5. Add the following sums of Dollars together, viz. $12,34565---7,8912,34 1 1, ,0011 Ans. $36,57775, or $36, 5:li. 7cts. 7,7 mills. 6. Add the following parts of an acre together, viz. ,7569 +,25 ,654 ,199. Ans. 1,8599 acres. 7. Add 72,5+32,071 - 2,1574 371,4; 2,75. Ans. 480,8784 8. Add 30,07 200,71 : 59,4 : 3207,1. Ans. 3497,28 9. Add 71,467 27,91 16,684. 90,0095 -€6,5. Ans. 300 10. Add ,7509 –,0974,69,4408- ,6109. Ans. 2,9 11. Add , 6 - ,099 - ,37+ ,905-1.,026. Ans, 2 12. To 9,999999 add one niilliouth part of a unit, and the sun will be 10. 13. Find the sum of Ans. 1,215009 SUBTRACTION OF DECIMALS, Rule.- Place in numbers according to their value: then subtract as in whole numbers, and point off the decimals as in Additiori, EXAMPLES. luches. 1. From 125,64 2. From 14,671 Take 95,58756 Take 5,91 3. From 761,8109 Take 18,9113 719,10009 7,121 27,15 6. From 480 take 245,0075 7. From 236 dols. take ,519 dolz, 8. From ,145 taku ,09584 9. Fronı ,2754 take ,2371 10. From 271 take 215,7 11. From 270,2 take 75,4075 12. From 107 take ,0007" Ans. 234,9925 Ans. 323,451 Ans. ,04-16 Ans. , 1383 Ans. 35,3 Ans. 191,79-25 Ans. 106,99:13 13. From a unit, or 1, subtract the millionth part of itself. Ans. ,999999 MULTIPLICATION OF DECIMALS. Rule.-1. Whether they be mixed numbers, or pure decimals, place the factors and multiply them as in whole numbers. 2. Point off so many figures from the product as there are decimal places in both the factors; and if there be not so many places in the product, supply the defict by prefixing cipliers to the left hand. EXAMPLES. 1. Multiply 5,236 2. Multiply 3,024 by ,008 by 2,23 ,000010 Product, ,041888 6,74352 3. Multiply 25,238 by 12,17. Answers, 307,14646 4. Multiply 2461 by ,0529. 130,1269 5. Multiply 7853 by 3,5. 27485,5 6. Multiply ,007853 by ,035. ,000274855 7. Multiply 001 by ,00 4. 8. Wliat cost 6,21 yards of clothi, at 2 dols. 32 cents, 5 mills, per yard? Ans. $14, 4d. 3c. 810 m. 9. Multiply 7,02 dollars by 5,27 dollars. Ans. 30,9951 dols. or $36 99 cts. 5,'.m. 10. Multiply 41 dols. 25 cts. by 120 dollars. Ans. $4950 11. Multiply 3 dols. 45 cts. by 16 cts. Ans. $0,5520=55 cts. 2 mills. 12. Multiply 65 cents, by ,09 or 9 cents. Ans. $0,0585=5 cts. 81 mills. 13. Multiply 10 dols. hy 10 cts. Ans. $1 14. Multiply 341,45 dols. by ,007 or 7 mills. Ans. $2,39 To inultiply by 10, 100, 1000, &c. remove the separating point so inany places to the right hand, as the multiplier las ciplicrs. Multiplied by 10, makes 4,25 hy 100, makes 42,5 by 1000, is ,425 For ,125 10 is 4,250, &c. DIVISION OF DECIMALS. RưLF.--1. The places of the decimal parts of the divisor and quolient countod together, must always be equal to those in the dividend, therefore divide as in whole numbers, and from the right hand of the quotient, point off so many places for decirnals, as the decimal places in the dividend exceed those in the divisor. 2. If the places in the quotient be not so many as the rule requires, supply the defect by prefixing ciphers to the left hand of said quotient. Nore. If the decimal places in the divisor be more than those in the dividend, annex as many ciphers to the dividend as you please, so as to make it equal, (at least,) to the divisor. Or, if there be a remainder, you may annex cipher's to it, and carry on the quotient to any degree of exactness. 00 00 3. Divide 780,517 by 24,3. Answers. 32,12 4. Divide 4,18 by ,1812. ,23068+ 5. Divide 7,25406 by 957. ,00758 6. Divide ,00078759 by ,525. ,00150+ 7. Divide 14 by 365. ,038356+ 8. Divide $246,1476 by $604,25. ,40736+ 9. Divide $186513,239 hy $304,81, 611,9+ 10. Divide $1,28 by $8,31 ,154+ 11. Divide 56 cts. by 1 dol. 12 cts. ,5 12. Divide 1 dollar by 12 cents. 8,333 + 13. If 21 or 21,75 yards of cloth cost 34,317 dollais, what will one yard cost? $1,577+ Note.-When decimals, or whole numbers, are to be divided by 10, 100, 1000, &c. (viz. unity with ciphers,) it is performed by removing the separatrix in the dividend, so inany places towards the left hand as there are ciphers ! the divisor. To reduce a Vulgar Fraction to its equivalent Deci . l. RULE.-Annex ciphers to the numerator, and divide by the denoIninator; and the quotient will be the decimal required. Note.So many ciphers as you annex to the given numerator, so many places must be pointed in the quotient; and if there be not so many places of figures in the quotient, make up the deficiency by placing ciphers to the left hand of the said quotient. EXAMPLES. ,75 1. Reduce to a decimal. 8)1,000 Ans. ,125 2. What decimal is equal to 1 ? Answers. ,5 3. What decimal is equal to ? 4. Reduce } to a decimal. 5. Reduce it to a decimal. ,6875 6. Reduce žī to a decimal. ,85 7. Bring to a decimal. ,09375 8. What decimal is equal to z'z? ,037037+ 9. Reduce ș to a decimal. ,333333 + 10. Reduce jizz to its equivalent decimal. - ,008 11. Reduce to a decimal. ,1923076+ CASE II, To reduce quantities of several denominations to a D. cimal. Rule.-1. Bring the given denominations first to a vu; var fraction by Problem III. page 71; and reduce said vulgar fraction to its equivalent decimal; or, 2. Place the several denominations above each other, !etting the highest denomination stand at the bottom ; then divide each denoma nation (beginning at the top) by its value in the next denomination the last quotient will give the decimal required. EXAMPLES. I. Reduce 12 s. 60. 3 qrs. to the decimal of a pound 12 4 5760 4800 4800 2. Reduce 15s. 9d. 3 qrs. to the decimal of a pound. Ans. ,790625 3. Reduce 9d. 3 grs, to the decimal of a shilling: ins. ,8125 4. Reduce 8 farthings to the decimal of a shilling: Ans. ,0625 5. Reduce 3s. 4d. New-England currency, to the decimai of a dollar. Ans. ,555555 + 6. Reduce 12s. to the decimal of a pound. Ans. ,6 Note. When the shillings we even, half the number, with a point prefixed, is their decimal expression; but if the number be odd, annex a cipher to the shillings, and then by halving them, you will have their decimal expression. 7. Reduce 1, 2, 4, 9, 16 and 19 shillings to decimals. Shillings 1 2 9 16 19 Answers. ,05 ,95 |