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V. Then the frałtions are of different denominations. Rrle. Reduce them to their proper quantities, and subtract as before.

EXAMPLES.
From of a £. take is of a shilling.

15 common denom.

d.
of a £.=15 6
is of a S. = 0 3 9

2

10

of

Rem.

15 315 2. From of a £. take of a fhilling. Anf. 145. 3d. 3. From of a lb. troy take 등

an ounce,

Anf. 8 oz. 16 dwt. 16 grs. 4.

From 7 weeks take gir days. Anf. 5w.4d. 7h. 12m. 5. From of a yard take of an inch. Anf. 5 inch, I bc.

MULTIPLICATION OF VULGAR FRACTIONS.

Rute. Reduce compound fractions to simple ones, and mixt numbers to jinproper fractions ; then multiply the numerators ta. gether for a new numerator, and the denominators for a new denominator.

EXAMPLES.
Multiply 41 by 1

41
2

4

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DIVISION OF VULGAR FRACTIONS. RULE. Prepare the fractions, if necessary; then invert the divisor, and proceed as in multiplication.

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ah

19 X 2 12 Then

= is = the aniwer,

6 X 19 3. Divide 5 by ko. 4. Divide in by 41. 5. Divide gi by 1 of 7. 6. Divide 5205 by $ of 91.

Anf. 74.

Ans. š. Anf. 2x Anf. 713.

MISCELLANEOUS QUESTIONS

IN THE PRECEDING RULES.

Anf.

What part is 2811 of 3371?
What will remain if 1345. and 7d. be taken from £..?

Anf. 55.61d. 3. Which is the greater fraction is or jo ?

Ant. iş is greater by ito 4. Of what number is 176 the part ?

Anf. 368 5. By how much must you multiply 13} that the product may be 493 ?

Ans. 3} 6. Find two numbers so that of the one will be as much as Is of the other.

Ans. 126 and 208, or 63 and 104, &c. 7. What is greater, ŝ of 6s. or is. 2{d. ?

Anf. 15. 2 d. is greater by agd. 8. A has į of of a ship, and B of which is the greater share, and by how much?

Anf. Ả's share is greater by š 9. A farmer being asked, how many sheep he had, answered, that he had them in 5 fields ; in the first he had of his flock, in the fecond ã, in the third s, in the fourth i'n and in the fifth

450;

how Anf. 1200.

many had he ?

RULE OF THREE DIRECT IN VULGAR FRACTIONS.

RULE. Having stated the question, make the necessary prepara. tions, as in Reduction of Fractions, and invert the first term ; then proceed as in multiplication of fractions.

EXAMPLES.

1. If of a yard of cloth cost of a shilling, what will of a yard come to ?

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2.. If is of a ship cost £.273 25. 63. what is I of her worth?

Ans. £.227 125. Id. 3. If of a yard cost } of a pound, what will of an ell En. glish come to, at the same rate ?

0 0 4. A person, having of a coal mine, sells of his share for £-171 ; what is the whole mine valued at ? Anf. £ -380.

Ans. £.2

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SINGLE RULE OF THREE INVERSE,

IN VULGAR FRACTIONS.

EXAMPLES. 1. If 25;s. will pay for the carriage of an cwt. 1451 miles, how far may 62 cwt. be carried for the same

money
?

Anf. 224 2. If 31 yds. of cloth that is l_ yard wide, be sufficient to make a cloak, how much must I have of that fort, which is $ yard wide, to make another of the same bigness?

Ani. 47 yds. 3.

If

3 men can do a piece of work in 41 hours, in how many hours will ten men do the same work ?

Anf. 15. 4. If the penny white-loaf weigh 7 oz. when a bushel of wheat cost 55. 6d. what is the bushel worth when the penny white-look weighs but 2 oz.?

Anf. 155. 434.

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PRACTICE

Is a contraction of the Rule of Three direct, when the first term happens to be an unit, or one, and has its name from its frequent use in business.

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When the price is an aliquot, or even part of a shilling. Rule. Divide the given number by the part, and the quotient s the answer in shillings; what remains is to be reduced in Come pound Division.

EXAMPLES.

1. What will 4596 yards coft at 6d. per yard ?

6d. 1 4596

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When the price is pence, or pence and farthings, and no even part

of a shilling RULE. Find the even parts for the price, and proceed as in Case I. and the sum of the quotients is the answer.

EXAMPLIS.

1. What will 4937 yards come to, at gd. per yard ?

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When the price is shillings, or shillings and pence, and an even par:

of a pound. RULE. Divide the given quantity by the even part, and the quotient is the answer in pounds. If there be a remainder, reduce it as in Compound Division.

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