Arithmetick vulgar, decimal, & algebraical. In a most plain and facile method for common capacities. Together with a treatise of simple and compound interest and rebate; with two tables for the calculation of the value of leases and annuities, payable quarterly; the one for simple, the other for compound interest, at 6. per cent. per annum; with rules for making the like for any other rate. To which is added a new, and most practical way of gauging of tunns. As also the art of cask-gauging, for the use of His Majesties Officers of the Excise.

REDUCTION.

TO reduce a vulgar Fraction into a decimal Fraction, your Rule is: Divide your Nu∣merator by your Denominator, and the Quotient will be a decimal Fraction of the same value with the vulgar Fraction. So 1/4, if reduced into a decimal Fraction, will be .25.

Example.

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Here note, That only the even parts of an Integer will be exactly reduced into a decimal Fraction, as 1/2, 2/8, 2/16, &c. In all Surds, there will be some Remainder, but if you carry your decimal Fraction to four or five places, making the last one more than it is, if the sixth Figure be above 5, or else leave them out, and your Calculation will come near the truth; but if any desire to be more exact, he may take as many as he please.

Examples.

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To reduce any decimal Fraction out of a greater denomination into a lesser, multiply the Fraction by those parts of the Integer into which you would have it reduced; as .65 being the parts of a Pound, you would know how many Shillings are contained in the Fraction, multiply it by 20: If you desire the Pence therein contained, multiply it by 240; or if Farthings, multiply by 960, the number of Farthings in a Pound or 20 Shillings.

〈 math 〉〈 math 〉 The decimal parts of a Foot are reduced, by multiplying them by 12; if parts of a Foot Square, by 144; and the decimal parts of a Foot Solid, by 1728, the Cubick Inches in a Foot of Solid. The decimal parts of a Pound, are re∣duced by 16, the Ounces in a Pound Aver∣dupois; and 12, the Ounces in a Pound Troy. The decimal parts of a Beer Barrel by 36, and by 32 reduceth the parts of an Ale Barrel, into Gallons; and Gallons into Pints, by 8; Gallons into Cubick Inches, by 282; and for Wine Gallons, by 231, the number of Cubick In∣ches in such a Gallon, &c.

As greater denominations are reduced to lesser, by a multiplication of the several parts of the Integer; so lesser denominations are

reduced to greater, by division. Any number of Shillings are reduced into Pounds, and the decimal parts of a Pound, if you divide them by 20; and Pence, if divided by 240.

Example.

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Hours are reduced into the decimal parts of a Day, if you divide them by 24, the Hours in a Day Natural; and Minutes into the parts of an Hour, if divided by 60.

Perches are reduced into the decimal parts of an Acre, if you divide them by 160, the number of Square Poles or Perches in an Acre; and any ••••mber of Feet into Poles, and the decimal parts of a Pole, if you divide them by 16.5 the Feet in a Pole, or by 15.8.25 the number of Square Feet in a Square Pole; but if Wood-land Measure by 18, or if a Square Pole by 324, the Square Feet in a Pole or Perch of such Measure.

Any number of Inches are reduced into the parts of a Beer Barrel, if divided by 10152; and into Ale Barrels and parts, by 9024; &c.

For the ease of the Reader here is made a Table of English Coin reduced into the decimal parts of a Pound sterling.