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QUESTIONS FOR EXERCISE IN FRACTIONs. , 127

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35. § 4-3 + 3 + 3 +4++ 36 3 + 3 ++++++++ Before the learner proceeds farther, let him prove the examples in Multiplication by Division, and those of Division by Multiplication.

QUESTIONS FOR EXERCISE IN FRACTIONS.

I.—What quantity is that, which added to re-F#-F# shall make one P

2.—What quantity is that from which if 4 of +; be subtracted, the remainder shall be $ 2

3.—What quantity is that to which if # of or of +4+ be added, the total shall be one *

128 questions for Exercise IN FRACTIons.

4.—There is a quantity, which if multiplied by # of 4 of 24, will produce no more than one ; what is the cube or third power of that quantity ? 5.—What quantity is that from which if r of # be subtracted, and to the remainder or of 13 added, the sum shall be 2 : .—There is a quantity, which if divided by 4 of #will quote 9; ; ; what is the square or second power of that quantity ? 7.—If 3 of ; of an cwt, is 121b how many pounds are in a hundred weight? , 8.—Of what number is 156 the # part 2 9.—What fraction of a £ is 8s. 9d P 10.-How much is the # of 4 of # of 30s? II.-Of what number is 18 the #: part? 12.-How much is the sum of #4-#94-6%d? 13.−A person being asked how much money he had, answered that 3, 4 and # of the sum would just make 1001 : how much money had he. 14.—There is a number, of which its #, ; and #, together with 54, will just make 25; what is the number? 15.—If 33 yards of cloth make a suit of clothes, and that 5 yards of cloth, 14 yards wide make a suit for the same person ; what was the breadth of the former cloth P 16.-Take #1 and #s from 4 of a £ sterl, and what remains 2 17—If 3 of # of # of my years make 174; I demand my age 2 18.-Four persons have a sum of money to divide, of which the first had #, the second or, the third + of both their shares, and the fourth had the remainder, which was just 45l 3s 4d ; the shares of the other three and the sum divided is required? 19.-lf my cattle are one-half sheep, one-fourth cows and one-sixth horses, and that I have 20 others of different descriptions; how many of each sort had I ? 20.-What part of 3 is 3 of 4? 21–What part of 5 is # of 7? 22–A schoolmaster being asked how many scholars he had, answered that as many more, and # as many more would just make 108; how many had he? 23.−If the sixteenth of 20,000l., was to be divided between 9 persons; what is the share of each? 24.—A man spent # of a legacy in 5 months, 3 of the remainder in 7 months; and had 180l left; what was the amount of the legacy?

IDECIMALS. -

Decisian, fractions are those in which no other denominators are used than 10, 100, 1000, &c. and are expressed by writing the numerators only with a point or comma before it on the left hand, which is called the decimal point; the denominators are not written but intimated by the position of this, point, for we understand as many ciphers following a unit in the denominator, as there are digits standing on the right hand of the decimal point. Thus, the decimal,7 is equivalent to the vulgar fraction or, the decimal 37 with too, and the decimal ,037 with +}{r.

A cipher placed to the right hand of a decimal, alters not its value, but if placed to the left hand of a decimal it decreases the value in a ten-fold proportion, for, as in notation of whole numbers, the values of figures increase in a ten-fold proportion from right to left; so on the contrary, in decimals, the values decrease from left to right, in the same ten-fold proportion, for ,5, ,50, ,500 are decimals of the same value, being each #, that is or, or, or ; but every cipher annexed to the left hand of a decimal decreases its yalue to the tenth of what it was, before so placed, thus 5 is equal to or, ,05 to row and ,005 to row. Hence unity is considered as a fixed point, from which whole mumbers proceed infinitely increasing, and decimals infinitely decreasing, as is farther explained by the following

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

Express in words the following decimals.

7, 841, ,073, 8605, 0005, 7419, 86402. . 75,843, 85,684, ,71008, 710,08, 7,1008, 7100,8 ,834, ,07503, 17,0084.

Express decimally,

Three tenths.

Five tenths one thousandth.

Six thousandth.

One tenth four thousandth.
Seven tenths, three thousandth and one millioneth.
Eight hundreth and seven thousandth.
Nine tenths, eight hundredth, seven thousandth,
Six ten thousandth and one thousandth millioneth.

Reduction of DECIMALs,

Reduction of Decimals is the converting of common fractional quantities and decimals into each other, the finding of the values of quantities decimally expressed, and expressing any given compound quantity decimally.

Cash 1st.—To reduce a common fraction to its equivalent decimal.

Divide the numerator by the denominator, annexing ciphers

as far as is necessary, the quotient will be the decimal required.

Cramples.

Let # be reduced to a decimal Leto be reduced to a decimal

8)5,000 16)30000.

Answer ,625 Answer ,l 875. 1. Reduce 3 to a decimal 2. Reduce 4 to a decimal 3. Reduce + to a decimal 4. Reduce 4 to a decimal 5. Reduce or to a decimal 6. Reduce ", to a decimal 7. Reduce 44 to a decimal 8. Reduce 33 to a decimal 8. Reduce #4 to a decimal 10. Reduce 4; to a decimal Case 2d.—To express any decimal by a vulgar or common fraction.

Under the given decimal place a unit, with as many ciphers annexed thereto, as there are places in the given decimal, and reduce the fraction thus formed to its lowest terms.

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What vulgar fractions are equal to the following decimals, each respectively.

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CASE 3d.—To find the value of a decimal in terms of the inferior denominations of the integer, of which it is a part.

Multiply the decimal by the number of parts in the next inferior denomination; and cut off from the right-hand, as many places for decimals as were in the given decimal.

Multiply the places cut off, by the parts in the next lower denomination, cutting off the first number of places as before, thus proceed until all the denominations are gone through, or until ciphers only remain, and the several parts separated on the left hand, will make up the answer.

Grampleg. Required the value of £894. Required the val. of,0625 cwt ,894 ,0625 20 4 * 17,880 - 2500 12 28 10,560 7,0000 4 2,240 6 Answer, 715 1000 F25

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