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Ans. 12 quarts.

17. From

18. From

an acre take of a rood.

of an hour take of an hour. Ans. 12 min,

19. Borrowed 40 dollars, paid of 110 dollars-What re

mains?

19. Take a moidore from an eagle.

Ans. 1 R. 30 P.

Ans. 18 dollars.

Ans. 2 dolls.

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.

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3. Multiply 3 by .

4. Multiply 62 by

5. Multiply 6 by 53.

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6. What is the product of of 9, multiplied by 3 of 13.

7. What is the continued product of 3, 14,

8. Multiply 74 by 1 of 2.

Ans. 2.

1, 3 and Ans. 55. Ans. 24.

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11. What is the continued product of 31, 2},

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12. Multiply 67 by 24.

Ans. 18.

13. Multiply 41 by 3 of 4.

Ans. 109.

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.

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Or, by reducing the compound fractions to single ones,

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10. Divide of 6 by 4 of 4 of 81.
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11. Divide 6 by 61.

12. Divide 620 by 2065.

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 were to be divided by ; is equal to 4, and 2 divided by 1 is 2, the quotient required.

13. Divide by 3.

and reduced to a common denominator, is and 13.

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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 5 pounds of butter cost 63 cents, what cost 24 pounds?

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15

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2. If lb. of sugar cost 9 cts. what cost 15 lbs. ?

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3. When 2 ounces of silver cost $1.944, what is the value

of of an ounce?

Ans. 3211 cts.

4. Sold 48 bushels of corn for $23.20-How much was it per bushel?

5. What will 94 pounds of tobacco pounds sell for 631 cents?

Ans. 48 cts. come to, when 3 Ans. $1.754. of 7 yards for 6 Ans. $4.95T

6. Bought 5 yards of silk, at the rate dollars-How much does it amount to? 7. What will 74 pounds of bees-wax come to, at 2713 cts.

Ans. $2.00. days, the time Ans. 377 days.

per pound? 8. If 16 men finish a piece of work in 28 is required in which 12 men should do it. 9. What quantity of stuff that is yd. wide, will line 71 yards of cloth, 1 yards wide? Ans. 15 yards.

10. How many yards of cloth, at 6 dollars per yard, must be given for 22 yards, at 4 dollars per yard. Ans. 167 yds. 11. A. lends to B. 124 dollars for 3 months-What sum should B. lend to A. for 1⁄2 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 24 years cost their father at that rate?

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CONTRACTED MULTIPLICATION OF DECIMALS.

2. If a footman perform a journey of 294 miles in 93 days of 12 hours long-How long will it take him to travel 763 miles when the days are 103 hours long?

Ans. 2 D. 9 H. 46% M. 3. When 12 persons use 13 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 7 gallons of beer in a week, what quantity will serve 8 persons 221 weeks? Ans. 280 gals. 5. If 70 dollars in of a year gain 12 dollars interest, in what time will 100 dollars gain 63 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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