither gain nor lose?

480. A man bought of a farm containing 371 acres for $2343.27; how much should he receive for 133 acres, so as to gain $342.42 on the amount sold?

LESSON XLVII.

481. Mr. Jones has a field 134 rds. long, 11 rds. wide, and he sells it for $73.46; what does he receive for 33 sq. rds.?

482. An English merchant paid 27£. 12s. 6d. for § of a bale of cloth; what did of the remainder cost? 483. If 7 cwt. of sugar cost $29.13, what will 93 cwt. cost?

484. If 3 tons of hay cost $49, what will 17 tons cost? 485. Gave $40 for 5 yards of broadcloth; what did 193 yards cost?

486. 7 bushels of rye cost $8.73; what did 187 bushels cost?

487. If I pay $13.84 for 23 yds. of broadcloth, what must I pay for 114 yds.?

488. If 93 cwt. of sugar cost $46.47, what must be paid for 7 cwt.

489. When $183 are paid for 3 cwt. of rice, how much may be purchased for $1?

490. If 3 tons of potash cost $276.43, how many tons can I purchase for $596.46?

491. If 34 acres of land cost $764, what will 13 acres cost?

492. If 43 tons of coal cost $703, what will one ton cost? what will 46 tons cost?

QUESTIONS.-What is the reduction of fractions? (141.) What is reduction ascending? (142.) What is reduction descending? (143.) Is the reduction of fractions to their lowest terms reduction ascending or reduction descending? (142.) What is the rule for reducing a fraction to its lowest terms? (145., 6.) Give the rule for reducing an improper fraction to a mixed number. (146.) A mixed number to an improper fraction. (147.)

LESSON XLVIII.

493. Sold a farm for $896.50; what was received for of it?

494. I gave $27% for 34 barrels of flour; what will 37 barrels cost?

495. Sold a house for $38743; what sum was received for % of it?

496. When $463 are paid for 100 gallons of molasses, what will of a gallon cost?

497. When 112 cents are paid for 94 gallons of molasses, what will 481 gallons cost?

498. If 3 barrels of flour cost 10%, what will 63 barrels cost?

499. Paid, in Liverpool, 1974£. for 50 bales of cloth; how many bales should be received for 4320£.?

500. 34 lbs. of coffee cost 50 cts.; what sum must be paid for 74 lbs.?

501. If 2 tons of hay cost $634, what will be the cost of 16 tons?

502. If a piece of land rods square cost $274, what will be the cost of 41⁄2 square rods?

503. A certain piece of land 34 rods square is worth $57.233; what will be the worth of 7 acres of land, at that rate?

QUESTIONS.-What is the rule for reducing a mixed number to an equivalent fraction having a given denomination? (148.) What is the addition of fractions? (149.) What is the subtraction of frac tions? (151.) What is the rule for the addition or subtraction of fractions, each having a unit for a numerator? (152.) What is the multiplication or the division of fractions? (158.)

LESSON XLIX.

504. 34 cwt. of iron cost $457; what must be paid for 6894 cwt.?

505. For 6 cords of wood I paid $63.41}; what must I pay, at the same rate, for 1864 cu. ft.?

506. Gave $243 for 96 barrels of tar; how much can I buy for $2000?

507. Paid $7888.30 for 724 acres of land; how much, at that rate, would 39 acres cost?

508. If for 17 days' work I pay $273, at that rate, how much should I pay for 474 days' labor?

509. Sold 5 bushels of apples, for $7.28}; what should I receive for 191⁄2 bushels?

510. of a ship is worth $37463; what is the entire

ship worth?

晷

511. of of a ship is worth $427, what is the entire vessel worth?

512.

of of a vessel is worth $374.26; what is of the vessel worth?

513. If of 5 times the value of a vessel is $46748, what is its value?

514. If 3 times of the value of a vessel is $4937.24, what is of its value?

515. I bought of a house for $347.22; at that rate, what should I give for of 19 such houses?

QUESTIONS.-What is the rule for multiplying a fraction by an integral number? (154.) What is the rule for dividing a fraction by an integral number? (155.) Give the rule for dividing a mixed number by an integral number. (156.) What is the rule for multiplying a fraction by a fraction? (157.) How can an integral number be changed to a fractional form? ANS.-By placing a unit for its denominator.

LESSON L.

REDUCTION OF FRACTIONAL DENOMINATE

NUMBERS.

164. Reduction Descending of fractional compound numbers is the same as that of integral compound