12 Numerator 7 The Numerator, in the Vulgar Form, is always wrote over the Denominator, and these are separated by a small Line, thus Or Denominator the first of thefe is called 5 Twelfths, and the latter 7 Twelfths of an Inch, Yard, Perch, &c. or of whatever the whole Thing originally was. Fractions are expreffed in two Forms, that is, either vulgarly or decimally. All Fractions whofe Denominators do not confift of a Cypher or Cyphers fet after Unity, are called vulgar ones, and their Denominators are always wrote under their Numerators. The treating of thefe would be foreign to our prefent Purpose. But Fractions whofe Denominators confift of an Unit, prefixed to one or more Cyphers, are called Decimal Fractions; the Numerators of which are wrote without their Denominators, and are distinguished from Integers by a Point prefixed: Thus, and in the Decimal Form, are expressed by .2 .42.172. 30 100 300 The Denominators of fuch Fractions always confifting of an Unit, prefixed to as many Cyphers as there are Places of Figures in the Numerators, it follows, that any Number of Cyphers put after thofe Numerators, will neither increase or leffen their Value: For and are all of the fame Value, and will ftand in the Decimal Form thus 3.30.300; but a Cypher or Cyhphers prefixed to thofe Numerators, leffen, their Value in a tenfold Proportion: For and which in the Decimal Form we denote by .3 .03 and .003, are Fractions, of which the firft is ten Times. greater than the second; and the fecond, ten Times greater than the third. 3 0 3 100 003 1000 Hence it appears, that as the Value and Denomination of any Figure or Number of Figures in common Arithmetic is enlarged, and becomes ten or or a hundred, or a thousand Times greater, by placing one, or two, or three Cyphers after it; fo in decimal Arithmetic, the Value of any Figure or Number of Figures, decreases, and becomes ten, or a hundred, or a thoufand Times lefs, while the Denomination of it increates, and becomes fo many Times greater, by prefixing one, or two, or three Cyphers to it: And that any Number of Cyphers, before an Integer, or after a decimal Fraction, have no Effect in changing their Values. Addition of DECIMALS. Having placed thofe Figures which are equidiftant from the Point, (as well Integers as Fractions) under each other, add them as if they were Integers. EXAMPLES. Add 4.7832 3.2543 7.8251 6.03 2.857 and 3.251 together. Place them thus. What is the Sum of 6.57 1.026 .75 146.5 8.7 526 3.97, and .0271? Aniwer 693.5431. What is the Sum of 4.51 146.071 .507 .0006 132 62.71 .507 7.9 and 10712? Anfwer 354-31272. Subtraction of DECIMALS. Having placed the Figures which are equi-diftant from the Point, under each other; deduct as if they were Integers. From 84 take 82.3412 Multiplication of DECIMALS. Place the Multiplicand, and Multiplier, after any Manner under each other; and having multiplied as in whole Numbers, cut off as many Places of Decimals in the Product, counting from the right Hand towards the left, as there are in the Multiplicand, and Multiplier: But if there be not a fufficient Number of Places in the Product the Defect may be fupplied, by prefixing Cyphers thereto. For the Denominator of the Product, being an Unit, prefixed to as many Cyphers, as the Denominators of the Multiplier and Multiplicand contain of Cyphers, it follows, that the Places of Decimals in the Product, will be as many as in the Numbers from whence it arofe. EXAMPLES. Multiply 48.765 by .003609 438885 292590 146295 Anfwer 175992885 Multiply .121 484 121 Anfwer .01694 Multiply Multiply 121.6 by 2.76 2.76 7296 8512 2432 Answer 335.616 Multiply .0089789 by 1085 Multiply .248723 by .13587 Devifion of DECIMALS, Having divided as in whole Numbers, annexing Cyphers to the Dividend if they be wanted; the Decimal Places in the Divifor and Quotient must be equal to those in the Dividend, and the Defect fupplied by prefixing Cyphers to the Quotient. For the Dividend is a Product contained under the Divifor and Quotient; and that Product contains as many Places of Decimals as the Numbers do from whence it arofe: Therefore the Difference between the Number of Decimals in the Dividend and Divifor, must be cut off in the Quotient. EXAMPLES. Divide 144 by .12 24 EXAM |