(10) A person, making his will, gave to one child of his estate, to another; and when these legacies came to be paid, one turned out 5401. 10s. more than the other. What did the testator die worth?

(11) A lad, having 4000 nuts, in his return home was met by Mad Tom, who took from him of of his whole stock. Raving Ned afterwards forced of of the remainder from him; unluckily Positive Jack found him, and required of 훌 of what he had left. Smiling Dolly was, by promise, to have of a quarter of what nuts he brought home. How many then had the boy left?

(12) A younger brother received 22001. which was just of his eldest brother's fortune; and 3 and times the elder's money was as much again as the father was worth. What was that?

(13) In distress at sea, they threw out 17 hhds. of sugar, worth 341. per hhd.; the worth of which came to but of the indigo they cast overboard: besides which, they threw out 13 iron guns worth 181. 10s. a-piece; the value of all amounted to off of that of the ship and lading. What part of the value came into port?

(14) If A. having of of the half of a trading sloop and cargo, worth 16131 l., sells his brother B. of 축 of his interest therein at prime cost; what did it cost the brother, and what did his cousin P. pay at the same time for of the remainder?

(15) X. Y. and Z. can, working together, complete a staircase in 12 days; Z. is able to do it alone in 24 days, and X. in 34. In what time then could Y. get it done himself?

(16) A father dying left his son a fortune, of which he ran through in six months; of the remainder lasted him a twelvemonth longer, at which time he had barely 348/. left. What did his father bequeath him?

(17) Kitty told her brother George that though her fortune on her marriage took 19312l. out of the family, it was but of two years' rent. Pray what was it?

(18) A merry young fellow in a short time ran through of his fortune; by advice of his friends he then gave 2200l. for an exempt's place in the guards; his

profusion continued till he had no more than 880 guineas left, which he found by computation was just

part of his money after the commission was bought.

What was his fortune at first?

(19) A person dying, left his wife with child, and making his will, ordered, that if she went with a son, of the estate should belong to him, and the remainder to his mother; and, if she went with a daughter, he appointed the mother, and the girl. But it happened that she was delivered both of a son and daughter; by which she lost in equity 2000l. more than if she had had only a girl. What would have been her dowry, had she only had a son ?

(20) A cistern holds 103 gallons; and being brim-full, has two cocks to run off the water: by the first of which a three-gallon pail will be filled in 60 seconds, by the other in 75. In what time will this cistern be emptied through both these apertures together, supposing the efflux of the water all the same?

(21) A person having about him a certain number of crowns, said, if ++ of what he had were added together, they would make just 45. How many crowns had he about him?

(22) A gentleman has an orchard of fruit-trees, one half of the trees bearing apples, one fourth pears, one sixth plums, and fifty of them bearing cherries. How many fruit-trees in all grow in the said orchard?

(23) A schoolmaster being asked how many scholars he had, answered, if I had as many, and as many, and as many, I should have 99. How many had he?

(24)

In the year I wrote this, if to my age you add
,,(thereof), with more,

The number 74 will then be had

Ingenious youths, my age explore.

(25) A. in a scuffle, seized on of a parcel of sugar-plums; B. catched of it out of his hands, and C. laid hold onmore; D. ran off with all A. had left, except , which E. afterwards secured slily for himself; then A. and C. jointly set upon B., who, in the conflict, shed he had, which were equally picked up by D. and E. who laid perdue. B. then kicked down C.'s hat, and they all scrambled anew for what it contained; of which A. got, B., D. 3. and C. and E. equal shares of what was left of that stock; D. then struck of what A. and B. last acquired out of their hands: they with difficulty recovered in equal shares again, but the other three carried off

of it

a-piece of the same. Upon this they called a truce, and agreed, that the of the whole left by A. at first should be equally divided among them. How much of the prize, after this distribution, remained with each of the competitors ?

PART III.

XLVI. DECIMAL FRACTIONS.

A DECIMAL fraction is a fraction whose denominator is always unity or 1, with one or more ciphers. Thus, a unit may be imagined to be equally divided into 10 parts, and each of these into 10 more; so that, by a continual decimal subdivision, the unit may be supposed to be divided into 10, 100, 1000, and so on without end, all being equal parts, called tenth, hundredth, or thousandth parts of unit

or 1.

In Decimal Fractions, the figures of the numerator only are expressed, the denominator being omitted, because it is always known to consist of a unit with so many ciphers as there are places in the numerator.

A decimal fraction is distinguished from an integer by a point or comma prefixed, thus,,5 which stands for, or; 75 foror; 2752 for; and 12,010 for 1200일 or 12, &c.

Ciphers at the right-hand of a decimal fraction alter not its value; for,,5 or,50 or, 5000 are each of them the same value, and are equal to oor; but ciphers at the left hand, in a decimal fraction, decrease the value in a tenfold proportion, for,05 із теб; also,, 0005 is rodo, &c. all of which will plainly appear by the following

TABLE.

& c.

Parts of Ten.

Parts of one Hundred.

Parts of one Thousand.

Parts of ten Thousand.

Parts of one C. Thousand.

Parts of a Million.

Millions.

Tens.

C. of Thousands.

Tens of Thousands.

Hundreds.

Thousands.

Units.

By the above Table it also plainly appears, that as whole numbers increase towards the left hand by a tenfold proportion, so decimal parts decrease towards the right hand by the same proportion.

A finite decimal is that which ends at a certain number of places; but an infinite is that which no where ends.

A circulating or recurring decimal is that wherein one or more figures are continually repeated.

Thus 64,766666, &c. or 64,76, is called a single circulating or recurring decimal.

And 147,642642, &c. or 147,642, is called a compound recurring decimal.

Note. In all operations, if the result consist of several nines, reject them, and make the next superior place a unit more. Thus, for 17,1999 write 17,2; and for 12,99 write 13, &c.

XLVII. ADDITION of DECIMALS.

Case 1. ADDITION and Subtraction in Decimals are performed after the same manner as Sect. 2, 3, of whole numbers: Care being taken that like parts be placed under one another; and from their sum or difference cut off so many decimal parts as there are the most in any of the given numbers.

EXAMPLES.

(1) What is the sum of,0476, 21,476,,0067, 64, 17,6, and ,20764?