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XL. SUBTRACTION of VULGAR FRACTIONS.

RULE.

1. PREPARE the fractions as before directed in Addition.

2. Subtract one numerator from the other, and their difference will be a new numerator, under which subscribe the common denominator.

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(5) From of take

(6) From 104 take 6.

(7) From 17 take 169.

(8) From 12 take

of

of of .

(9) From of a shilling take of a penny.

(10) From of a cwt. take of an oz.

(11) From of a yard take

of an inch.

(12) From of a chaldron take of a peck.

(13) From of a day take

of an hour.

XLI. MULTIPLICATION of VULGAR FRACTIONS.

RULE.

1. REDUCE compound fractions to simple ones, per Case II.; bring mixed numbers into improper fractions, per Case III.

2. Multiply the numerators together for a new numerator; and the new denominators for a new denominator; or, if the fractions will cancel, do it as in Case II.

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1. PREPARE the fractions as before directed in multiplication.

2. Multiply the numerator of the dividend into the denominator of the dividing fraction for a new numerator, and multiply the other numerator and denominator together for a new denominator; or invert the divisor, and then proceed as in the last rule.

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THERE are two methods to perform this rule: the second of which is the easiest and most expeditious.

RULE.

1. Prepare the fractions, if required, as directed in multi

plication; then proceed as in Sect. 12.-Or,

2. Having reduced the fractions, and stated the question, as before directed;

3. Multiply the donominator of your first number into the numerators of the second and third, for a new numerator; then multiply the numerator of the first number into the denominator of the second and third, for a new denominator, and place it under the new numerator, for an answer, which reduce to its proper quantity: or invert the first term, and then proceed as in Case 2, Sect 38; or as in Multiplication.

EXAMPLES.

(1) If 2 yards of silk cost 341. what will 4 yards cost at the

same rate ?

(2) If of a lb. cost 5s. 6d. what will 42 lb. of the same cost?

(3) Suppose I give 14s. 8d. for 3 cwt. what must be given for

8 cwt. of the same at that rate?

(4) A merchant makes an assurance upon a ship and cargo bound to a certain port, value 2700l. 10s. and agrees to pay 10 guineas per cent. To what comes the premium or charges of the assurance?

(5) How much South-sea stock, at 1121. per cent. will 1270l. purchase?

(6) A mercer bought 4 pieces of silk, each piece containing 22 yards, and was to give 8s. 9d. per yard. I demand the value of the whole.

(7) If I give 100l. 10s. 6d. for 12 pieces of Holland, at the rate of 5s. 6d. per ell Fiemish; I demand how many elis English each piece contained.

XLIV. THE RULE of THREE INVERSE,

In VULGAR FRACTIONS.

AS I observed in the Rule of Three Direct, of there being two methods of performing it, so likewise in this.

RULE.

1. Prepare the fractions as before directed, and then pro ceed as in Sect. 13. - Or,

2. Multiply the denominator of the third number into the numerator of the first and second for a new numerator; then multiply the numerator of the third number into the denominator of the first and second, for a denominator, which place under the numerator for an answer, and find the proper quantity as before; or invert the last term, and proceed as in the last rule.

EXAMPLES.

(1) A. lends B. 251. for 6 months. How long ought B. to let A. have 10%. to requite his kindness?

(2) If 4 men can do a piece of work in 12 hours, in how many hours will 12 men do the same?

(3) If the penny loaf weigh 124 oz. when the bushel of wheat is sold for 5s. what is the load worth when the penny loaf weighs 8 oz.?

(4) Suppose A. lends to B. 100. for 6 months, what sum must B. lend A. for 3 years to requite him?

(5) How many yards of cloth, at 8s. 6d. per yard, must be given for 20 yards, at 5s. 7d. per yard?

XLV. THE DOUBLE RULE of THREE,

In VULGAR FRACTIONS.

PREPARE the numbers, as before directed, and then proceed as in page 74.

EXAMPLES.

(1) What principal, put to interest, will gain 47. 15s. in 9 months, at 61. per cent. per annum?

(2) Suppose 12 students spend 14l. 6s. 8d. in 16 days, how

much will 18 students spend in 34 days?

(3) If the carriage of 40 cwt. 30 miles, cost 16l. 13s. 4d. what weight may I have carried 80 miles for 6l. 17s. 6d. at the same rate?

(4) Six men with their wives, upon calculation, found that their expenses for three months past (allowing 30 days to one month) amounted to 26/. 19s. 4d. I demand in what time 147. 15s, may be spent by 36 men in the like proportion.

(5) If 30 men can perform a piece of work in eleven days, how many will accomplish another four times as large in one fifth of the time?

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(6) Agreed for the carriage of 24 tons of goods, 3 miles wanting to, for off of a guinea. What was that per cwt. for a mile?

QUESTIONS for Exercise in FRACTIONS.

(1) FOUR figures of nine may be so placed and disposed of as to denote and read for 100, neither more nor less.

Pray how is that to be done?

(2) What number is that, to which if

added, the total will be 1?

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(3) What number is that, from which if you deduct the

5 of, and to the remainder add

will be 3?

(4) What number is that, to which if you add

TO

19

of 44, the sum

of 12, more of

of 27, and from the total subtract of 7 less 14, the remainder shall be 8?

(5) There is a number, which, if multiplied by of of 24, will produce no more than 1. What is the cube of that number?

(6) There is a number, which, if divided by of will quote 9. What is the square of that number?

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(7) If of of of a ship be worth of of of the cargo, value at 1200l. what did both ship and cargo stand the owners in?

(8) A person was possessed of a share of a copper mine, and sold of his interest therein for 1710l. what was the reputed value of the whole property at the same

rate?

(9) A father devised of his estate to one of his sons, and of the residue to another, and the surplus to his relict, for her life; the children's legacies were found to be 2571. 3s. 4d. different. Pray what money did he leave the widow the use of?

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