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118.

49

2. From 6ş take 41.

Ans. 25. 3. From 14} take 127. 4. From į subtract.

12. 5. From 19 take į of 17.

13. 6. From 75 take 47}.

274. 7. From of ii subtract of . 8. From į a dollar take of a cent. Ans. 494 cts. 9. From į of a mile take it of a league. Ans. 88 yds. 10. From of a week take 3 of a year. Ans. 1 day. 11. From it of a day take i of an hour. Ans. 51 min. 12. From 4 weeks take 21} days. Ans. 64 days. 13. From of a yard take ž of a foot. Ans. 3 inches. 14. From an eagle take a dollar. Ans. 84.50. 15. From į of a pound Troy take 2 ounces. Ans. 1 oz. 16. From ă a bushel take a peck. Ans. 12 quarts. 17. From of an hour take 1 of an hour. Ans. 12 min, 18. From an acre take of a rood. Ans. 1 R. 30 P

19. Borrowed 40 dollars, paid } of 110 dollars—What remains?

Ans. 18 dollars. 19. Take a moidore from ž an eagle. Ans. 2 dolls.

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MULTIPLICATION OF VULGAR FRACTIONS.

RULE. If a mixed number be given, reduce it to an improper fraction, or if a whole number, put it to a fractional form, by writing 1 for the denominator. . Compound fractions, in the operation, may retain their original form.

Multiply the numerators together for a new numerator, and the denominators for a new denominator-which reduce to their proper terms for the answer required.

Where several fractions are to be multiplied, if the numerator of one fraction be equal to the denominator of another, their equal numerators and denominators may be omitted.

Examples.
1. Multiply · of of 4 by of 63.

63 28
Then, 1, of ' of 4' X $ of 2% žo
2. Multiply To of by } of 11.

Ans. 50

29

Ans.

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3. Multiply 3} by .

Ans. 4. Multiply 623 by is.

41 5. Multiply 6; by 53.

3312. 6. What is the product of of 9, multiplied by of it.

Ans. 2. 17. What is the continued product of s, lì, à, 3) and 12.

Ans. 56 8. Multiply 7) by 1 of .

Ans. 23. 9. Multiply 64 by 1 of 6.

Ans. 9. 10. Multiply 100 by of į of i of of off of Ž of of :

Ans. 10, 11. What is the continued product of 31, 2}, }, 4 and 17?

Ans. 2258 12. Multiply 67 by 23.

Ans. 181. 13. Multiply 41 by { of 4.

Ans. 1091.

20

DIVISION OF VULGAR FRACTIONS.

RULE. Prepare the fractions, if necessary, as in multiplication; then multiply the denominator of the divisor by the numerator of the dividend for a numerator; and the numerator of the divisor by the denominator of the dividend for a denominator.

Examples. 1. Divide ; by 63. 6

(= Answer. 2. Divide i of } by sof

of) of (* = 1 Answer. Or, by reducing the compound fractions to single ones, Thus, of of

)(

las as before. 3. Divide 4 by 4.

Ans. 16. 4. Divide 271 byl of 27.

Ans. 227. 5. Divide by a.

Ans. 13. 6. Divide 9 by 6.

Ans. 124. 7. Divide 4 by of 4.

Ans. 64. 8. Divide 1 of 4 by 47.

Ans. 9. Divide ý by

5 18

3 10

27

Ans. 21

10. Divide 7 of 6 by i of of 8.

Ang. 1. 11. Divide 63 by 63.

Ans. 115. 12. Divide 620 by 2064.

Ans. 3. Note. When the denominator of the divisor and of the dividend are equal, the quotient may be found by common division, viz. by dividing the numerator of the dividend by the numerator of the divisor: or this rule may be rendered more general, by reducing the fraction to a common denominator, and dividing as before, rejecting the common denominator entirely.

As, if i were to be divided by \ ; 1 is equal to , and % divided by 1 is 2, the quotient required. 13. Divide by š.

and reduced to a common denominator, is and 34. and 15:14

11 Answer. 14. Divide & by .

Ans. 3. 15. Divide by si

Ans. 5. 16. Divide by s.

Ans. . 17. Divide 1 by t.

Ans. 131.

THE SINGLE RULE OF THREE IN VULGAR

FRACTIONS.

RULE. Prepare the given terms, if necessary, by reduction, and state them as in whole numbers ; multiply the second and third terms together, and divide that product by the first term : Or,

Multiply the denominator of the first and the numerators of the second and third terms continually together, for a numerator; and the numerator of the first, and denominators of the second and third terms for a denominator.

Examples. 1. If 54 pounds of butter cost 63 cents, what cost 27 pounds ? 5163 = 595

21.
lb.

cts,
As 1 : 4 :: 588 : 1735 2534 cts. Answer.

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2. If i. lb. of sugar cost 9 cts. what cost 154 lbs.?

Ans. $1.52). 3. When 2 ounces of silver cost $1.944, what is the value of į of an ounce?

Ans. 32;} cts. 4. Sold 48} bushels of corn for $23.20—How much was it per bushelt

Ans. 48 cts. 5. What will 9 pounds of tobacco come to, when 31 pounds sell for 634 cents ?

Ans. $1.754. 6. Bought 57 yards of silk, at the rate of 7 yards for 6 dollars-How much does it amount to ?

Ans. $4.95 1. 7. What will 7è pounds of bees-wax come to, at 27} cts. per pound

Ans. $2.00. 8. If 16 men finish a piece of work in 281 days, the time is required in which 12 men should do it. Ans. 375 days.

9. What quantity of stuff that is å yd. wide, will line 73 yards of cloth, 14 yards wide!

Ans. 15 yards. 10. How many yards of cloth, at 6 dollars per yard, must be given for 22 yards, at 41 dollars per yard. Ans. 167 yds.

11. A. lends to B. 125 dollars for 33 months—What sum should B. lend to A. for 1 month, to requite his kindness?

Ans. 81 dollars.

THE DOUBLE RULE OF THREE IN VULGAR

FRACTIONS.

RULE. Prepare the terms, when necessary; then state and work them agreeably to the directions given in whole numbers: or invert the dividing terms, and multiply the upper figures continually for the numerator, and those below for the denominator, of the fractional answer.

Examples. 1. Two brothers at school compute the expenses of their boarding, tuition, &c. for of a year to be 80 dollars—How much will the education of 3 sons for 2 years cost their father at that rate ?

s. is.

yr. 1 yr.
*xx{xx^= 54740 – 681f dolls. Answer.

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162

CONTRACTED MULTIPLICATION OF DECIMALS.

2. If a footman perform a journey of 294 miles in 9 days of 121 hours long—How long will it take him to travel 76% aniles when the days are 103 hours long?

Ans. 2 D. 9 H. 463 M. 3. When 12 persons use 1} pounds of tea per month, how much should a family of 8 persons provide for a year?

Ans. 9 lbs. 4. If 5 persons drink 74 gallons of beer in a week, what quantity will serve 8 persons 224 weeks? Ans. 2804 gals.

5. If 70 dollars in į of a year gain 13 dollars interest, in what time will 100 dollars gain 6 do dollars ?

Ans. 12 months.

CONTRACTED MULTIPLICATION OF

DECIMALS.

RULE.

Place the units place of the multiplier under that place of the multiplicand that is intended to be kept in the product; then invert the order of all the other figures, that is, write them all the contrary way; then in multiplying, begin at the figure in the multiplicand, which stands over the figure you are then multiplying with, and set down the first figure of each particular product directly one under the other, and have a due regard to the increase arising from the figures on the right hand of that figure you begin to multiply at in the multiplicand.

Note-That in multiplying, the figure left out every time next the right hand in the multiplicand, if the product be 5 or upwards, to 15, carry 1 : if 15, or upwards, to 25, carry 2: and if 25, or upwards, to 35, carry 3, &c.

Examples. 1. Multiply 296.14364 by 12.71584, and let there be only 4 places of decimals in the product.

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