ADDITION OF DECIMALS. R ULE. In setting down the proposed numbers to be added, great care must be taken in placing every figure directly underneath those of the same value, whether they be mixed numbers, or pure decimal parts; and to perform which there must be a due regard had to the commas or separating points which ought always to stand in a direct line, one under another, and to the right hand of them carefully place the decimal parts, according to their respective values; then add them as in whole numbers. EXAMPLES. 1. Add 72,5+32,071+2,1574+371,4+2,75. Facit 480,8784. 2. Add 30,07+2,0071+59,432+07,1. 3. Add 3,5+47,25+927,01+2,0073+1,5. 4. Add 52,75+47,21+724+31,452+,3075. 5. Add 3275+27,514+1,005+725+7,32. 6. Add 27,5+52+3,2675+,5741+2720. SUBTRACTION OF DECIMALS. RULE. Subtraction of Decimals differs but little from whole numbers, only in placing the numbers, which must be carefully observed, as in Addition. MULTIPLICATION OF DECIMALS. RULE. Place the factors, and multiply them, as in whole numbers, and from the product towards the right-hand, cut off as many places for decimals as there are in both factors together; but if there should not be so many places in the product, supply the defect with cyphers to the left hand. EXAMPLES. 1. Multiply,2365 by,2435 2. Multiply 2,071 by 2,27 3. Multiply 27,15 by 25,3 4. Multiply 72347 by 23,15 5. Multiply 17105 by,3257 6. Multiply 17105 by,0237 ,0075 Facit ,05758775. 7. Multiply 27,35 by 7,70071 8. Multiply 57,21 by 9. Multiply ,007 by 10. Multiply 20,15 by 11. Multiply ,907 by ,007 ,2705 ,0025 When any number of decimals is to be multiplied by 10, 100, 1000, &c. it is only removing the separating point in the multiplicand so many places towards the right-hand as there are cyphers in the multiplier; thus, ,578×10=5,78.,578 × 100=57,8. ,578 x 1000578. 578×100005780. CONTRACTED MULTIPLICATION OF DECIMALS. RULE. Put the unit's place of the multiplier under that place of the multiplicand that is intended to be kept in the product, then invert the order of all the other figures, i. e. write them all the contrary way; then in multiplying, begin at the figure in the multiplicand, which stands over the figure you are then multiplying with, and set down the first figure of each particular product directly one under the other, and have a due regard to the increase arising from the figures on the right-hand of that figure you begin to multiply at in the multiplicand Note, That in multiplying the figure left out every time next the right-hand in the multiplicand, if the product be 5, or upwards, to 15 carry 1; if 15, or upwards, to 25, carry 2; and if 25, or upwards, to 35, carry 3, &c. 115401 6474 3077377 264 23080329 48 115401647 4 14169,2065 03851C Facit,1166. 13. Multiply 3,141592 by 52,7438, and leave only 4 places of decimals. Facit 165,6994. 14. Multiply 2,38645 by 8,2175, and leave only 4 places of decimals. Facit 19,6107. 15. Multiply 375,13758 by 16,7324, and let there be only t place of decimals. Facit 6276,9 16. Multiply 375,13758 by 16,7324, and leave only 4 places of decimals. 17. Multiply 395,3756 by ,75642, and let places of decimals. Facit 6276,9520. there be only a Facit 299,0700. DIVISION OF DECIMALS. THIS Rule is also worked as in whole numbers; the only difficulty is in valuing the quotient, which is done by any of the following rules: RULE 1. The first figure in the quotient is always of the same value with that figure of the dividend, which answers or stands over the place of units in the divisor. 2. The quotient must always have so many decimal places, as the dividend has more than the divisor. Note 1. If the divisor and dividend have both the same number of decimal parts, the quotient will be a whole number. 2. If the dividend hus not so many places of decimals as are in the livisor, then so many cyphers must be annexed to the dividend as will make them equal, and the quotient will then be a whole number. 3. But if, when the division is done, the quotient has not so many figures as it should have places of decimals, then so many cyphers must Le prefixed us there are places wanting. EXAMPLES. 1. Divide 85643,825 by 6,321. Facit 13549,09428 +. 2. Divide 48 by 144. 3. Divide 217,75 by 65. 4. Divide 125 by,1045. 5. Divide ,709 by 2,574. 6. Divide 5,714 by 8275. 7 Divide 7382,54 by 6,4252. 8 Divide,0851648 by 423. 9 Divide 267,15975 by 13,25. 10 Divide 72,1564 by 1347. 11 Divide 715 by 30,75. When umbers are to be divided by 10, 100, 1000, 10,000, &c. it is pe. formed by placing the separating point in the dividend so many places towards the left hand, as there are cyphers in the divisor. 1000=5,78410000,5784 X. CONTRACTED DIVISION OF DECIMALS. RULE. By the first rule find what is the value of the first figure in the quotient; then by knowing the first figure's denomination, the decimal places may be reduced to any number, by taking as many of the left-hand figures of the dividend as will answer them; and in dividing omit one figure of the divisor at each following operation. Note. That in multiplying every figure left out in the divisur, you must carry 1, if it be 5, or upwards, to 15; if 15 or upwards, to 25, carry 2; if 25, or upwards, to 35, carry 3, &c. EXAMPLES. 12. Divide 721,17562 by 2,257432, and let there be only three places of decimals in the quotient. L REDUCTION OF DECIMALS. TO REDUCE A VULGAR FRACTION TO A DECIMAL. RUD ULE. Add cyphers to the numerator, and divide by the denominator, the quotient is the decimal fraction required. 1. Reduce 4. 2. Reduce 3. Reduce 4. Reduce 5. Reduce 14 EXAMPLES. to a decimal. ...to a decimal. ...to a decimal. to a decimal. .to a decimal. 4)1,00(25 Facit. Facit ,75. Faeit 1923076+. 6. Reduce of 19......to a decimal. Facit ,6043956+. Note. If the given parts be of several denominations, they may be redused either by so many distinct operations as there are diferent parts, by the first reducing them into their lowest denomination, and ther aride as before; or, 2dly, Bring the lowest into decimals of the next superior donomika. tion, and on the right hand of the decimal found, place the parts given of the next superior denomination; so proceeding till you bring out the decimal parts of the highest integer required, by still dividing the product by the next superior denominator; or, 3dly, To render pence, shillings, and farthings. If the number off shillings be even, take half for the first place of decimals, and let the second and third places be filled up with the farthings contained in the remaining pence and farthings, always remembering to add 1, when it is or exceeds 25. But if the number of shillings be odd, the second place of decimals must be increased by 5. 7. Reduce 5s. to the decimal of a £. 8. Reduce 9s. to the decimal of a £. 9. Reduce 16s. to the decimal of a £. 11. Reduce 16s. 7 d. to the decimal of a £. first. 12 199 4 Facit ,25. Facit 45. Facit,3. Facit,4166. Facit ,8322916. third. 2)16 second. 4)3,00 12)7,75 ,832 39 20)16,64583 ,8322916 960)799,8322916 Facit,972916. 12. Reduce 19s. 5d. to a decimal of a £. Facit ,002083. 14. Reduce 12 drams to the decimal of a lb. avoirdupoise. Facit,046875. 15. Reduce 2 qrs. 14 lb. to the decimal of an cwt. Facit,625. 16. Reduce two furlongs to the decimal of a league. Facit ,0833. 17. Reduce 2 quarts, 1 pint, to the decimal of a gallon. Facit,625 18. Reduce 4 gallons, 2 quarts of wine, to the decimal of an hogshead. Facit ,0714284. 19. Reduce 2 gallons, 1 quart of beer, to the decimal of a barrel. Facit ,0625. 20. Reduce 52 days to the decimal of a year. Facit,142465+. To find the value of any Decimal Fraction in the known parts of an Integer. RULE. Multiply the decimal given by the number of parts of the next interior denomination, cutting off the decimals from the product; then multiply the remainder by the next inferior denomination; thus proceeding, till you have brought in the least known parts of an Iuteger, |