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Examples.

(1.) If 243 shillings will pay for the carriage of a cwt. 1377 miles, how far may 5 cwt. be carried for the same money?

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(2), How many yards of matting, of a foot wide, be sufficient to cover a floor that is 15 feet broad, and 27 feet long?

(3.) How many yards of cloth at 5s. 8d. per yard, may I give for 573 yards of cloth at 4s. 3d. per yard, that I may lose nothing?

(4.) What quantity of shalloon, of a yard wide, will line 112 yards of cloth 14 yard wide?

(5.) If I have 34 cwt. carried 15 miles for 4 guineas, how far ought 94 cwt. to be carried for the same money?

COMPOUND PROPORTION IN VULGAR
FRACTIONS.

RULE.

State the question, as in whole numbers. Reduce mixed numbers to improper fractions, complex and compound fractions to simple ones, and the terms in the divisors to the same denomination as those in the dividends. Then invert the terms, which are to be multiplied together for a divisor, and take the continued product of all the terms for the answer.

Examples.

(1.) If £3 be the wages of 13 men for 7 days, what will be the wages of 20 men for 15 days?

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(2.) What is the interest of 4907. 15s. for 74 years, at 4 per cent. per annum?

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(3.) If a footman travel 294 miles in 7 days of 12 hours long, in how many days, of 103 hours each, will he travel 147 miles?

(4.) Bought 5000 deals, of 15 feet long, and 24 inches thick, how many deals are they equivalent to, of 12 feet long, and 12 inch thick?

(5.) If 13 ells of cloth, yard wide, cost 5 guineas, what will 334 yards, of an ell English wide, and of the same goodness come to?

(6.) If 248 men, in 5 days of 11 hours each, dig a trench of 7 degrees of hardness, 232 yards long, 33 wide, and 2 deep; in how many days, of 9 hours long, will 24 men dig a trench of 4 degrees of hardness, 337 yards long, 53 wide, and 31 deep?

A PROMISCUOUS COLLECTION OF QUESTIONS, EXERCISING ALL THE PRECEDING RULES IN VULGAR FRACTIONS.

(1.) What part of 3d. is of 6d. ?

(2.) A gentleman bought 3 suits of clothes, containing 7 yards each; the first suit cost 178. per yard, the second of 17s. and the third of 17s. what did the whole cost him?

(3.) What number is that from which if 14g be deducted, the remainder will be 477%?

(4.) If of a ship be worth 4000 guineas, what is the whole worth?

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(5.) Suppose a ship be worth 160007. of which my share is; what part of her shall I have left if I dispose of of of of my share; and what money is that part worth? (6.) What number is that, from which if you. deduct of, and to the remainder add of, the sum will, be 45?

(7.) Suppose A can do a piece of work in 63 days, B can do the same in 4 days, and C in 3 days; if you set them all at work together, in what time will they finish it?

(8.) I have employed 5 people, A, B, C, D, and E, upon a piece of work. Now I am told, that A, B, C, and D, can finish it in 13 days; A, B, C, and E, in 15 days; A, B, D, and E, in 12 days; A, C, D, and E, in 19 days; and B, C, D, and E, in 14 days; pray in what time may I reasonably expect to have my work done by. their all working together; and, suppose I should wish to discharge 4 of them, which of them would finish the work soonest, when left to himself?

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(9) A reservoir has three cocks, A, B, and C, to let in water, and three others, D, E, and F, to discharge it :now, if A be opened by itself, the reservoir, when empty, will be filled in 6 hours; if B be opened by itself, it will be filled in 8 hours; and, if C be opened by itself, it will be filled in 10 hours. Again, if D be opened by itself, when the reservoir is full, it will be emptied in 9 hours; if E be opened by itself, it will be emptied in 11 hours; and, if F be opened by itself, it will empty the reservoir in 13 hours;-in what time will the empty reservoir be filled, if all the cocks, A, B, C, D, E, F, are set open together, supposing the weight of the column of water in the reservoir, and the pressure of the atmosphere to be uniform during the influx and efflux of the water? (10.) What is the difference between 3 of 3 of a crown and of of a guinea?

(11.) Multiply of 3 of 5},

17 14
94' 95

and § of 17 together, for the numerator of a fraction; and

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and 51, together for a denominator, and

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reduce the new fraction to its proper terms.

(12.) Five boys, A, B, C, D, and E, put a number of marbles into a ring in order to play; but, a dispute happening amongst them, A snatched of the marbles out of the ring; B snatched of those out of his hand before he got off, and C, who was near, got of the remainder; D ran off with all A had left in the ring, except part, which E got.-A and C, not satisfied with what they got, jointly set upon D, and snatched of what he had got from him, of which number B, in the scaffle, got, and E the rest; C snatched from E of the number he had then in hand, and A got of what B had left. Here D observed, that he had got just as many marbles as he put into the ring; and, if E would give A of what he had got, and C likewise give A of what he had in hand, then they would all have equal shares. Pray how many marbles were first put into the ring, supposing each boy put in an equal number, and none were lost in the scuffle?

(13.) A father had two sons; to the eldest he left 33 of his estate, and 35 of the remainder to the younger son; the residue was allotted to the widow; now, if the elder son had £500 more than the younger, pray what was left for the widow, and what was the gentleman's whole estate worth?

(14.) If a wall of 573 yards long, 127, feet high, and 1 brick thick, cost 3427. 15s. building, what will a wall of 34 yards long, 11 feet high, and 24 bricks thick, cost at the same rate per rod?

(15.) The diameter of the earth is 7970 miles, and the circumference is 3 times the diameter: if a man of 6 feet in height were to travel round the earth, how many yards would his head go farther than his feet?

(16.) A young man received 667. 13s. 4d. which was of of his elder brother's portion, and 31⁄2 times his elder brother's portion was 14 times his father's estate; the question is, what was the value of their father's estate?

(17.) Suppose the cargo of a ship to be worth 10,0007. and that of of of the ship be worth of of of the cargo; what is the whole value of the ship and the cargo?

(18.) Required to find the least three whole numbers, such that of the first, of the second, and of the third, shall ali be equal to each other?

of his property to A,

to B, ¦

(19.) A person left to C, to D, to E, to F, and the rest, which was 800l. to his executor; what was the value of the whole property, and of each person's share?

(20.) How many deals 12 feet long and 7 inches broad will be required to floor a room 74 yards long by 5 yards wide, allowing for a vacancy 7 feet long by 5 feet broad?

(21.) There is an island 120 miles in circuit; 7 footmen all start together to travel the same way round it, and continue to travel till they all come together again : A goes 5 miles a day, B 61, Č 71⁄2, D 81⁄2, E 91⁄2, F 101, and G 114. In how many days will they all be together a second time?

(22.) The hour, minute, and second hands of a watch are together at 12 o'clock, when will they all be together a second time?

DECIMAL FRACTIONS.

25 225

Definition 1. Decimal Fractions, or Decimals, are such as have 10, 100, 1000, &c. for their denominator; thus To, T, 75%, &c. are decimal Fractions, and these are expressed by writing the numerator only, with a point before it on the left hand; thus, 1, 25, 225, &c.

2. When the numerator of a decimal fraction is written without its denominator, it must always consist of as many figures as there are ciphers in the denominator, thus, 5, Tε='05, To‰='005, &c. Hence the denominator of a decimal fraction is an unit with as many ciphers as there are figures in the decimal.

3. Ciphers on the right hand of decimals make no alteration in their value, thus, 5, 500, 5000, &c. are decimals of the same value, for 100 500

the nature of vulgar fractions.

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4. Ciphers on the left hand of decimals decrease their value; thus, 5, 05, 005, &c.=16, Too, Tood, &c.

Note 1. Decimals, as well as whole numbers, decrease in a ten-fold proportion towards the right-hand; therefore, decimals have the same properties as whole numbers, and are subject to the same rules.

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