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twelvemonth longer, at which time he had bare 348l. left: Pray what did the father bequeath him? Answ. 1284!. 18s. 5; d.

8. A younger brother received 2200l. which was just # of his elder brother's fortune; and 3; times the elder's money was as much again as the father was worth: what was that ? Answ. } 1000l.

9. How many stones of 13 foot long, 3 foot broad, and 3 foot thick, are equal to 50 stones of 3; foot long, 2; foot broad, and 1; thick? Answ. 5713.

10. A merchant hath # of a ship, and sells of his interest therein for 250l. I demand the value of the whole ship at that rate 2 Answ. 1333l. 6s. 8d.

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12. A father devised 33 of his estate to one of his sons, # of the residue to another, and the surplus to his relict, for life; the children’s legacies were found to be 257 l. 3s. 4d, different : what money did he leave the widow the use

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14. If a wedge of gold, weighing 17; b. be worth 679;1. what is the value of 13, grain Answ. 2d.

15. A man dying gave to his eldest son 3 of ; of his estate; to his second of #, and when he counted their portions, the one had 40l. more than the other; the remainder was given to the wife and younger children; how much had each Answ. The eldest son 100l. the second 60l. the wife and younger children 440l.

16l. In the year I wrote this, if to my age you add
3, #, #, (thereof) with # more,
The number 74 will then be had :
Ingenious youths my age explore?
Anyw. 36 years.

17. A in a scuffle, seized on 3 of a parcel of sugarplumbs, B catched # of it out of his hands, and C laid hold on 5's more: Dran 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, let fall # he had, which were equally picked up by D and E-B then kicked down Cos hat, and to work they went anew for what it contained; of which A got #, B #, D #, 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 of it in equal shares again, but the other three carried off ; 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? Answ. A got 2863– B 6335–C 2438–D 10294–E 4950. >

Book II—PART II.
CHAP. I.

OF DECIMAL FRACTIONS.

ECIMAL Fractions are a kind of fractions, which vary in the same proportion, and are managed by the same Methods of Operation as whole Numbers are. For this purpose every Proper Fraction is supposed to be reducible to another whose Denominator shall be 10, 100, 1000, &c. viz. Unity with some multitude of Cyphers annexed: and Fractions with such Denominators are called Decimal Fractions: Such are no los' osAs the denominator of a decimal fraction is always 10, or 100, or 1000, &c, the said denominators need not be expressed. For the numerators only may be made to express the true value of a decimal: for this purpose it is oniy required to write the numerator, with a point before it, to distinguish it from a whole number, when it consists of as many figures as the denominator hath cyphers annexed to unity; so is may be written .5; os, 15; os, .625N. B. The point prefixed is called the Separatrix. * M 3 But But if the numerator hath not so many places, as the denominator hath cyphers, put as many cyphers before it, viz. to the left hand as will make up the defect; so write ršo .05, Toss 005. “And thus do these fractions receive the form of whole numbers.

We may consider unity as a fixed point, from whence whole numbers proceed infinitely increasing, and decimals infinitely decreasing towards o, as in the following

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Trom this Table it is manifest that In decimals, as well as in whole numbers, each figure taketh its value by its distance from units place: if it be in the first place after units (or the separating point), it signifies tenths; if in the second, hundredths, &c. decreasing in each place in a tenfold proportion. - Consequently every single figure expressing a decimal, hath for its denominator 1, with as many cyphers as its place is distant from units place. Thus 2 in the Table is **, 3 13s. 4 is roos, &c., And if a decimal be expressed by several figures, the denominator is 1, with as many cyphers as the lowest figure is distant from units place. So 234 signifies too. A cypher (or cyphers) placed at the right hand of a decimal fraction, altereth not its value, since every significant figure continueth to possess the same place, So.5 .50—.500 are all of the same value. But a cypher or cyphers put to the left hand of a decimal, do alter its value, every cypher depressing it to or of the value it had before, by removing every significant figure one place farther from the place of units. - Se

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So .5, .05 .005, all express different decimals, viz. .5 is ; .05 rés ; .005 ross. *

Hence likewise may be observed the contrary effect of cyphers being annexed to whole numbers, and decimals : Every cypher to the right hand of a whole number encreaseth its value ten times; but cyphers to the right hand of a decimal do not alter its value. Again, cyphers put to the left hand of a whole number do not alter its value; but every cypher put to the left hand of a decimal, depres

seth its value to the ro, of what it would be without them. - t

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It is likewise manifest from the Table, that since the places of decimals decrease in a tenfold proportion from units downwards, so they consequently increase in a tenfold proportion from the right hand towards the "left; as the places of whole numbers do, for ten hundredth parts make one tenth, ten tenths make 1; ten units ten; ten tens one hundred, &c. viz. oc = 3, #3= 1, 1 x 10= 10, which proves that decimals are subject to the same law of notation and consequently of operation, as who'e numbers are.

Decimal fractions of unequal denominators are reduced.

to one common denominator, when they are annexed to
the right hand of those which have fewer places, as man
cyphers as make them equal in places, with that which hath
most. So these decimals. .5, .04, . 125, may be reduced
to the decimals .500, .040, . 125, which have all 1000
for their denominator.
. Of decimals, that is the greatest, whose highest figure
is greatest, whether they consist of an equal or unequal
number of places. Thus, .575 is greater than .395, and .5

greater than .395, for if it be reduced to the same deno

minator with .395, it will be .500, which is manifestly

the greater. : .
A mixt number, viz. a whole number with a decimal
annexed is equal to an improper fraction, whose numera-
tor is all the figures of the mixed number, taken as one
whole number and the denominator that of the decimal
part. So 32.405 is equal to o, as is manifest from the
method laid down to reduce a mixed number to an improper
fraction,

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fraction, for 32 the integral part being multiplied by 1000 the denomiaator of the fractional 32000 part produces 32000, to which adding 405, the 405 numerator of the fractional part, the sum 32405 is the numerator to 1000 for an improper fraction 32405 equal to the given mixed number.

CHAP. II. -
REDUCTION OF FRACTIONS.

To Reduce a Vulgar Fraction to a Decimal.

O the Numerator annex a competent number of Cyphers; then divide by the Denominator and the Quo

tient will be the Decimal required. But note that the Decimal must always consist of as many Places as there are Cyphers annexed to the Numerator. :

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1. What decimal is equal to #f
2. Reduce : to a decimal equal thereto?
3. What is the declimal equal to #2
4. What is the decimal equal to #2 *
5. What decimal is equal to #2
6. Reduce #: to a decimal *
7. What decimal is equal to #
8. Bring #3 to a decimal?
If the quotient doth not consist of as many figures as

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there are cyphers annexed, &c. make up the deficiency by putting cyphers to the left hand of the said quotient.

Application.

50)2010 Let # be reduced to a decimal. I annex

two cyphers, and the quotient results 4, which

.04 beingone figure less thant he cyphers annexed,

'I put a cypher to the left hand to make up the deficiency.

What

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