bers, giving the name of the lowest denomination, or right hand figure to the whole. Thus,52 is read 52 hundredths; ,425 is read 425 thousandths, &c. 11. When whole numbers and decimals are expressed in the same number, it is called a mixed number. Write, in decimals, the following mixed numbers. 1. Twenty-five and six tenths=25,6. 2. Sixteen, and seventy-five hundredths. 3. Forty-one, and one hundred and forty-five thousandths. 4. 362, and nine millionths. 5. Nineteen, and 34756 hundred thousandths. 6. 794, and twenty-five ten thousandths. 51 12 24 10%; 5684; 411000; 9510000; 1451000000, &c. ADDITION OF DECIMALS. RULE. 1. Place the numbers, whether mixed or pure decimals, under each other, according to the value of their places. 2. Add them together as whole numbers, and place the separatrix exactly under the separating point above. EXAMPLES. 1. What is the sum of 28,753; 365,41; 18,75; 145,6. 28,753 365,41 18,75 145,6 558,513 We place tenths under tenths, hundredths under hundredths, &c., according to the value of their places, and add the columns as whole numbers; and the amount is 558 units, and 513 thousandths of a unit. Note. We may here observe, that the denominations of Federal Money correspond exactly with decimals, the dollars being units, dimes being tenths, cents hundredths, and mills thousandths of dollars, &c. 2. Add together the following sums of dollars and decimals of a dollar, viz: 13,755, 2,50, 25,3, and 41,144. Ans. $82,699-82dols. 69cts. 9m. 3. Find the amount of 79,45dols., 36,045dols., 128,5 dols., 95,006dols., 135,25dols., and 14,146dols. 4ns. 488dols. 39cts. 7m. 4. Add together the following mixed numbers, viz: 5,98471+18,568+2,005+9,15+35,1009+,35762. Ans. 71,16623. 5. What is the whole sum of 5,91 acres, 3,5 acres, 8,596 acres, ,795 acres, and 14 acres? Ans. 32,801 acres. 6. Required the sum of 25,164lbs., 9,56lbs., 87,31lbs., 256,25lbs., 9,18lbs., and 125,9lbs. Ans. 513,364lbs. 7. Add together 276, 54,321,,65, 112, 12,5 and,0463. Ans. 455,5173 00 25 000 8. What is the sum of 5 ounces; 795 ounces, 3,850 ounces, 1515 ounces and 2500 ounces? 6 Ans. 56,985. 9. Find the amount of forty-five hundredths, two hundred and fifty-six thousandths, sixty-five hundredths, ten, and six hundred and forty-four thousandths. SUBTRACTION OF DECIMALS. RULE. Ans. 12. Place the numbers according to their value, then subtract as in whole numbers, and point off the decimals as in addition of decimals. 6. From 295 subtract 201,9. Ans. 93,1. Ans. 318,0875. Ans. 34999,965. Ans. 57,05. Ans. 9,999999. 10. From 10, subtract one millionth part of a unit. MULTIPLICATION OF DECIMALS. RULE. Multiply as in whole numbers, and point off as many figures in the product for decimals, as there are decimal places in both factors. If the number of figures in the product be less than the decimal places in both factors, prefix ciphers to the left to supply the defect. 1. Multiply 75 by,8. Operation. 75 ,8 Ans. =60,0 EXAMPLES. Multiplying by a fraction is taking a certain part of the multiplicand for the product consequently, multiplying a whole number by a certain part of a whole number, as 8 tenths, produces a product less than the whole number: in this example, the number of decimal places in the factors being one, therefore we point off one figure in the product, and the answer is 60. Likewise multiplying one decimal fraction by another, produces a fraction smaller than either of the factors. 2 Multiply 4,25 by 3,6. 3,6 2550 1275 Ans. 15,300 In this example, the whole number of decimal places in both multiplier and multiplicand is three, therefore we point off three figures in the product. 3. Multiply 5,34 by ,008. ,008 In this example, the number of ,04272 figures in the product is less than the decimal places in both factors; the defect must be supplied by prefixing a cipher; that is, placing it at the left hand. 4. Multiply 36,5 by 7,27. 5. Multiply 3,92 by 196. 6. Multiply 29,831 by ,952. 7. Multiply 79,347 by 23,15. 8. Multiply ,009 by ,009. Ans. 265,355. Ans. 768,32. Ans. 28,399112. Ans. 1836,88305: Ans. ,000081. 9. Multiply 25 dollars by 25 cents, and what is the product? 10. What cost 8,75 yards of cloth, at Ans. $6,25. $3,96 per yard? Ans. $34,65. 11. What cost 18,75 barrels of flour, at $6,75 per barrel ? Ans. $126, 56c. 25m. 12. What is the value of 18,25lbs. of butter, at $,125 Ans. $2 28c. 125 m. per pound? 13. At ,03cts. profit on a dollar, what is the profit on $18,75? Ans. 56cts. 25m. 14. Multiply 135 dollars by $,06 or cents. Ans. $8,10. 15. Multiply $14,56 by $1,25. 16. Multiply 3672 by,85. Ans. $18,20. Ans. 3121,2. 17. Multiply 235,45 dollars by ,007, or 7 mills. Ans. 1dol. 64cts. 815 m. 18. Multiply $,95 or 95cts. by $,125, or 12cts. 5m. Ans. 11cts. 875 m. 19. How much is ,5 of 138. 100 Ans. 69. Ans. $89,70. Note. To multiply by 10, 100, 1000, &c., remove the decimal point as many places to the right as the multiplier Division of decimals differs from the division of whole numbers only in pointing off the decimal places. We have seen, in Multiplication of decimals, that the decimal places in the product must be equal to the number of decimal places in both factors counted together.-So in division of decimals, the number of decimal places in the divisor and quotient counted together, must be equal to the number of decimal places in the dividend; because the divisor and quotient are the factors which produce the dividend. RULE. 1. Divide as in whole numbers, and from the right hand in the quotient point off as many figures for decimals, 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 deficiency by prefixing ciphers. 3. If the divisor has more decimal places than the dividend, annex as many ciphers as you please to the dividend so as to make it equal at least to the divisor. You may also annex ciphers to the remainder, if any, and carry on the quotient to any degree of exactness; but the ciphers annexed must be counted as so many decimals of the dividend. EXAMPLES. 1. Divide 89,756 by,8. ,8)89,7560 We divide as in whole numbers, and there being a remainder, we annex a cipher and divide: there are now four decimal places in the dividend and one in the divisor. We therefore, by the rule, point off three figures in the quotient for decimals, which makes the number of decimal places in the divisor and quotient counted together, equal to the number of decimal places in the dividend. 2. Divide,36792 by 4,2. 4,2),36792(,0876 336 319 294 252 252 and quotient counted places in the dividend. In this example, there are five decimal places in the dividend, and only one in the divisor; therefore we must point off four figures in the quotient. Now, because there are only three figures in the quotient, we place a cipher on the left, and the decimal places in the divisor together, are equal to the decimal 3. Divide 44,98 by 1,3. 9. Divide $256,125 by 12,5. 10. Divide $510, by $1256. Ans. 34,6. Ans. 17,825. Ans. ,00812 X. Ans. 1,1955. Ans. ,00031 X. Ans. ,0645 X. Ans. $20,49. Ans. $,40605 X. 11. If 8,75 yards of cloth cost $34,65, what is that a yard? Ans. $3,96. 12. Bought 18,75 barrels of flour for $126,5625; how much was that a barrel? Ans. $6,75cts. 13. If 148,5lbs. of butter cost $18,5625, what will 1lb. cost? Ans. $,125 124cts. 14. At $1,79 per barrel, how many barrels of cider can Ans. 151. be bought for $270,29 ? 15. If a bushel of wheat cost $1,87, how many bushels Ans. 15,5bu. can be bought for $28,985 ? 15дbu. |