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and take the difference of the numerators, under which write the common denominator, which will give the difference of the fraction required. Multiply each numerator by the other denominator, and subtract the less (product) from the greater, for the numerator sought; multiply one denominator by the other for a common denominator.

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Hence a fraction is subtracted from a whole number, by taking the numerator of the fraction from its denominator, and placing the remainder over the denominator, then taking one from the whole number.

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Reduce compound fractions to simple ones, and mixed numbers to improper fractions; if an integer be given, reduce it to an improper fraction, by putting a unit for its

denominator; then multiply the numerators together for a new numerator, and the denominators together for a new denominator.

NOTE. 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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6. Required the continued product of 75, 24, 31, and

of 14.

Ans. 39.

DIVISION OF VULGAR FRACTIONS.

RULE.

Prepare the fractions as before; then invert the divisor and proceed exactly as in Multiplication. The products will be the quotient required.

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NOTE.-The above may be abridged by cancelling the like numbers in the numerators and denominators.

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2. Reduce 6 to a fraction whose denominator shall be 8.

Ans. 43.
Ans..

3. Reduce 2s. 6d. to the fraction of a pound.
4. Reduce 36 to its equivalent improper fraction.

5. Reduce

Ans. 293.

to its equivalent whole number. Ans. pe.

6. Reduce of 3 of 4 to a single fraction. 7. Reduce 1, 1, and

common denominator?

Ans. 4.

to equivalent fractions, having a

8. What is the value of of an acre?

9. What is the sum of

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and?

10. What is the sum of 72 and 5? 11. Add of a dollar to of a dollar. 12. Add 1⁄2 of a pound troy, to

13. From of a dollar take 14. From of a cwt. take

Ans.,

and 31. Ans. 3r. 174p. Ans. .

Ans. 132.

Ans. $1.62,5.

of an oz.
Ans. 6oz. 11dwt. 16gr.

of a cent. Ans. $ .74,25.
of a pound.

Ans. 1qr. 27lb. 6oz. 10dr. . 15. If a merchant own § of a ship, valued at $900, and sell of his share, what part has he left, and what is it worth? Ans. left, worth $187.50.

16. Multiply of 8 by 3 of 5. Ans. 21. 17. Divide $259, equally among 15 persons, and tell the share of each. Ans. $17.297.

18. What part of 3 pence is of 2 pence? 19. A has of a ship, of which he sells what is the value of the whole ship at that rate?

Ans..

for £100

Ans. £533 6s. 8d.

SINGLE RULE OF THREE IN VULGAR

FRACTIONS.

RULE.

Reduce the given numbers if necessary; mixed numbers to improper fractions; like terms to the same denomina. tions, and each to their lowest terms.

Then state the question as in whole numbers; invert the first term, and multiply all the numerators together for a new numerator, and all the denominators for a new denominator, and divide the upper term by the lower for the

answer.

d

122 SINGLE RULE OF THREE IN VULGAR FRACTIONS.

1. If

EXAMPLES.

of a yard of cloth cost $2§, what will 5 yards

cost at the same rate?

Ans. $16.25.

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2. If a man drink daily a dram which costs 64cts. how much will he expend in this manner in 20 years of 365 days each? Ans. $456.56,25. 3. What is the value of of of 5 of a pound, at the rate of a dollar for & of a pound? Ans. $37, or 42, cts. 4. How many yards of baize, ell English wide, will be sufficient to line 20 yards of camlet yard wide? Ans. 12 yards.

of

Ans. 15 yards.

5. What quantity of shalloon, yard wide, wil line 71⁄2 yards of cloth, 14yd wide? 6. Bought 5 pieces of muslin, each piece containing 27 yards, at of a dollar per yard-what

did they cost?

Ans. $55.50. 7. If A can mow an acre of grass in 5 hours, and B can mow 14 acres in 93 hours, in what time can they jointly cut 84 acres? Ans. 22 hours, or 22 hours 40min.

8. If a coat and waistcoat can be made of 3 yards of broadcloth 1yd. wide, how many yards of stuff yd. in breadth, will it require to fit the same person? Ans. 9yds. 9. How much in length that is 73in. broad, will make & foot square? Ans. 1818 inches. 10. How many pounds of potash can I purchase for 124 cents, if a pound cost 12 cents? Ans. 7 pounds. 11. A gentleman owning of a vessel, sells share for $312-what is the whole vessel worth?

of his

Ans. $1300.

12. If of a gallon cost of a dollar, what will of a ton cost? Ans. $140. 13. If 3 men can finish a piece of work in 4 hours, how many hours will it require one man to do the same? Ans. 13 hours.

DOUBLE RULE OF THREE IN VULGAR
FRACTIONS.

RULE.

Prepare the terms if necessary; then state them agreeably to the directions given for whole numbers.

Invert the dividing terms, and multiply the upper figures continually for the numerator, and those below for the denominator of the fractional answer.

NOTE.--Like figures in the numerators and denominators may be cancelled.

EXAMPLES.

78 dols.

1. If 3 yards of cloth 2 yd. in width, cost $7%, what will cost 93 yards of wide?

yds. yds.

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Then If 20
:

yds. yds.

$

옷 : 급 :: 일

3x divisor.

$cts.m.

XIX V=÷W=w=w=24.78.14.

256

Or, invert the dividing term, &c.

5376

$3

2X 4X 39x7x 61-4758

793

$24.78,1

7x3x4x8x8 192 32

2. If the wages of 5 men for 17 days be $3213, what sum will 15 men earn in 26 days, at the same rate? 15 men

Ans. $147.65,61. 3. If a footman travel 294 miles in 93 days of 12 hours long, how many days of 103 hours will it require him to travel 76 miles? Ans. 211 days, or 2 days 22 hours. 4. If the interest of $257 for 7 of a year be $74, haw much interest will be due on $773 in 3 years?

Ans. $140.40. 5. If $50 in 5 months gain $2,37, what time will $13 require to gain $1,? Ans. 9 months.

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