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remainder add the less numerator, and set the sum of both for a new numerator over the common denominator, and carry one to the integral part, and proceed as in whole numbers.

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V. When the fractions are of different denominations.

RULE. Reduce them to their proper quantities, and subtract as before.

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RULE. Reduce compound fractions to simple ones, and mixt numbers to improper fractions; then multiply the numerators together for a new numerator, and the denominators for a new denominator.

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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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1. What part is 2811 of 33?

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Ans. .

2. What will remain if 13gs. and 7ğd. be taken from £11

3. Which is the greater fraction or?

Ans. 5s. 68d.

Ans. 368.

Ans. is greater by 4. Of what number is 176 the part? 5. By how much must you multiply 133 that the product may be 491? Ans. 33.

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6. A farmer being asked, how many sheep he had, answered, that he had them in 5 fields; in the first he had his flock, in the second, in the third, in the fourth, and in the fifth 450; how many had he? Ans. 1200.

RULE OF THREE DIRECT IN VULGAR FRACTIONS.

RULE. Having stated the question, make the necessary preparations 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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of a ship cost £273 2s. 6d. what are of her Ans. £227 12s. 1d.

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2. If worth? 3. If of a yard cost of a pound, what will g of an ell English come to, at the same rate? Ans. £2. 4. A person having of a coal mine, sells of his share for £171; what is the whole mine valued at? Âns. £380.

SINGLE RULE OF THREE INVERSE IN VULGAR FRACTIONS.

EXAMPLES.

1. If 254s. will pay for the carriage of 1 cwt. 145 miles, how far may 6 cwt. be carried for the same money?

Ans. 22 miles.

2. If 31 yards of cloth that is 1 yard wide, be sufficient to make a cloak, how much must I have of that sort, which is yard wide, to make another of the same bigness?

Ans. 4 yards.

3. If 3 men can do a piece of work in 4 hours, in how many hours will 10 men do the same work?

Ans. 17.

4. If the penny white-loaf weigh 7 oz. when a bushel of wheat cost 5s. 6d. what is the bushel worth when the penny white-loaf weighs but 2 oz.? Ans. 15s. 44d.

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12. How much is

of 43?

13. Take from 43.

14. Multiply 4 by . 15. Divide 4 by

16. Divide by 43.

17. Add ,, of 74, and together.

18. Multiply of 51 by

19. Divide of 94 by 3 of 14.

20. Reduce d. to the fraction of a penny.

DECIMALS.

21. Add nine tenths, ninety thousandths, four, and four hundredths, one hundred, and one thousandth together.

22. Take two hundred and seventeen thousandths from two thousand, and seventeen thousandths.

23. Multiply fifty-six, and 875 thousandths by one, and eight thousandths.

24. Divide fourteen, and one thousandth by fifty-four ten thousandths.

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 is the answer in shillings; what remains is to be reduced as in Compound Division.

EXAMPLES.

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

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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.

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