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If 22 melons cost $2.505, what must I give for 41?

MODEL OPERATION.

$2.505÷22 × 43-$.508. ANS.

Anal. Steps.-1. Find cost of 1 melon.

2. Find cost of 4 melons.

530. If I can buy 22 lemons for $1.124, what will 56 lemons cost?

531. If 27 yd. of ribbon cost $4.90, what will 58 yd. cost? 532. How much must be given for 19 umbrellas, if 5 cost $14.37.

533. How many cords in 15 piles of wood, if there are 793 cords in 11 piles?

534. How many words can a man write in 15 minutes if he can write 159 words in 3 minutes?

535. If there are on the average 9 damaged pens in a gross, how many in 112 gross ?

536. What will be the cost of 12 pianos, if 7 cost $2620 ? 537. If 9 horses cost $1305, what will 13 cost?

538. If 11 pineapples cost $2.231, what will 25 cost? 539. If 17 pecks of turnips are worth $3.124, what are 27 pecks worth?

LESSON XL.

MISCELLANEOUS EXAMPLES IN FRACTIONS.

540. 34÷4+34×57; 59-37 × 4.

541. 384; 635-20§×8.

542. 412÷467; 9×5÷413. 543. 46++; 373 +1÷÷}·

544. 143+}; 31+ 8×8.

REVIEW.-What is the rule for changing a fraction to its lowest terms? (189., a.) Give the formula for changing an improper fraction to an integral or mixed number. (140.) Give the formula for changing an integral or mixed number to an improper fraction. (141.) What is meant by reducing fractions to a common denominator? (142.)

If a man can saw 13 cords of wood in of a month, how many can he saw in of a month?

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545. If a bird can fly 10 miles in of an hour, at that rate how far can it fly in 24 hours?

546. If yd. of velvet cost 744 ct., at that rate how much must be given for 13 yd.?

547. In of the wall of a house there are 2200 bricks, how many bricks in a wall twice as great?

548. If in of a ream of paper there are of a pound, how many pounds in 6 reams?

549. If a man's postage amounts to $14 for of a year, to how much will it amount for 23 years?

550. A man's salary is $3560 for of a year; how much is that for 5 years?

551. If in length of a steeple cast a shadow 83 ft. long, what is the length of the shadow cast by f of it?

552. If a man can plow 4 acres in of a month, how many

acres can he plow in 4 months?

553. If there are 18 acres in of a lot, how many acres in 51 lots of the same size?

554. If there are 12 lb. of rice in of a box, how many pounds in 3 boxes?

555. If you can buy 4 oranges for 1 of a dollar, how many can be bought for $23?

LESSON XLI.

556. 4÷67+3; 44+34÷4.

557. 41÷6+; 34×3÷71.

REVIEW.-When have fractions a common denominator? (143.) Recite the rule for reducing fractions to a common denominator. (143., a.) In how many ways can fractions be reduced? (189.) (140.) (141.) (142.) Derive a rule for the addition of fractions from the analysis. (144.) For the subtraction of fractions.

558. 34 x÷31; 26×+2; 64×4÷4.
559. 44-24×34; 84÷3×; 34÷34 × √.
560. 23÷34731; 6×5÷8; 4×6÷23.
561. 4×34÷2; 34+26×4; 4×1÷31..
562. 2+6÷; 85+4÷83; 65 × 31÷7.
563. 443-4; 43−(4÷3); 31+(43÷3).
564. 43÷(34+); (14—8)÷4; (3÷1)−24.
565. (15—3)–(24 × 5) × 34 ; (43+})÷(34−12) × 2.

LESSON XLII.

566. If 164 yd. of ribbon are worth $3.45%, what are 584 yd. worth?

567. A man paid $19.324 for 240 melons; what was the cost of 6 melons?

568. If 3 shawls cost $254, what will 13 cost?

569. If a man can make 46 baskets in 3 weeks, how many can he make in 72 weeks?

570. If there are 129 lb. of coffee in 2 bags, how many pounds in 15 bags?

571. A man had $56428, and divided of it among his three sons; how much did each son receive?

572. If 12 bu. beans cost $23.10%, what will 19% bu. cost? 573. If 11 boxes of tin are worth $138%, what are 15

boxes worth?

574. If 13 lb. of lead cost 95 ct., what is the cost of 34 pounds?

575. If 3 lb. of wool are worth $2.25, what is the value of 4 of a pound?

LESSON XLIII.

152. To simplify compound and complex fractions. (a.) Simplify of 4 of 34.

REVIEW. Recite the rule for adding two fractions having one for a numerator. (146., a.) For finding the difference of two such fractions. (146., b.) Recite the rule for adding two fractions having a common numerator. (147., a.) For finding the difference of two such fractions. (147., b.)

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FORM.-(a.) Since of in this connection signifies times, the expression is simply an example of multiplication of fractions.

(b.) As the numerator 44 is a dividend, and the denominator 8 is a divisor, according to the Principle (138., b., I.) if both numerator and denominator be multiplied by the same number the quotient will not be changed, it follows that 4×7_30 15 44_15 therefore, 17 = or ; 28

44

8 x7 56

28

Hence, for simplifying complex fractions, the following

(a.) Rule.-I. Multiply both numerator and denominator by any number that will cancel the denominators, OR

II. Treat the expressions as unperformed operations in multiplica tion and division of fractions.

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NOTE.-To add or subtract complex or compound fractions, it is necessary first to simplify them, and then to perform the required additions and sub

tractions.

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REDUCTION OF DENOMINATE FRACTIONS.

153. Reduction descending is the same as that of

compound numbers.

Change £ to farthings.

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(a.) FORM.-1. Since in 1 pound there are 20 shillings, in 18 of a pound there are 20 times as many shillings as pounds, which is Tos.

2. Since in 1s. there are 12 pence, in

pence as shillings, which is d.

s. there are 12 times as many

3. Since in one penny there are 4 far., in far. there are 4 times as many farthings as pence, which is far.

Therefore £160 is equal to of a farthing.

REVIEW.-Recite the rule for multiplying a fraction by an integral number. (148., a.) For dividing a fraction by an integral number. (149., a.) Recite the rule for multiplying by a fraction. (150., a.) For dividing by a fraction. (151., a.) Recite the rule for simplifying complex fractions. (152., a.)

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