DIVISION OF VULGAR FRACTIONS.

RULE. Prepare the fractions, if necessary; then invert the divisor, and proceed as in Multiplication.

1. What part is 28 of 33?

Ans. 7.

Ans. 5s. 6d.

2. What will remain if 135s. and 7d. be taken from £1?

3. Which is the greater fraction or ?

Ans. is greater by

Ans. 368.

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

Ans. 33.

6. 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 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?

2. If of a ship cost £273 2s. 6d. what are

worth?

16

Ans. £227 of a pound, what will

same rate?

3. If of a yard cost English come to, at the 4. A person having for £171; what is the whole mine valued at?

of a coal mine, sells

12s. 1d.

of an ell

Ans. £2.

of his share

Ans. £380.

SINGLE RULE OF THREE INVERSE IN VULGAR FRACTIONS.

EXAMPLES.

1. If 2548. will pay for the carriage of 1 cwt. 1451 miles, how far may 6 cwt. be carried for the same money?

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. 47 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 21 oz.? Ans. 158. 44d.

19. Divide

of 51 by .

of 91 by 3 of 11.

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.

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? 6d. 4596

CASE II.

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.

EXAMPLES.

1. What will 4937 yards come to at 9d. per yard? 64937

When the price is shillings, or shillings and pence, and an even part 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.

EXAMPLES.

1. At 6s. 8d. per yard, what will 473 yards come to?

68. 8d.

473

When the price is shillings, or shillings and pence, which make no even part of a pound.

RULE. Find the even parts for the price, and divide as in Case III. or multiply the given quantity by the shillings, and take the even parts of shillings for the pence, as in Case II.